Do Bots Help Revisited
Andrew Bokelman
bots can help someone improve their rating. Here is my follow-up after
buying Snowie.
After I was on FIBS for awhile I got back into practice and my average was
usually around 1665. A couple times I got up to the low 1670s but only
stayed there a short time. Then my play seemed to get worse and for awhile I
was usually around 1655.
Then I got Snowie. I immediately learned why my play had gotten worse.
There was a new habit I had developed that Snowie said was wrong. After I
corrected this my average started to rise. And as I studied more it went up
more. I had one bad day where I dropped 20 points but the next day I started
to climb again. And today I hit 1686 -- higher than I have ever
been before.
I don't know if these changes are statistically significant. And there
could be luck involved. But I really think I have improved as a backgammon
player. As for how good I can get with the help of Snowie, I don't know. My
concentration is not that good and I make mistakes that even I know are
wrong. But I am happy with the level of improvement I've made so far.
Gary Wong
> After I was on FIBS for awhile I got back into practice and my average was
> usually around 1665. A couple times I got up to the low 1670s but only
> stayed there a short time. Then my play seemed to get worse and for awhile I
> was usually around 1655.
>
> Then I got Snowie. I immediately learned why my play had gotten worse.
> There was a new habit I had developed that Snowie said was wrong. After I
> corrected this my average started to rise. And as I studied more it went up
> more. I had one bad day where I dropped 20 points but the next day I started
> to climb again. And today I hit 1686 -- higher than I have ever
> been before.
>
> I don't know if these changes are statistically significant.
Personally I would say that they are not. Search on Deja News for
articles about FIBS ratings and you will read that fluctuations of
well over 100 points and back again are not unheard of. (As an
example, Abbott plays on FIBS with an estimated ability of around
1470. Its play hasn't changed at all for several months, but over
that time its rating has reached lower than 1300 and higher than 1600
through random noise alone.) I don't have any measurements of the
accuracy of FIBS ratings, but I would guess that the standard error in
a rating is of the order of 50 points. (Loosely speaking, this means
that all else being equal, if you take a large sample of FIBS players,
you'd expect about 2/3 of them to have a rating within 50 points of
their "true" ability.)
To judge whether you are improving based on your rating is very
difficult. Several months ago I posted an article here estimating how
long it takes for a rating to change, and I concluded that the "half
life" of a FIBS rating is of the order of 200 experience points. (One
way of interpreting this is that for any sufficiently experienced
player, the last 200 experience points contribute as much to your
rating as all previous matches put together). Therefore I would be
very reluctant to compare two measurements made within, say, 400
experience points of each other, because they won't be sufficiently
independent.
When you put all of this together, I would argue that you need samples
made more than 400 experience points apart to be independent, and more
than two standard deviations (ie. 100 points) to be significant. So,
if your current rating is over 100 points higher than it was 400
experience points ago, you can be reasonably confident that you are
improving; if it's 100 points lower, that suggests you're getting
worse!
(Strictly speaking, you can't ever prove a hypothesis is _true_ with
sampled data: you can only gather data that suggests some hypothesis
seems to be false. If, over 400 experience points, your rating
increases by 100, then that's pretty strong evidence against the
hypothesis that your ability remained the same or decreased. If it
went down by 100, that tends to reject the hypothesis that you stayed
the same or improved. If it changed by less than 100 points, then
your ability could well have changed during the sample period, but not
by enough to be detected by this fairly crude test.)
I think a better way of determining whether you are improving is to
trust your instincts. If you can identify concepts that are
significant in a particular position that you wouldn't have recognised
a month or a year ago, then that could well indicate improvement. Or
if you have since learned why a particular play you once made was
wrong, that probably constitutes improvement too. Or take a quiz (for
instance Robertie's _Reno 1986_, or Clay's _Backgammon: Winning
Strategies_, or the online positions at Backgammon By The Bay); wait
until you've "forgotten" the answers, and take the test again. If
your score has improved by, say, 10% of the total (my very rough
estimation -- long quizzes need smaller differences to be significant;
short quizzes require more) then that probably indicates significant
improvement.
Last of all, I've learned so much from reading rec.games.backgammon
that I find it very hard to believe that anybody here is not improving
at least a little bit. If you're so good that you can read several
months' r.g.b. and not learn a thing, then get off the computer and
go out and play for money; if you're not that good, then you're
improving -- congratulations! :-)
Cheers,
Gary "I suck less than I used to" Wong.
--
Gary Wong, Department of Computer Science, University of Arizona
ga...@cs.arizona.edu http://www.cs.arizona.edu/~gary/
David Montgomery
>Andrew Bokelman <73457...@CompuServe.COM> writes:
>> After I was on FIBS for awhile I got back into practice and my average was
>>changes are statistically significant.
>
>To judge whether you are improving based on your rating is very
>I think a better way of determining whether you are improving is to
If you have Snowie, there is an even better way. Use Snowie to
create an account for yourself. Play on FIBS or GG, and import
and analyze all of your matches. On the statistics window,
associate the statistics with your account.
After you have played a few matches this way, go to the Account
Manager window and look at what it says in the "Overall", "Moves"
and "Cube" panels. Pretty quickly you'll see how you do on
average.
This way, every match you play becomes like a quiz that you can
use both to improve and to objectively evaluate how well you
are playing. Since Snowie looks at your choice for every single
move, sometimes hundreds of moves per match, you get an accurate
reading much more quickly than by watching your rating go up
and down.
David Montgomery
mo...@cs.umd.edu
monty on FIBS
Murat Kalinyaprak
>.... and you will read that fluctuations of well over 100
>points and back again are not unheard of. (As an example,
>Abbott plays on FIBS with an estimated ability of around
>1470. Its play hasn't changed at all for several months,
>but over that time its rating has reached lower than 1300
>and higher than 1600 through random noise alone.)
Thanks for sharing such info with us here. Could
you be any more specific about what you mean by
"random noise"? 300 points is a huge swing... Do
you know what may be the average points won/lost
per 1-point game by Abbott? At 2 points per game
it would take 150 wins/losses (not consecutively
of course) for such a swing. Would be interesting
to know the ratio of this to the total number of
games played during a period when Abbott has gone
from 1300 to 1600 or from 1600 to 1300... Given
that Abbott is a robot without emotions, good or
bad days, etc. a 300 point fluctuation in its
rating may indicate something much worse and/or
difficult to explain...
>I don't have any measurements of the accuracy of FIBS
>ratings, but I would guess that the standard error in a
>rating is of the order of 50 points. (Loosely speaking,
>this means that all else being equal, if you take a large
>sample of FIBS players, you'd expect about 2/3 of them to
>have a rating within 50 points of their "true" ability.)
Such statements bother me a little. Where do we
get the "true ability" to compare FIBS ratings
with...?
We know for example that a "kilogram" equals the
weight of one cubic decimeter of water. So, if I
want to know whether my bath-scale measures my
"true weight" accurately enough, I can resort to
that fact as a reference outside of "me and my
bath-scale"...
How do we do that with FIBS ratings...? Saying
that one's FIBS rating is withing N points of
their "true ability as measured by FIBS points"
is circular...
If we start with a brand new FIBS, have Jim and
Joe sign on, have them start playing matches,
and then try to begin awarding them points based
on some formula like the one used now, we can see
that there is "a little too much" of a circular
hocus-pocus in it... I hope it's not necessary to
play out the scenario step by step to illustrate
this.
It may be that there is no better choice and that
we have to make do with whatever we can... That's
fine. But it needs to be acknowledged that things
are such, as far as FIBS rating system goes...
Let me ask a question specificly to Gary: with no
obligation to adopt or promote any other system,
do you think that a "much simpler" rating system
could achieve an accuracy/inaccuracy similar to
FIBS' (i.e. in the order of 50 points)...?
FIBS rating formula may be "beautiful", but it's
not "real". Imagine some players could break off
from the pack and reach ratings of 2800, 3400, etc.
while others dip to 720, 290, etc... I would say
that the "real winning chances" of a 290 player
against a 3400 player may be "zero". I chose such
extreme numbers to start making the point, but if
we work backwards from those, we may be able to
say the same for players rated at 720 and 2800, or
1230 and 1920...
On FIBS, I regularly see players with 700+ points
difference in their ratings play for points. I'm
of the opinion that the stage where a player may
have practicly zero chance of winning would occur
much earlier than 700+ FIBS-points difference. And
I see this as a problem with FIBS rating system. I
think that pretending a "rosy" hypothetical world
can exist where anyone can play against any other
player without regard to ratings (i.e. because they
win/lose proportionately based on "probabilities")
is unrealistic...
There was snide remarks made in the past about my
not believing in "probabilities". It's true that
when the term is used for some figures obtained
from "circular data", I don't believe that it has
anything to do with what it should mean...
Having mentioned again ratings like 2800, 3400,
etc. one thing I still haven't figured out (and
nobody else offered opinions on it either) is why
haven't robots like JF and SW reached ratings well
past 2000 or 2100's...? They play large volumes of
matches and against players of all skill levels
indiscriminately. Assuming that top players in the
world have better things to do than playing against
those robots on game servers in order to keep their
ratings in check, 90?+% of their opponents should be
easy prey for them to generate lots of surplus wins
and keep increasing their ratings indefinetely. Why
isn't it happening...?
Anyway, before the people who have me in their kill
file complain about my writing long articles again,
I better stop for now... :)
MK
Andrew Bokelman
>>>>I think a better way of determining whether you are improving is to
trust your instincts. If you can identify concepts that are
significant in a particular position that you wouldn't have recognized
a month or a year ago, then that could well indicate improvement. Or
if you have since learned why a particular play you once made was
wrong, that probably constitutes improvement too.
This has happened too. For example, discovering that I had developed a bad
habit in moving my back checkers up to soon. Hitting and slotting in my home
board when I could just give up one point and make another while hitting.
Breaking and running too soon in a two-way holding position. Not being bold
enough in my doubling.
Which brings me to another good thing about having a bot tutor. After I
learn the new thing it is very easy to apply it in the wrong places. So by
reviewing later matches I can see if Snowie tells me if I'm applying it
correctly.
Patti Beadles
Murat Kalinyaprak <mu...@cyberport.net> wrote:
>Having mentioned again ratings like 2800, 3400,
>etc. one thing I still haven't figured out (and
>nobody else offered opinions on it either) is why
>haven't robots like JF and SW reached ratings well
>past 2000 or 2100's...?
Maybe because the ratings system works a lot better than you
think, and the bots reach their "true rating" and then hover
there, plus or minus the hundred or so points that one would
expect for random swings.
-Patti
--
Patti Beadles |
pat...@netcom.com/pat...@gammon.com | You are sick. It's the kind of
http://www.gammon.com/ | sick that we all like, mind you,
or just yell, "Hey, Patti!" | but it is sick.
Murat Kalinyaprak
>In <72bhu5$c0p$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>>.... why haven't robots like JF and SW reached ratings well
>>past 2000 or 2100's...?
>Maybe because the ratings system works a lot better than you
>think, and the bots reach their "true rating"......
I have a little problem with the term "true rating" as
used in relation to FIBS (and likes) rating systems...
"True rating" by what unit of measure...?
I think that the only way we could even come close to
using such a term in a rating system would be after a
process like the following:
We take let's say 100 players and have them let's again
say 100 matches against a *common opponent* who/which
would preferably be impartial and static in stregth.
Robots are ideal for that and we can use any robot of
any stregth (like Gary's Abbott), because we just want
to use it as a *unit of measure*...
After this, we can rate/sort those players based on the
number of matches they won against that robot like:
John rated at 92 robot units
Joe rated at 87 robot units
Jim rated at 81 robot units
Jack rated at 77 robot units
5 Etc...
Then, we make all those players play 100 matches against
each other and from the results we can derive some
conclusions as to the *relative probabilities* of their
winning chances against each other (i.e. devise a formula
to reflect the discovered relativity).
The most sensible way to add a new player to this bunch
then would be to make him/her play 100 matches against
the same *measuring stick* robot and base his/her initial
rating on the result of those matches. But this may be
totally impractical in the long term. So alternatives may
be to insert a new player at the midpoint of the ratings
range, or better yet at the most common rating, etc.
I would consider a similar process as a required *minimal*
in order to speak about a "true rating" of any sort...
Of course, if the rating formula will take into account
factors like single-point, multi-point, cubeless, cubeful
matches, etc. then the above process should include enough
samples of each of them.
My question is whether FIBS rating formula is based on
such a foundation containing some amount of *concrete*
(pun intended:) or build out of wet beach sand...?
MK
Murat Kalinyaprak
>In <72bhu5$c0p$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>>... why haven't robots like JF and SW reached ratings well
>>past 2000 or 2100's...?
>Maybe because the ratings system works a lot better than you
>think, and the bots reach their "true rating" and then hover
>there, plus or minus the hundred or so points that one would
>expect for random swings.
What I would like to know is whether we are trying to
observe a result or trying to artificially create a
result...?
Why do we expect that any/all players ratings will
*reach* a "whatever rating" and hover around it forever
after...?
Some time ago I had argued that after a certain amount
of ratings difference, the lesser rated player's winning
chances would rely on dice alone and I had received (I
believe from you) a counter-argument that FIBS formula
was calculating (reflecting) those probablilities based
on mistakes the higher rated player is expected to make.
I'll leave the subject of "what is a mistake" for another
time but here we are talking about JF and SW, who play
based on statistics/probabilities alone and don't make the
"mistakes" that humans make. In fact, so many people have
such a high esteem of them that they are often regarded
as the ultimate judge on what are right/wrong moves, etc...
It had been claimed that perhaps only as few as 10 people
in the world can beat those robots in the long term. Of
the tens of thousands of games those robots had played,
the ones they played against each other and/or against
those 10 people must be a very very small number.
For the practical scope/purpose of this argument, those
robots don't make "mistakes" (on which the FIBS rating
formula does supposedly depend on). And after that many
thousand games the luck factor should certainly be no
longer a factor. Yet, they have so far failed to produce
enough surplus wins against the "*losing masses*" to get
past 2000-2100 ratings...? How can that be...?
I don't care which way the reality goes but something
doesn't add up as far as I can see. What could be some
possibilies here...?
a) JF and SW are not as good as some people make it
sound. But then, only 3-4 people at the most have ever
openly claimed in this newsgroup that they beat those
robots. The rest said they lose (and pretty badly at it).
b) The crowd on FIBS is very different than the crowd
in this newsgroup. People in this newsgroup wrongly
think that there are only 10 or so people in the world
who can beat those robots but in reality there are tens
of thousands of people on FIBS that can beat JF and SW...
c) Those robots don't play differently based on cube
ownership and are beaten by people on FIBS who play
very differently based on cube ownership. And since
cube ownership is not a factor in FIBS formula, those
poor robots are inadvertently kept from reaching their
full potential (i.e. "true") ratings... :)
d) FIBS dice is rigged to maintain the ratings/ranges
in a way to artificially validate its own formula...
e) Any other ideas...?
MK
limill...@my-dejanews.com
mu...@cyberport.net (Murat Kalinyaprak) wrote:
>
> Why do we expect that any/all players ratings will
> *reach* a "whatever rating" and hover around it forever
> after...?
>
Because the ratings system on Fibs works properly.
>
> For the practical scope/purpose of this argument, those
> robots don't make "mistakes" (on which the FIBS rating
> formula does supposedly depend on). And after that many
> thousand games the luck factor should certainly be no
> longer a factor. Yet, they have so far failed to produce
> enough surplus wins against the "*losing masses*" to get
> past 2000-2100 ratings...? How can that be...?
You seem to be saying that the mythical perfect player
will beat all inferior players %100 of the time. If that
were the case, then yes, the perfect player's rating would
increase with no upper bound.
However, the perfect player will always lose a significant
number of matches, due to the element of luck in the game.
Using made up numbers: Let's say the perfect player can beat
your average intermediate player, rated 1700, about 75% of
the time in 5 point matches. The perfect player would gain
+2.236 rating points for every win, and lose -6.708 for every
loss. Averaging 3 wins for every loss, the perfect player's
rating will in the long run remain unchanged, at approximately
2126.75.
If you log on to fibs and type "help formula" you can see
exactly how the ratings changes are calculated.
L.Miller
-----------== Posted via Deja News, The Discussion Network ==----------
http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own
Patti Beadles
Murat Kalinyaprak <mu...@cyberport.net> wrote:
>For the practical scope/purpose of this argument, those
>robots don't make "mistakes" (on which the FIBS rating
>formula does supposedly depend on). And after that many
>thousand games the luck factor should certainly be no
>longer a factor. Yet, they have so far failed to produce
>enough surplus wins against the "*losing masses*" to get
>past 2000-2100 ratings...? How can that be...?
Because the formula works.
Let's assume for the sake of argument that every player has a skill
level to which we can assign a number. To further simplify the
argument, let's say that the skill level for an average player is
exactly 1500.0.
Let's choose a player, and give him a skill level of 1800.0. What this
skill level means is that he has a 65% of beating an average player in
a 3-point match, and a 71% chance of beating an average player in a
7-point match.
Our 1800 player now goes off and plays a very large number (say 10000)
of 7-point matches against an average player. He'll win around 71%
of them, and lose 29%. All in all, his rating will stay close to
1800, and his opponent's rating will stay close to 1500.
Why is that? It's because the FIBS rating system calculates what it
thinks the probability of winning a match is, based on the skill
(rating) difference of the players, and assigns points accordingly.
For example, in our hypothetical 1800 vs 1500 7-point match:
If player #1 wins:
Changes for player#1 +3.029076, new rating 1803.03
Changes for player#2 -3.029076, new rating 1496.97
If player #2 wins:
Changes for player#1 -7.553929, new rating 1792.45
Changes for player#2 +7.553929, new rating 1507.55
The underlying assumptions of the FIBS rating system are:
(a) Every player has a skill level that can be assigned a
numeric value,
(b) based on those skill levels, the probability of one
player beating another in a match of a paritcular
length can be determined.
If we don't take (a) as true, then the whole thing falls apart.
(b) is the tricky one, but I believe the system is fairly good
if not perfect. It's been shown, for example, that the formula
overestimates the chances of a weaker player winning a very short
match. It seems to work well for longer matches.
Remember that luck is still a factor in backgammon. I'm only an
intermediate player, but I've beaten world-class players in short
(5, 7, 9-point) matches.
-Patti
--
Patti Beadles |
pat...@netcom.com/pat...@gammon.com |
http://www.gammon.com/ | The deep end isn't a place
or just yell, "Hey, Patti!" | for dipping a toe.
Michael J Zehr
Murat Kalinyaprak <mu...@cyberport.net> wrote:
>For the practical scope/purpose of this argument, those
>robots don't make "mistakes" (on which the FIBS rating
>formula does supposedly depend on). And after that many
>thousand games the luck factor should certainly be no
>longer a factor. Yet, they have so far failed to produce
>enough surplus wins against the "*losing masses*" to get
>past 2000-2100 ratings...? How can that be...?
> [options snipped]
f) The ratings are accurate in the sense that the "average" FIBS player
has a rating in the 1500s, and a rating difference of 500 points
accurately predicts the ratio of games SW and JF win on average.
There seems to be a misunderstanding that a "perfect" player should have
their rating arbitrarily high. If perfect play lets you win 75% of the
time in a 9 point match against the "average" player on FIBS, then using
the rating system you can determine the rating that perfect player ought
to have. It might well be 2000-2100.
The expectation that a player's rating will move towards some point and
then hover there is based on statistical and empirical data. One can
run simulations to see how a rating system behaves. (Start two players
with ratings of 1500. Assume one of them wins 60% of the time in a 7
point match. Simulate matches by using a psuedo random sequence, or
some other method of generating a 60% chance. Adjust the ratings using
the FIBS formula (which you can get from the help on FIBS). See what
happens to the ratings over the long run.)
Remember that althought SW and JF might have vastly winning records,
they get far fewer points when they win than when they lose, so they
need to win more often than they lose just to maintain their high
ratings.
Regarding the comments that the ratings differences don't reflect the
assertion that only 10 or so people in the world can maintain a winning
record against SW or JF, I would say that the ratings _do_ reflect
that. After all, how many people on FIBS consistenly have a higher
rating than SW or JF? Isn't it just possible that robots have the
highest ratings on FIBS because they're the best players?
-Michael J. Zehr
Murat Kalinyaprak
>In <72u8m1$rm8$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>>For the practical scope/purpose of this argument, those
>>robots don't make "mistakes" (on which the FIBS rating
>>formula does supposedly depend on). And after that many
>>thousand games the luck factor should certainly be no
>>longer a factor. Yet, they have so far failed to produce
>>enough surplus wins against the "*losing masses*" to get
>>past 2000-2100 ratings...? How can that be...?
>Because the formula works.
Well, maybe I'll become convinced later... :)
>Let's assume for the sake of argument that every player has
>a skill level to which we can assign a number. To further
>simplify the argument, let's say that the skill level for an
>average player is exactly 1500.0.
Ok, I'll use the same figure in my examples.
>Let's choose a player, and give him a skill level of 1800.0.
>What this skill level means is that he has a 65% of beating
>an average player in a 3-point match, and a 71% chance of
>beating an average player in a 7-point match.
>Our 1800 player now goes off and plays a very large number
>(say 10000) of 7-point matches against an average player.
>He'll win around 71% of them, and lose 29%. All in all, his
>rating will stay close to 1800, and his opponent's rating
>will stay close to 1500.
Fine. Let's look at this from a different angle also.
Let's have Snowie (rated at 2089?) play each opponent
a 1-point match and only once. With about 600 points
difference (2089-1500), its winning chances would be
around 65%? for 1-point matches. If Snowie does indeed
win 65% of those matches, then we can reword your above
statement as: "Snowie can beat 65% of its opponents"
(among players on FIBS with 1500 average rating)...
If the players on FIBS represent a good sampling of all
players in the world, then we can expand that statement
to say: "Snowie can beat 65% of all players on earth".
(When talking about matches of other lengths, the "65%"
can be replaced by the appropriate figure).
If we have Snowie play another set of matches against
the same players again, and again, and again... this
ratio will not change. Therefore, we can say that 35%
of the players will beat Snowie consistently (i.e. in
the long run), which sounds much less impressive than
claims made previously in this newgroup...
>Why is that? It's because the FIBS rating system calculates
>what it thinks the probability of winning a match is, based
>on the skill (rating) difference of the players, and assigns
>points accordingly. For example, in our hypothetical 1800 vs
>1500 7-point match: ...............
> (a) Every player has a skill level that can be assigned a
> numeric value,
> (b) based on those skill levels, the probability of one
> player beating another in a match of a paritcular
> length can be determined.
I had already made an argument about two requirements
for this to work. Only "one particular form of skill"
can be measured (i.e. single-point, multi-point, etc.
matches), not a combination of many kinds at the same
time. This is not the case with FIBS rating system, as
you and others acknowledge also. And at least an initial
sample of players need to be measured against a common
"unit" before they can be used to measure each other or
players. I don't know if this was done in establishing
the FIBS formula or not. It would be good if we get an
answer on this from somebody who knows...
>If we don't take (a) as true, then the whole thing falls apart.
>(b) is the tricky one, but I believe the system is fairly good
>if not perfect. It's been shown, for example, that the formula
>overestimates the chances of a weaker player winning a very short
>match. It seems to work well for longer matches.
And my argument is that such inconsistencies can add up
and should even be expected to do so in the long term.
There could possibly be other elusive elements such as
"style/strategy", for example. It has been argued in
this newsgroup that robots play unlike-humans and that's
why they do better and that's why humans aspire to play
like them. So one question could be whether a 2100 rated
human and a 2100 rated robot really have the same winning
chances against a 1500 rated player (human and/or robot)
in any/all variations of backgammon?
For the moment, let's stick with the match length and
assume that a robot can do slightly better in 1-point
matches against weaker opponents and it's "true" winning
chances (referring to the previous examples used above)
is 66% instead of 65%. Let's also say that half of the
30000 experience Snowie has consists of 1-point matches
(which would had to be played against almost all weaker
players from the beginning). At about 1.5? points earned
per match, that 1% would translate to 150x1.5=225 rating
points and would put Snowie at 2325. This is only with
a mere 1% inaccuracy in calculating the probability of
winning...
Of course, it's possible that a few human players may
end up not fitting the "standard mold" and cause such
irregularities/extremes also. I'm just using robots as
likely cases because they play large amounts of matches
and arguments have been made about their being superior
and/or different than at least most humans...
And with the seemingly arbitrary round number constants
in it, the FIBS formula looks just too crude to be able
to prevent such possible or even expected irregularities.
Yet, no such irregularities are observed...
Some people had argued that inflating ratings by taking
advantage of deficiencies in FIBS ratings was possible.
If it's possible on purpose, why couldn't it be possible
for it to happen inadvertently, which I believe would be
more likely than not to happen. I just can't see how a
some "crude" formula with some round/arbitrary constants
can result in the apparent stability/smoothness/neatness
in FIBS ratings and their ranges and can't help wonder
if some other mecahnism/s are used to ensure that...
MK
Murat Kalinyaprak
>In <72u8m1$rm8$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>>longer a factor. Yet, they have so far failed to produce
>>enough surplus wins against the "*losing masses*" to get
>>past 2000-2100 ratings...? How can that be...?
>There seems to be a misunderstanding that a "perfect" player
>should have their rating arbitrarily high. If perfect play
>lets you win 75% of the time in a 9 point match against the
>"average" player on FIBS, then using the rating system you
>can determine the rating that perfect player ought to have.
>It might well be 2000-2100.
This is what I don't understand. How can "*perfect*"
(or close to it) play can only win 75% of the time...?
We either have to reassess the stregth of those robots,
redefine "perfect", argue that FIBS rating measures not
skill but luck, or something else whatever... We can't
have it all.
>The expectation that a player's rating will move towards some
>point and then hover there is based on statistical and empirical
>data.
What data...? Where did that data come from...?
>One can run simulations to see how a rating system behaves.
>(Start two players with ratings of 1500. Assume one of them
>wins 60% of the time in a 7 point match. Simulate matches by
>using a psuedo random sequence, or some other method of
>generating a 60% chance. Adjust the ratings using the FIBS
>formula (which you can get from the help on FIBS). See what
>happens to the ratings over the long run.)
>Remember that althought SW and JF might have vastly winning
>records, they get far fewer points when they win than when
>they lose, so they need to win more often than they lose just
>to maintain their high ratings.
I think the problem with your argumant is that JF/SW in
this case are not playing against a single opponent but
against a crowd of claimedly tens of thousands (50000?)
of players with an average rating (at least at the very
start) of 1500. It would take an enormous amount of wins
on their part to lower that average to such a low level
that the winning wouldn't earn them much... If they won
1 match of 1-point against each and every player on FIBS
(i.e. 50000 wins), that average rating of 1500 would go
down by only 1.5? (please correct me if I'm off on this
and use a more accurate number) points... Could someone
calculate what JF/SW rating would be by the time they'd
pull the average rating on FIBS by just 1.5 points...?
>Regarding the comments that the ratings differences don't
>reflect the assertion that only 10 or so people in the world
>can maintain a winning record against SW or JF, I would say
>that the ratings _do_ reflect that. After all, how many
>people on FIBS consistenly have a higher rating than SW or
>JF? Isn't it just possible that robots have the highest
>ratings on FIBS because they're the best players?
While discussing rating systems, somebody had tried to
differentiate between "rankings" and "ratings", which
wasn't applicable in that context but is in this case.
The rating difference between #1 and #2 player can be
a million points while the difference between #2 and #3
players can be ten points and they still would rank as
#1, #2 and #3...
The issue here is the closeness of those robots ratings
to a good number of other players. If SW earned 30000
experience by playing 3 point matches on the average,
that would mean it played against a pool of 10000 people
with an average rating of 1500. If it could consistently
beat 9990 of them, top 10 players on FIBS couldn't even
come close to making a dent towards keeping its rating
"stabilized" at around 2000-2100 (even if they were the
same people as the top 10 players in the world)...
Something just doesn't add up...
MK
Murat Kalinyaprak
>In <72u8m1$rm8$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>> Why do we expect that any/all players ratings will
>> *reach* a "whatever rating" and hover around it forever
>> after...?
>Because the ratings system on Fibs works properly.
I don't believe the results we observe could simply be
achieved by the current formula used by FIBS. I don't
see how that formula could prevent some players from
straying far away from the pack...
>> longer a factor. Yet, they have so far failed to produce
>> enough surplus wins against the "*losing masses*" to get
>> past 2000-2100 ratings...? How can that be...?
>You seem to be saying that the mythical perfect player
>will beat all inferior players %100 of the time. If that
>were the case, then yes, the perfect player's rating would
>increase with no upper bound.
I am not the one turning certain robots into "mythical
perfect players". I'm only making multi-edged arguments,
without any intention to prove which way they cut. There
seem to be a case where we have to decide whether we want
to eat the cake or have it...
My argument is that even a less than "perfect" player can
produce *enough* surplus of wins against a large mass of
opponents with a much lower average rate. It doesn't have
to be a boundless process in order for it to produce huge
differences in ratings...
>However, the perfect player will always lose a significant
>number of matches, due to the element of luck in the game.
The luck factor is supposed to even out in the long run.
But I personally don't mind hearing this comment because
it leaves room for the possibility that a ceratin luck
factor may be artificially maintained by FIBS dice... :)
>Using made up numbers: Let's say the perfect player can beat
>your average intermediate player, rated 1700, about 75% of
>the time in 5 point matches. The perfect player would gain
>+2.236 rating points for every win, and lose -6.708 for every
>loss. Averaging 3 wins for every loss, the perfect player's
>rating will in the long run remain unchanged, at approximately
>2126.75.
With the luck factor eliminated, why would a "perfect"
player or even a player close to that would only win
75% of the time, regardless of whether his opponent is
rated at 1000, 500, 200, 50 or 2 points below him...?
As a side comment, when talking about certain robots if
"perfect" had to mean "75%", I would have no problem
with it... :)
MK
David Montgomery
Having P% chances against players of level L
does not mean you have P% against any group
whose average level is L. Playing 10 matches
against 1700-level players is different than
5 matches aginst 2000 combined with 5 matches
against 1400.
Saying a player will win P% of its matches
against a group of players G is not the same
thing as saying that P% of the players in
G consistently beat the player. At my club
I consistenly lose about 1/3 of my matches.
But no one beats me consistently.
Perfect play could win only 75% of the time
if the other player plays well enough to
win 25% of the time. If the other player
played better, the perfect player might win
only half the time.
The rating formula prevents players from
straying far from the pack by requiring that
players win a higher and higher percent of their
matches to go to a higher level. If you can't
win with that percent, you don't go higher.
The fact that luck evens out in the end does
not mean that the better player eventually wins
all of the matches. It means that the percentage
of matches won converges arbitrarily close to the
the result you would get if you played an infinite
number of matches. The weaker player keeps
winning matches, even when the luck has evened out.
You cannot eliminate the luck factor in backgammon.
It is always there. If you play many, many matches
then both players will get approximately equal
amounts of luck, but that doesn't take the luck
away.
An analogy. Let's say you played perfect (but
honest, non-prescient) blackjack. What percent
of the hands would you win? You still win only
about 1/2 the hands, even though you are playing
perfectly. If you played 10,000,000,000,000,000,000
hands, to "eliminate" the luck factor, you would
still win only about 1/2 the hands.
Me Again
> This is what I don't understand. How can "*perfect*"
> (or close to it) play can only win 75% of the time...?
You roll 5 - 2 and play 13-8 24-22. Your opponent rolls 5-5 and points
on both your blots. You roll any of the 9 numbers (6-6, 6-3, 3-6, 3-3,
1-1, 6-1, 1-6, 3-1, 1-3) that fail to bring in either of your hit men.
Your opponent doubles, you drop.
Did you make any mistakes? (Depending on the match score, your opponent
may have made a mistake in doubling and should have played for a gammon,
but in a money game using the jacoby rule it's a given that this is a
double/drop.)
This is not an isolated position, there are several other 2 roll and 3
roll scenarios (usually involving doubles, something that is rolled 1
out of every 6 rolls) that with "perfect play" will result in a
double/drop.
Thus, even with "perfect play" you can (and will) lose many games,
because of the luck of the dice. Any game that has a luck factor will
be a game in which it will always be impossible to win 100% of your
games, even with perfect play.
HTH
jc
Michael J Zehr
Murat Kalinyaprak <mu...@cyberport.net> wrote:
>In <72vf4c$a...@senator-bedfellow.MIT.EDU> Michael J Zehr wrote:
>
>>In <72u8m1$rm8$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>
>>>longer a factor. Yet, they have so far failed to produce
>>>enough surplus wins against the "*losing masses*" to get
>>>past 2000-2100 ratings...? How can that be...?
>
>>should have their rating arbitrarily high. If perfect play
>>lets you win 75% of the time in a 9 point match against the
>>"average" player on FIBS, then using the rating system you
>>can determine the rating that perfect player ought to have.
>>It might well be 2000-2100.
>
>(or close to it) play can only win 75% of the time...?
Suppose someone did write a "perfect" backgammon program, by whatever
definition you chose for perfect... and then it played itself. What do
you think it's percentage of wins would be?
50% right?
So what should its win percent be against an "almost perfect" opponent?
(Feel free to define "almost perfect" however you want.) What about an
"slightly less than almost perfect" opponent?)
-Michael J. Zehr
Graham Price
Murat Kalinyaprak <mu...@cyberport.net> wrote in article
<73a4l3$snp$2...@news.chatlink.com>...
> In <72vj16$tqc$1...@nnrp1.dejanews.com> limill...@my-dejanews.com wrote:
> With the luck factor eliminated, why would a "perfect"
> player or even a player close to that would only win
> 75% of the time, regardless of whether his opponent is
> rated at 1000, 500, 200, 50 or 2 points below him...?
>
> As a side comment, when talking about certain robots if
> "perfect" had to mean "75%", I would have no problem
> with it... :)
>
> MK
>
I always thought that backgammon was a combination of skill + luck
so it's pretty difficult to eliminate the luck factor.
If the ratio is say 50% skill and 50% luck
then wouldn't a perfect robot's winning rate be
calculated by adding the skill factor + the luck factor.
If it approached perfect then it's winning rate would be
~ .5 for skill + (somevariable)* .5 for luck factor
If it got an even split on luck then somevariable would at that
time be .5 and it would win 75% of its matches.
Maybe skill difference might even be a better variable because
if the opponent were weaker then skill would be more telling and
luck would have less influence whereas if the opponent were
closer in strength then skill difference would decrease and
luck would therefore increase.
Anyway one of the enjoyable (sort of) paradoxes with backgammon
is that you can play a "perfect" game and still get punished by
being backgammoned, just the way it is.
Graham
EdmondT
pretty difficult to eliminate the luck factor. If the ratio is say 50% skill
I think luck is MUCH less than a 50% factor. If you spend some time playing
much stronger players than you, I think you'll find this out quickly.
limill...@my-dejanews.com
mu...@cyberport.net (Murat Kalinyaprak) wrote:
>
> Fine. Let's look at this from a different angle also.
> Let's have Snowie (rated at 2089?) play each opponent
> a 1-point match and only once. With about 600 points
> difference (2089-1500), its winning chances would be
> around 65%? for 1-point matches. If Snowie does indeed
> win 65% of those matches, then we can reword your above
> statement as: "Snowie can beat 65% of its opponents"
> (among players on FIBS with 1500 average rating)...
>
> If the players on FIBS represent a good sampling of all
> players in the world, then we can expand that statement
> to say: "Snowie can beat 65% of all players on earth".
> (When talking about matches of other lengths, the "65%"
> can be replaced by the appropriate figure).
>
> If we have Snowie play another set of matches against
> the same players again, and again, and again... this
> ratio will not change. Therefore, we can say that 35%
> of the players will beat Snowie consistently (i.e. in
> the long run), which sounds much less impressive than
> claims made previously in this newgroup...
I honestly can't tell, are you simply trolling this newsgroup?
If not, I can tell you that that the two statements
"Snowie beats a 1500 player 65% of the time" and
"Snowie can beat 65% of all players" are not equivalent.
> I had already made an argument about two requirements
> for this to work. Only "one particular form of skill"
> can be measured (i.e. single-point, multi-point, etc.
> matches), not a combination of many kinds at the same
> time. This is not the case with FIBS rating system, as
> you and others acknowledge also. And at least an initial
> sample of players need to be measured against a common
> "unit" before they can be used to measure each other or
> players. I don't know if this was done in establishing
> the FIBS formula or not. It would be good if we get an
> answer on this from somebody who knows...
>
The ELO formula is based entirely on basic probability
theory and not on empircal data. Empirical data is highly
error prone and impossible to generalize into a formula.
The derivation of the formula is loosely explained at
the netgammon site:
http://ibs.nordnet.fr/netgammon/elobis_usa.html
>
> For the moment, let's stick with the match length and
> assume that a robot can do slightly better in 1-point
> matches against weaker opponents and it's "true" winning
> chances (referring to the previous examples used above)
> is 66% instead of 65%. Let's also say that half of the
> 30000 experience Snowie has consists of 1-point matches
> (which would had to be played against almost all weaker
> players from the beginning). At about 1.5? points earned
> per match, that 1% would translate to 150x1.5=225 rating
> points and would put Snowie at 2325. This is only with
> a mere 1% inaccuracy in calculating the probability of
> winning...
Your math is wrong. A player who wins 65% of the time over
1500 rated opponents will have a rating of 2037, a player
who wins 66% of the time over the same opponents will have
a rating of 2076. Given the known error rate in the formula,
a 1% difference in skill is in practice difficult to observe.
>
> Of course, it's possible that a few human players may
> end up not fitting the "standard mold" and cause such
> irregularities/extremes also. I'm just using robots as
> likely cases because they play large amounts of matches
> and arguments have been made about their being superior
> and/or different than at least most humans...
>
> And with the seemingly arbitrary round number constants
> in it, the FIBS formula looks just too crude to be able
> to prevent such possible or even expected irregularities.
> Yet, no such irregularities are observed...
>
You're right that the constants are arbitrary, since they
could be changed to anything and the formula would still
work. However, the range of the ratings and magnitude of
the changes would be different.
I don't know what you mean by "expected irregularities".
> Some people had argued that inflating ratings by taking
> advantage of deficiencies in FIBS ratings was possible.
> If it's possible on purpose, why couldn't it be possible
> for it to happen inadvertently, which I believe would be
> more likely than not to happen. I just can't see how a
> some "crude" formula with some round/arbitrary constants
> can result in the apparent stability/smoothness/neatness
> in FIBS ratings and their ranges and can't help wonder
> if some other mecahnism/s are used to ensure that...
>
Your argument translates to, "I don't understand Fibs'
ratings formula, therefore Fibs is rigged".
limill...@my-dejanews.com
mu...@cyberport.net (Murat Kalinyaprak) wrote:
>
> This is what I don't understand. How can "*perfect*"
> (or close to it) play can only win 75% of the time...?
>
"Perfect" in backgammon, means, I believe, playing every
move and making every cube decision such that they maximize ones
chance of winning the match.
Perfection does not imply winning every match.
It seems perfectly reasonable to me that a perfect strategy would
beat intermediate opponents 75% of the time in 5 point matches.
> We either have to reassess the stregth of those robots,
Computer programs aren't perfect, I'll give you that if
it's what you really wanted to hear.
> I think the problem with your argumant is that JF/SW in
> this case are not playing against a single opponent but
> against a crowd of claimedly tens of thousands (50000?)
> of players with an average rating (at least at the very
> start) of 1500. It would take an enormous amount of wins
> on their part to lower that average to such a low level
> that the winning wouldn't earn them much... If they won
> 1 match of 1-point against each and every player on FIBS
> (i.e. 50000 wins), that average rating of 1500 would go
> down by only 1.5? (please correct me if I'm off on this
> and use a more accurate number) points... Could someone
> calculate what JF/SW rating would be by the time they'd
> pull the average rating on FIBS by just 1.5 points...?
>
I can't for the life of me see what your point is here.
You seem to enjoy deflecting an argument by re-phrasing it
in incomprehensible terms. (which is what leads me to
believe that you're very cleverly trolling the newsgroup)
>
> While discussing rating systems, somebody had tried to
> differentiate between "rankings" and "ratings", which
> wasn't applicable in that context but is in this case.
> The rating difference between #1 and #2 player can be
> a million points while the difference between #2 and #3
> players can be ten points and they still would rank as
> #1, #2 and #3...
>
> The issue here is the closeness of those robots ratings
> to a good number of other players. If SW earned 30000
> experience by playing 3 point matches on the average,
> that would mean it played against a pool of 10000 people
> with an average rating of 1500. If it could consistently
> beat 9990 of them, top 10 players on FIBS couldn't even
> come close to making a dent towards keeping its rating
> "stabilized" at around 2000-2100 (even if they were the
> same people as the top 10 players in the world)...
You seem to have forgotten that the formula on fibs works
properly. Snowie's rating will fluctuate just like everyone
else's, irrespective of its experience. (once its experience
is greater than 400). There is no conspiracy needed by the
masses to "make a dent" in its rating.
Since you prefer hand-waving arguments to those based on fact,
here comes mine. Don't look at things in the big picture, look at
it on the microscopic level. A good player does not win all of the
time, right? Why, because of luck. When a good player beats
a bad player, he gets a modest reward. When a good player loses
to a bad player, he sufferes a big loss. It all evens out
in the end.
>
> Something just doesn't add up...
>
You can say that again. And I'm sure you will.
limill...@my-dejanews.com
mu...@cyberport.net (Murat Kalinyaprak) wrote:
>
> With the luck factor eliminated, why would a "perfect"
Wow! You've eliminated luck from backgammon?!!?
> player or even a player close to that would only win
> 75% of the time, regardless of whether his opponent is
> rated at 1000, 500, 200, 50 or 2 points below him...?
Please tell me how often you would expect a perfect player
to beat a player rated 2 points below her.
>
> As a side comment, when talking about certain robots if
> "perfect" had to mean "75%", I would have no problem
> with it... :)
>
Me neither, 75% is damn good.
Murphy McKalin
>In <73a32u$snp$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>>This is what I don't understand. How can "*perfect*"
>>(or close to it) play can only win 75% of the time...?
>Suppose someone did write a "perfect" backgammon program, by
>whatever definition you chose for perfect... and then it played
>itself. What do you think it's percentage of wins would be?
>50% right?
Yes, assuming there is no "luck factor"...
>So what should its win percent be against an "almost perfect"
>opponent? (Feel free to define "almost perfect" however you
>want.) What about an "slightly less than almost perfect"
>opponent?)
100%
BTW: notice that I wasn't the one who used the
term "perfect" first. I carried it over from
the article I was responding to and used it
within quotation marks ever since...
MK
Murphy McKalin
>MK:
>Having P% chances against players of level L
>does not mean you have P% against any group
>whose average level is L. Playing 10 matches
>against 1700-level players is different than
>5 matches aginst 2000 combined with 5 matches
>against 1400.
What you say could be possible only if the FIBS
formula was lop-sided (i.e. used the "ratings"
themselves in some fashion). But it only uses
the difference between two ratings...
Just to avoid any calculation errors I may make,
I just logged on to FIBS and was lucky enough to
spot 3 players with ratings of 1965, 1565 and
1766 (close enough) all at once. The on-screen
calculator showed that my winning chances against
them were 43.49%, 54.95% and 49.18% respectively.
If I adjust the last one for 1765, I get 49.21%
while the average of first two is 49.22%...
>Saying a player will win P% of its matches
>against a group of players G is not the same
>thing as saying that P% of the players in
>G consistently beat the player. At my club
>I consistenly lose about 1/3 of my matches.
>But no one beats me consistently.
Ok, I'll give in on this one. What I said was true
for one round but not necessarily so at all to say
"consistently" (unless the same players repeated
the same performance each and every match, which
is possible but very unlikely/unrealistic).
However, in order to say one won against another,
it's enough that one wins 51% of the time, which
is quite lower than the 65% used in the examples.
So, with the figures that were used as examples,
the number of people who would win consistently
would be much less than 35% but much more than 10.
I'm not sure if this is something that can even be
truely calculated with the variables at hand...?
>Perfect play could win only 75% of the time
>if the other player plays well enough to
>win 25% of the time. If the other player
>played better, the perfect player might win
>only half the time.
If I have to accept this as true, then I would have
to argue that there is no such thing as "perfect"
or even anything close to it in bg. 75% is just too
far from it... Given this, the FIBS forfula can't
be claimed to rate "skill" either...
>The rating formula prevents players from
>straying far from the pack by requiring that
>players win a higher and higher percent of their
>matches to go to a higher level. If you can't
>win with that percent, you don't go higher.
So...? Their ratings will go up in ever smaller
increments (i.e. slower) but what would prevent
them from going much higher? Imagine a Martian
with a potential rating of 3000 lands on earth
and joins FIBS. Are you guys saying that even
after 20000, 50000, 100000 matches he will never
get past achieveing a rating of 2000-2100...?
>You cannot eliminate the luck factor in backgammon.
>It is always there. If you play many, many matches
>then both players will get approximately equal
>amounts of luck, but that doesn't take the luck away.
I don't know about others but to clarify things
just speaking for myself, when I say "eliminating
the luck (factor)" I mean "*equal enough* luck"
for both/all players...
>An analogy. Let's say you played perfect (but
>honest, non-prescient) blackjack. What percent
>of the hands would you win? You still win only
>about 1/2 the hands, even though you are playing
>perfectly. If you played 10,000,000,000,000,000,000
>hands, to "eliminate" the luck factor, you would
>still win only about 1/2 the hands.
I barely know blackjack but I agree that what you
say would be true between equal players in bg. If
the players are unequal and the luck is equal, then
the better player can generate a surplus of wins
without limit. When awarding points as is done now
with the FIBS formula, the points earned may get
increasingly small but should never reach zero
and stop...
I understand the argument that within the FIBS
rating scheme any player will eventually settle
at around a certain rating. What I'm arguing is
that any player claimed to be one of the top 10
players in the world (human or robot) would break
away from the pack by a larger gap before reaching
their so-called "true rating"...
MK
Patti Beadles
Murphy McKalin <mu...@cyberport.net> wrote:
>>So what should its win percent be against an "almost perfect"
>>opponent? (Feel free to define "almost perfect" however you
>>want.) What about an "slightly less than almost perfect"
>>opponent?)
>100%
No way. There will always be some luck involved.
For example, Perfect Player opens with 51 and plays 13/8 24/23, the
commonly accepted best move.
Total Idiot rolls 55 and plays 8/3(2) 6/1(2)*. PP now dances, TI
rolls 64 and plays 8/2* 6/2. PP continues to dance while TI rolls
just the right numbers to close him out and bear off safely.
PP played his single move flawlessly, but TI got lucky.
-Patti
--
Patti Beadles | Not just your average purple-haired
pat...@netcom.com/pat...@gammon.com | degenerate gambling adrenaline
http://www.gammon.com/ | junkie software geek leatherbyke
or just yell, "Hey, Patti!" | nethead biker.
Gary Wong
don't think I have anything else to contribute. Here is one last post all
the same. Apologies to everybody who is sick of this stuff :-)
mu...@cyberport.net (Murphy McKalin) writes:
> In <73ap54$g...@krackle.cs.umd.edu> David Montgomery wrote:
> >Having P% chances against players of level L
> >does not mean you have P% against any group
> >whose average level is L. Playing 10 matches
> >against 1700-level players is different than
> >5 matches aginst 2000 combined with 5 matches
> >against 1400.
>
> Just to avoid any calculation errors I may make,
> I just logged on to FIBS and was lucky enough to
> spot 3 players with ratings of 1965, 1565 and
> 1766 (close enough) all at once. The on-screen
> calculator showed that my winning chances against
> them were 43.49%, 54.95% and 49.18% respectively.
> If I adjust the last one for 1765, I get 49.21%
> while the average of first two is 49.22%...
Unfortunately that's just a special case where the total probability
IS roughly the average of the three parts (because your rating is very
close to the median of a symmetric distribution). David is right: the
probability against the average rating is not necessarily the same as
the average probability against all ratings. A counterexample:
- suppose I am only rated at 1165, and play 9-point matches against the
three players you found (1565, 1765 and 1965);
- my probabilities of winning against the three are 20.1%, 11.2% and
6.0% respectively;
- my average probability of winning against the 1565 and 1965 players
is 13.1%, but against the 1765 player is only 11.2%. They are NOT
the same.
> >Perfect play could win only 75% of the time
> >if the other player plays well enough to
> >win 25% of the time. If the other player
> >played better, the perfect player might win
> >only half the time.
>
> If I have to accept this as true, then I would have
> to argue that there is no such thing as "perfect"
> or even anything close to it in bg. 75% is just too
> far from it...
There is such a thing as perfect -- perfection is never making any
mistakes. (A precise definition of a perfect strategy is one that
maximises your "security level" -- ie. a maximin strategy, one that
maximises your minimum expected gain across all possible opponents.
Since the rules in backgammon are symmetric (as opposed to games like
blackjack, where the dealer follows different rules than the players)
and backgammon is a zero-sum game, this maximum security level is
zero.)
Perhaps one issue that is causing confusion is that the idea of
perfection in backgammon is somewhat abstract. (This is because we
haven't reached perfection, and we don't always know what a mistake
is.) If a concrete example would clarify things, consider Hugh
Sconyer's programs which play all bearoff positions (though the
publically available versions only play as many positions as will fit
on the CD-ROMs), and every position in Hyper-Backgammon (essentially
backgammon played with three chequers per player) perfectly for money.
These players are PERFECT. No mistakes. Maximum security level,
etc. etc. Yet they cannot win every game. The probability of them
winning depends on the position, and the opponent. Imagine Hugh was
somehow able to extend his exhaustive search to include every
backgammon position -- this would be the perfect player we're talking
about. And it could not win every match, either. Even against an
intermediate player like me it would probably only win about 2/3 of
the games; it could win 75% or 90% or even more of the matches, as long
as the matches were long enough.
> Given this, the FIBS forfula can't be claimed to
> rate "skill" either...
Yes, it can. Skill is the ability to play without making mistakes.
The more mistakes you make, the less matches you expect to win. If
both players play without making any mistakes, then they each expect
to win 50% of the matches. If only one player makes mistakes, then he
expects to win less than 50%. The more (and costlier) mistakes he
makes, the fewer matches he expects to win. You can view FIBS ratings
as measuring skill, or the ability to play without making mistakes, or
the rate of matches won -- they are all equivalent.
> >The rating formula prevents players from
> >straying far from the pack by requiring that
> >players win a higher and higher percent of their
> >matches to go to a higher level. If you can't
> >win with that percent, you don't go higher.
>
> So...? Their ratings will go up in ever smaller
> increments (i.e. slower) but what would prevent
> them from going much higher? Imagine a Martian
> with a potential rating of 3000 lands on earth
> and joins FIBS. Are you guys saying that even
> after 20000, 50000, 100000 matches he will never
> get past achieveing a rating of 2000-2100...?
For one thing, it is impossible to have a potential rating of 3000
(without cheating). My guess is that the best humans and computers in
the world today make mistakes which would cost them at most an
expected 0.4 points per game for money against a perfect player
(that's including chequer play and cube decisions). This is only
worth about 200 FIBS rating points. If we assume that the best
current players could consistently maintain a rating of 2100 without
cheating (which is very generous), then even a perfect player would
have difficulty remaining above 2300. In truth it's very likely to be
lower. The other players on FIBS simply do not make enough mistakes
for anybody to be consistently rated higher than that, no matter how
good they are.
In general I believe that 1000 matches is sufficient to "reach" a
rating, regardless of your previous rating and experience: by that I
mean that after 1000 matches, the bias from your old rating will be
insignficant compared to random fluctuations. (Part of the justification
is given in an old article at <http://www.bkgm.com/rgb/rgb.cgi?view+471>.)
Therefore I claim that if your perfect Martian really did deserve a
rating of 2300, I'm sure it could reach it within 1000 matches (in
fact since ratings change more quickly for new players, the number
would be significantly less).
> >An analogy. Let's say you played perfect (but
> >honest, non-prescient) blackjack. What percent
> >of the hands would you win? You still win only
> >about 1/2 the hands, even though you are playing
> >perfectly. If you played 10,000,000,000,000,000,000
> >hands, to "eliminate" the luck factor, you would
> >still win only about 1/2 the hands.
>
> I barely know blackjack but I agree that what you
> say would be true between equal players in bg. If
> the players are unequal and the luck is equal, then
> the better player can generate a surplus of wins
> without limit. When awarding points as is done now
> with the FIBS formula, the points earned may get
> increasingly small but should never reach zero
> and stop...
It is perfectly possible for the sum of an infinite series to remain
below some limit, even though the individual terms never "reach zero
and stop". Add 1/2 + 1/4 + 1/8 + 1/16 + ... for instance; you can
come arbitrarily close to 1, but never exceed it.
But you don't even need this mechanism to show that a FIBS rating will
not increase without bound. The points earned are only half the
story, you have to consider the points _lost_ as well! Suppose you
are much better than me, and you win 2/3 of the games (this is what is
expected to happen if you are rated at 1800 and I am rated at 1200,
for instance). If we played for money, then yes, you would expect to
generate a "surplus of wins" (money) without limit. But on FIBS, 2/3
of our games will result in a win to you (you gain 1.33 rating points,
and I lose 1.33); the other 1/3 will result in a win to me (I gain
2.67 points, and you lose 2.67). If we play 300 1-point matches, then
you expect to win 200 of them for a gain of 267 points; but you lose
the other 100 which also costs you 267 points. In the long run, you
don't expect to change at all! A "surplus of wins without limit"
(ie. winning more than 50% of the matches) does NOT imply a surplus of
RATING POINTS without limit. To maintain a rating over 1800, you
would have to consistently win more than 2/3 of the games against me.
> I understand the argument that within the FIBS
> rating scheme any player will eventually settle
> at around a certain rating. What I'm arguing is
> that any player claimed to be one of the top 10
> players in the world (human or robot) would break
> away from the pack by a larger gap before reaching
> their so-called "true rating"...
But right behind the top 10 players in the world are another 100 that
are very nearly as good as them. If there WERE a group of 10 players
on FIBS who were far better than anybody else then we would expect a
gap between their ratings and those of all other players; but there
are not. In any case, you're talking about the distribution of the
population, not the ratings mechanism. Just because you're one of the
top 10 players in the world doesn't mean a different set of rules
apply to you; the same reasoning in the example above (you can't
expect to raise above 1800 no matter how much you play me, if you only
win 2/3 of the games) applies to top 10 players, just like it does to
everybody else.
Cheers,
Gary.
Murat Kalinyaprak
><739vq4$k67$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>> Fine. Let's look at this from a different angle also.
>> Let's have Snowie (rated at 2089?) play each opponent
>> a 1-point match and only once. With about 600 points
>> difference (2089-1500), its winning chances would be
>> around 65%? for 1-point matches. If Snowie does indeed
>> win 65% of those matches, then we can reword your above
>> statement as: "Snowie can beat 65% of its opponents"
>> (among players on FIBS with 1500 average rating)...
>> If the players on FIBS represent a good sampling of all
>> players in the world, then we can expand that statement
>> to say: "Snowie can beat 65% of all players on earth".
>> (When talking about matches of other lengths, the "65%"
>> can be replaced by the appropriate figure).
>> If we have Snowie play another set of matches against
>> the same players again, and again, and again... this
>> ratio will not change. Therefore, we can say that 35%
>> of the players will beat Snowie consistently (i.e. in
>> the long run), which sounds much less impressive than
>> claims made previously in this newgroup...
> I honestly can't tell, are you simply trolling this newsgroup?
No.
> If not, I can tell you that that the two statements
> "Snowie beats a 1500 player 65% of the time" and
> "Snowie can beat 65% of all players" are not equivalent.
It could be but not necessarily is so. The wins/losses
can be distributed in a way that it could beat more than
65% or less than 65% of players. (Let's also keep in mind
that 51% is enough for winning).
>> I had already made an argument about two requirements
>> for this to work. Only "one particular form of skill"
>> can be measured (i.e. single-point, multi-point, etc.
>> matches), not a combination of many kinds at the same
>> time. This is not the case with FIBS rating system, as
>> you and others acknowledge also. And at least an initial
>> sample of players need to be measured against a common
>> "unit" before they can be used to measure each other or
>> players. I don't know if this was done in establishing
>> the FIBS formula or not. It would be good if we get an
>> answer on this from somebody who knows...
> The ELO formula is based entirely on basic probability
> theory and not on empircal data. Empirical data is highly
> error prone and impossible to generalize into a formula.
After questioning whether I'm trolling, are these empty
statements all you can offer...? We don't need data to
know the probability of a coin or a die landing on one
of it's faces because we know a coin has two faces and
a die has six faces. If we want to know the probabiliy
of getting snow on Christmas day however, we would need
statistical data. Error proneness is not an issue since
there are no other ways of predicting probabilities in
such cases. And yes, what is observed from data can be
generalized into a formula, although it may have to be
much more complicated than a crudely invented formula,
depending on how much accuracy would be desired. Such a
formula can also be further fine-tuned based on future
accumulations of data without being circular. Unless the
FIBS formula is based on some real statistical data, it
would be nothing more than a hocus-pocus invention. Why
is this so hard to accept for you guys? Are you a cult
or something...?
> The derivation of the formula is loosely explained at
> the netgammon site:
> http://ibs.nordnet.fr/netgammon/elobis_usa.html
I know what the formula is. What I would like to know is
whose bright idea was to multiply by the square-root of
match length, divide by 2000, etc. and based on what...?
Is this too much ask...?
>> For the moment, let's stick with the match length and
>> assume that a robot can do slightly better in 1-point
>> matches against weaker opponents and it's "true" winning
>> chances (referring to the previous examples used above)
>> is 66% instead of 65%. Let's also say that half of the
>> 30000 experience Snowie has consists of 1-point matches
>> (which would had to be played against almost all weaker
>> players from the beginning). At about 1.5? points earned
>> per match, that 1% would translate to 150x1.5=225 rating
>> points and would put Snowie at 2325. This is only with
>> a mere 1% inaccuracy in calculating the probability of
>> winning...
> Your math is wrong. A player who wins 65% of the time over
> 1500 rated opponents will have a rating of 2037, a player
> who wins 66% of the time over the same opponents will have
> a rating of 2076. Given the known error rate in the formula,
> a 1% difference in skill is in practice difficult to observe.
Based on SW's rating and experience being 2100 and 30000
and the assumption that 15000 of those consist of 1-point
matches played against 1500 rated opponents, at the start
it would earn 1.34 points per win. By the time it would
reach a rating of 2325, its earnings per match would drop
to 1.12 points. But if I used a more accurate points-per-
match figure than the 1.5 I had used, then it wouldn't
reach a point where it would drop to 1.12. So let me just
approximate it to 1.15 and replace 1.5 with the average
of 1.34 and 1.15 = 1.24. In that case 150 extra wins would
result in 186 point that would raise its rating to about
2286...
BTW, I'm not talking about any error rate due to the FIBS
formula itself. Even if the FIBS formula was based on some
statistical data (which it seems to be not), a player who
would later deviate from the statistics by a mere 1% would
cause "visible" enough irregularities/extremes in ratings.
>> Of course, it's possible that a few human players may
>> end up not fitting the "standard mold" and cause such
>> irregularities/extremes also. I'm just using robots as
>> likely cases because they play large amounts of matches
>> and arguments have been made about their being superior
>> and/or different than at least most humans...
>> And with the seemingly arbitrary round number constants
>> in it, the FIBS formula looks just too crude to be able
>> to prevent such possible or even expected irregularities.
>> Yet, no such irregularities are observed...
> You're right that the constants are arbitrary, since they
> could be changed to anything and the formula would still
> work. However, the range of the ratings and magnitude of
> the changes would be different.
Yes, simply replacing them wouldn't accomplish any more
than what you described. The fact is, FIBS formula just
doesn't have enough buttons and knobs to fine-tune it
against possible irregularities that may be caused by
external factors. Let alone that, any error rate coming
from the formula itself is apt to be compounded when it's
applied recursively and in a relative manner. If the FIBS
formula is so sacred to be touched, then maybe we could
redefine what "works/doesn't work" mean...
>> Some people had argued that inflating ratings by taking
>> advantage of deficiencies in FIBS ratings was possible.
>> If it's possible on purpose, why couldn't it be possible
>> for it to happen inadvertently, which I believe would be
>> more likely than not to happen. I just can't see how a
>> some "crude" formula with some round/arbitrary constants
>> can result in the apparent stability/smoothness/neatness
>> in FIBS ratings and their ranges and can't help wonder
>> if some other mecahnism/s are used to ensure that...
> Your argument translates to, "I don't understand Fibs'
> ratings formula, therefore Fibs is rigged".
probability of the favorite winning the match =
1/(10^(rating-difference*SQRT(match-legth)/2000)+1)
points earned by the favorite =
4*SQRT(match-length)*favorite's-probability-winning
This is the formula in short and produces some results in
recursively self-validating manner. The question is what
those results can mean in terms of "measuring", etc... I
say that this formula can't be said to "measure" anything,
unless we change again the definition of what "measuring"
means...
MK
Murat Kalinyaprak
><73a32u$snp$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>> I think the problem with your argumant is that JF/SW in
>> this case are not playing against a single opponent but
>> against a crowd of claimedly tens of thousands (50000?)
>> of players with an average rating (at least at the very
>> start) of 1500. It would take an enormous amount of wins
>> on their part to lower that average to such a low level
>> that the winning wouldn't earn them much... If they won
>> 1 match of 1-point against each and every player on FIBS
>> (i.e. 50000 wins), that average rating of 1500 would go
>> down by only 1.5? (please correct me if I'm off on this
>> and use a more accurate number) points... Could someone
>> calculate what JF/SW rating would be by the time they'd
>> pull the average rating on FIBS by just 1.5 points...?
> I can't for the life of me see what your point is here.
> You seem to enjoy deflecting an argument by re-phrasing it
> in incomprehensible terms. (which is what leads me to
> believe that you're very cleverly trolling the newsgroup)
All of the arguments made on this issue had been based on
two players playing against each other. In that case, for
each point the winner wins, the loser loses a point and
the gap between their ratings widen quickly, so that a 1%
surplus of wins would take extremely long time to become
visible. In my argument, I'm making a certain player play
against the entire FIBS. Imagine a player plays 100 games
against 1000 different players and generates 1 extra win
against each one of them. After 100000 games, the average
rating of all its 1000 oppenents would go down much more
slowly while its own rating skyrockets. I don't know why
this should be so difficult to understand.
>> The issue here is the closeness of those robots ratings
>> to a good number of other players. If SW earned 30000
>> experience by playing 3 point matches on the average,
>> that would mean it played against a pool of 10000 people
>> with an average rating of 1500. If it could consistently
>> beat 9990 of them, top 10 players on FIBS couldn't even
>> come close to making a dent towards keeping its rating
>> "stabilized" at around 2000-2100 (even if they were the
>> same people as the top 10 players in the world)...
> You seem to have forgotten that the formula on fibs works
> properly. Snowie's rating will fluctuate just like everyone
> else's, irrespective of its experience. (once its experience
> is greater than 400). There is no conspiracy needed by the
> masses to "make a dent" in its rating.
Maybe I'm not expressing myself clearly. By "winning"
I mean "not breaking even" (i.e. winning at least one
match more than predicted in a 100)...
> Since you prefer hand-waving arguments to those based on fact,
> here comes mine. Don't look at things in the big picture, look at
> it on the microscopic level. A good player does not win all of the
> time, right? Why, because of luck. When a good player beats
> a bad player, he gets a modest reward. When a good player loses
> to a bad player, he sufferes a big loss. It all evens out
> in the end.
A 2100 rated player's having a 65% chance of winning
against a 1500 rated player is an average. It doesn't
mean that each and every 2100 rated player will win
exactly 65% of the time against a 1500 rated player,
in every type of match. The average would still be
the same regardles of whether there would be "stray"
ratings or not. I'm making an issue of the fact that
with the current FIBS formula, I would expect to see
some strays which I don't. I feel that everything is
intriguingly too neat despite the known/acknowledged
deficiencies in the formula...
>> Something just doesn't add up...
> You can say that again. And I'm sure you will.
I may say even more later. I'm working on it... :)
MK
Murat Kalinyaprak
><73a4l3$snp$2...@news.chatlink.com> Murat Kalinyaprak wrote:
>> With the luck factor eliminated, why would a "perfect"
> Wow! You've eliminated luck from backgammon?!!?
Not me, the notion of "perfect" necessitates the
assumption that "luck" is eliminated. "Luck" and
"perfect" don't mix...
>> player or even a player close to that would only win
>> 75% of the time, regardless of whether his opponent is
>> rated at 1000, 500, 200, 50 or 2 points below him...?
> Please tell me how often you would expect a perfect player
> to beat a player rated 2 points below her.
100% of the time. If that's not what we are observing,
then we must be "measuring" something different than
just skill...
At the bottom of all this is my past argument that when
there is a large enough gap between the skills of two
players, skill would stop being a factor in predicting
the winning chances of the players (i.e. the mistakes
the better player will make, etc.) I believe that past
a certain amount of skill difference between two players,
the better player just wouldn't make the type of errors
that the lesser player would be capable of exploting to
his advantage (the lesser player woudln't even be able
to recognize it as an error). At that point, it would
be the better player basicly just playing against the
dice and possibly haphazard moves of the lesser player.
Let's not kid ourselves that we can let a world class
player against a beginner and claim that we can measure
the difference of skill between them, make predictions
and award winning points based on that. I propose that
the only way we could come close to accomplishing this
would be by making people play against their approximate
peers...
MK
David desJardins
> The FIBS rating formula is based on theoretical laws of statistics.
No, it isn't. There's no theoretical statistical reason why, if A beats
B x% of the time, and B beats C y% of the time, then A should beat C z%
of the time, for any particular choice of x,y,z. The formulas used by
FIBS (and all other Elo-style rating systems) are simply ad hoc choices
with no particular statistical justification except that they work
reasonably well.
> It's constructed so that if 2 people at their "true rating" play each
> other, the average number of fibs rating points each will win is zero.
There's no reason to believe that this is true, and lots of reasons to
believe that it's not true in general. It would be quite a miracle if
somehow the probability of winning a match exactly followed the FIBS
formula for all pairs of players and all match lengths.
Clearly you understand this stuff far better than Murat, and I don't
disagree especially strongly with your explanation of why it is the way
it is. But it overstates the case to describe it as perfect.
David desJardins
adz...@dartmouth.edu
Allow me to jump out of lurk mode to post a little bit. Hope no one minds the
interruption. :-)
In article <365DE4...@cyberport.net>,
Murat Kalinyaprak <mu...@cyberport.net> wrote:
> Unless the
> FIBS formula is based on some real statistical data, it
> would be nothing more than a hocus-pocus invention. Why
> is this so hard to accept for you guys? Are you a cult
> or something...?
Oh, absolutely not! It's a fundamental tenet mathematics and physics that
the world follows theoretical laws. Empirical laws are only approximations -
"as good as we can get right now" as opposed to "the way the world acutally
is".
It's a difference people take for granted. It's because we have these
theoretical laws that we have a right to make mathematical deductions.
There's one last law in Newtonian mechanics which isn't known; for turbulent
fluid flow, resistance is roughly proportional to the 7/4th power of
temperature, I believe (I don't have an engineering reference handy). That's
an empirical law that people have developed, by observation. You can't do
all those neat mathematical things, like calculus, to the function for
resistance and still have much meaning.
The FIBS rating formula is based on theoretical laws of statistics. It's
constructed so that if 2 people at their "true rating" play each other, the
average number of fibs rating points each will win is zero. A player's true
rating can be expressed as a function of the chance of winning against a
baseline (say 1500) player.
In article <365DF4...@cyberport.net>,
Murat Kalinyaprak <mu...@cyberport.net> wrote:
> limill...@my-dejanews.com wrote:
> All of the arguments made on this issue had been based on
> two players playing against each other. In that case, for
> each point the winner wins, the loser loses a point and
> the gap between their ratings widen quickly, so that a 1%
> surplus of wins would take extremely long time to become
> visible. In my argument, I'm making a certain player play
> against the entire FIBS.
Whether a fixed player's opponent is also fixed or instead varies over all
the players in FIBS doesn't make a difference. What's important is the
average number of FIBS ratings points won against each opponent. Here's why:
A player's true rating is a function of the chance he has of winning
against a baseline player. As a player's chance approaches 100%, his true
rating approaches infinity. No one wins 100% of the time, so each player's
true rating is finite. Therefore, in order for a player's rating to increase
without bound, his rating must increase over his true rating.
The average ratings points per game won against a player of skill 1500 is
lower when a player's rating is higher. This should be obvious from the
formula; as the difference between players increases, the number of points
that the favorite wins decreases. So, if a player's rating is going to
increase without bound, it can only help him if we reward him points as if he
were at his true rating when he's actually above it; we'll be rewarding him
more points. However, the average number of points a player wins at his true
rating is 0. If 0 is more points than the player will win on average, it's
clear that his rating on average will not go up. And you know that as the
number of games a player plays goes up, his winnings approach their average
value.
You asked why the ratings formula has that square root involved ... it's
that way in order to force the average number of points won between 2 players
at their true ratings to be 0. That's the theoretical law.
You may note that true ratings fluctuate. Well, unless a player's getting
so good that he's approaching winning 100% of the time, his rating will have
to go above his true rating if his rating is going to increase without bound,
and then the above argument will apply.
What if you play players rated 1500 who are all below their true rating? I
don't know. I know your rating will increase above it's true rating, but I
don't know if it's without bound. Even if the average amount of points you
win per per game is positive, and you play an inifite number of games, your
total winnings can still be bounded, as Gary pointed out in another post. I
would guess that so long as the difference between your opponents' ratings
and true ratings were bounded, your rating would also be bounded, but I
wouldn't make a strong claim for it without thinking about it more first.
I hope this helps your understanding. I'd guess also that your next
question is going to be why the average ratings increase limits on 0, but I
think that's been answered enough here - your losses count more against you
than your wins. All I can say is to do the math to convince yourself that the
losses count against you enough. Start with an percentage chance of winning
against a player rated 1500, and have him play different players rated 1500
ad inifinitum, and see that the rating of your player stops going up.
Dan
Robert-Jan Veldhuizen
MK> limill...@my-dejanews.com wrote:
>><739vq4$k67$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>>> If we have Snowie play another set of matches against
>>> the same players again, and again, and again... this
>>> ratio will not change. Therefore, we can say that 35%
>>> of the players will beat Snowie consistently (i.e. in
>>> the long run), which sounds much less impressive than
>>> claims made previously in this newgroup...
>> I honestly can't tell, are you simply trolling this newsgroup?
MK> No.
Then you are simply very ignorant but fail to recognize it.
>> If not, I can tell you that that the two statements
>> "Snowie beats a 1500 player 65% of the time" and
>> "Snowie can beat 65% of all players" are not equivalent.
MK> It could be but not necessarily is so.
You don't understand what you're talking about (again). limiller is
absolutely right (no question at all) that the two statements are not
equivalent. If you don't understand, do some study of your own instead
of making all sorts of false claims and assumptions.
MK> The wins/losses
MK> can be distributed in a way that it could beat more than
MK> 65% or less than 65% of players. (Let's also keep in mind
MK> that 51% is enough for winning).
This is just plain nonsense and shows you don't understand at all what
you're talking about (again). Do some self study, ask some questions if
you wish but please stop making statements about things you don't
understand, I think it's tiresome.
[ELO-rating based on probability]
MK> After questioning whether I'm trolling, are these empty
MK> statements all you can offer...?
Just get a clue first maybe?
MK> I know what the formula is. What I would like to know is
MK> whose bright idea was to multiply by the square-root of
MK> match length, divide by 2000, etc. and based on what...?
MK> Is this too much ask...?
If you are so convinced of your own observations and conclusions, you'll
probably never understand the formula. Just do some experimenting with a
calculator or read some text about rating systems, then come back and we
can have a sensible discussion instead of repeatedly tell you that
you're wrong.
>> Your math is wrong. A player who wins 65% of the time over
>> 1500 rated opponents will have a rating of 2037, a player
>> who wins 66% of the time over the same opponents will have
>> a rating of 2076. Given the known error rate in the formula,
>> a 1% difference in skill is in practice difficult to observe.
MK> Based on SW's rating and experience being 2100 and 30000
MK> and the assumption that 15000 of those consist of 1-point
MK> matches played against 1500 rated opponents, at the start
MK> it would earn 1.34 points per win. By the time it would
MK> reach a rating of 2325, its earnings per match would drop
MK> to 1.12 points. But if I used a more accurate points-per-
MK> match figure than the 1.5 I had used, then it wouldn't
MK> reach a point where it would drop to 1.12. So let me just
MK> approximate it to 1.15 and replace 1.5 with the average
MK> of 1.34 and 1.15 = 1.24. In that case 150 extra wins would
MK> result in 186 point that would raise its rating to about
MK> 2286...
You're wrong.
[more nonsense snipped]
MK> This is the formula in short and produces some results in
MK> recursively self-validating manner. The question is what
MK> those results can mean in terms of "measuring", etc... I
MK> say that this formula can't be said to "measure" anything,
MK> unless we change again the definition of what "measuring"
MK> means...
It is a relative measure. Any absolute measure of bg skill is impossible
(as of today and the near future at least) because we don't know what
perfect play in all possible situations is.
--
Zorba/Robert-Jan
Robert-Jan Veldhuizen
MK> limill...@my-dejanews.com wrote:
>><73a4l3$snp$2...@news.chatlink.com> Murat Kalinyaprak wrote:
>>> With the luck factor eliminated, why would a "perfect"
MK>
>> Wow! You've eliminated luck from backgammon?!!?
MK> Not me, the notion of "perfect" necessitates the
MK> assumption that "luck" is eliminated.
No. Perfect play doesn't mean winning every game/match.
MK> "Luck" and
MK> "perfect" don't mix...
Yes they do. Perfect in bg means *maximizing* winning chances, *not*
necessarily make them 100%. If you don't understand this, any further
discussion about the ratings system is absolutely useless.
>> Please tell me how often you would expect a perfect player
>> to beat a player rated 2 points below her.
MK> 100% of the time. If that's not what we are observing,
MK> then we must be "measuring" something different than
MK> just skill...
Or you "must" be completely ignorant and don't have any idea what
you're talking about.
This whole discussion resembles of someone discussing differential
equations and how modern theoory about it is wrong while he himself
still has trouble taking a square root.
--
Zorba/Robert-Jan
adz...@dartmouth.edu
David desJardins <da...@desjardins.org> wrote:
> No, it isn't. There's no theoretical statistical reason why, if A beats
> B x% of the time, and B beats C y% of the time, then A should beat C z%
> of the time, for any particular choice of x,y,z. The formulas used by
> FIBS (and all other Elo-style rating systems) are simply ad hoc choices
> with no particular statistical justification except that they work
> reasonably well.
>
You're correct. For some reason, I was thinking that the ratings formula
was derived from some probability distribution, but that's not true.
> > It's constructed so that if 2 people at their "true rating" play each
> > other, the average number of fibs rating points each will win is zero.
>
> There's no reason to believe that this is true, and lots of reasons to
> believe that it's not true in general. It would be quite a miracle if
> somehow the probability of winning a match exactly followed the FIBS
> formula for all pairs of players and all match lengths.
>
I didn't consider different match lengths. I'd agree that there's no way
to relate a player's rathing to his cahnces of winning an n length match. 2
different players could achieve the same rating because one is a good checker
player, and the other a good cube player.
So I looked a the ratings formula more closely. It's clear that for all
match lengths, if the underdog actually does win P(upset) of the time, then
the average ratings points increase is 0. It's also the case that for a
ratings difference of 4000 pts, fibs expects the better player to win 10/11%
of 1 pt matches. I'd imagine everyone could agree that no player can win 99%
of the time against an opponent who's trying (maybe even against an opponent
who's not trying, too :-) ), so that expert will lose points on average.
That's enough to show that no player's rating can increase without bound
(which was what I was posting about originally).
What I was really wanted to do is point out that there's a "true ratings
difference" between 2 players (without considering skill improvement, of
course). If the 2 players play each other in fixed length matchs ad
infinitum, their average (expected) ratings after the ith game will converge,
since it'd be a monotonically increasing bounded sequence. Not too
interesting, in general, but it's enough to show that continually playing
someone who's just terrible won't keep increasing your rating. I believe
this also shows that ratings angle players, newbie predators, and the like
shouldn't expect their ratings to go up forever. Even if the inferior
player's rating remains constant, the expected rating of the better player
will still converge, since the fibs formula replies on ratings difference
only.
> Clearly you understand this stuff far better than Murat, and I don't
> disagree especially strongly with your explanation of why it is the way
> it is. But it overstates the case to describe it as perfect.
>
> David desJardins
>
-----------== Posted via Deja News, The Discussion Network ==----------
Michael J Zehr
Murat Kalinyaprak <mu...@cyberport.net> wrote:
>> Please tell me how often you would expect a perfect player
>> to beat a player rated 2 points below her.
>
Am I understanding correctly that what you want is a measure of skill
level such that a player always beats a less skillful player, always
wins against a more skillful player, and wins with 50% probability
against a player of equal skill?
-Michael J. zehr
Michael J Zehr
Patti Beadles <pat...@netcom.com> wrote:
>For example, Perfect Player opens with 51 and plays 13/8 24/23, the
>commonly accepted best move.
>
>Total Idiot rolls 55 and plays 8/3(2) 6/1(2)*. PP now dances, TI
>rolls 64 and plays 8/2* 6/2. PP continues to dance while TI rolls
>just the right numbers to close him out and bear off safely.
>
>PP played his single move flawlessly, but TI got lucky.
I'm reminded of a quote which I'll attribute to Evan Diamond with an 80%
confidence level (15% Rick Barabino, 5% someone else at NEBC):
"A perfect player wouldn't have danced after 55."
:-)
-Michael J. Zehr
Murat Kalinyaprak
>In <73gedb$l6s$1...@news.chatlink.com> Murphy McKalin wrote:
>>>So what should its win percent be against an "almost perfect"
>>>opponent? (Feel free to define "almost perfect" however you
>>>want.) What about an "slightly less than almost perfect"
>>>opponent?)
>>100%
>No way. There will always be some luck involved.
>For example, Perfect Player opens with 51 and plays 13/8 24/23,
>the commonly accepted best move.
>Total Idiot rolls 55 and plays 8/3(2) 6/1(2)*. PP now dances, TI
>rolls 64 and plays 8/2* 6/2. PP continues to dance while TI rolls
>just the right numbers to close him out and bear off safely.
>PP played his single move flawlessly, but TI got lucky.
Ok, so would you agree that when the gap between
ratings is wide enough to be between an "almost
perfect" player and a "total idiot", what we can
measure is no longer skill but just luck...?
Previously you had defended that any miniscule
probability of winning a much underrated player
may have against a highly rated one was based on
the mistakes that the better player would make.
Given your above example, the "almost perfect"
player's chance of winning would depend rather
on the "total idiot"s somehow messing up those
rolls... :) I bet that there will be times the
moves will be forced and the "total idiot" won't
be able to mess up (even if he could)...
If the dice alone can beat an "almost perfect"
player, then a real fancy formula claiming to
measure skill would account for the probablity
of that happening (i.e. the probabilities of
winning/losing can't go above/below a certain
percentage).
Of course, there is nothing wrong with measuring
the combination of skill and luck but the problem
is that when you get to the extremes there isn't
much of a combination to speak of anymore (i.e.
it becomes a matter of pure luck).
Dice can't hurt a "total idiot" any more than an
"almost perfect" player can hurt him by his skill
but dice can hurt an "almost perfect" player much
more than a "total idiot" could hurt him with his
total lack of skill. Allowing rated matches between
"almost perfect" players and "total idiots" is one
of the problems in the FIBS rating system...
MK
Murat Kalinyaprak
>Murat Kalinyaprak wrote:
>> This is what I don't understand. How can "*perfect*"
>> (or close to it) play can only win 75% of the time...?
>You roll 5 - 2 and play 13-8 24-22. Your opponent rolls 5-5
>and points on both your blots. You roll any of the 9 numbers
>(6-6, 6-3, 3-6, 3-3, 1-1, 6-1, 1-6, 3-1, 1-3) that fail to
>bring in either of your hit men. Your opponent doubles, you drop.
>..................
>Thus, even with "perfect play" you can (and will) lose many games,
>because of the luck of the dice. Any game that has a luck factor
>will be a game in which it will always be impossible to win 100%
>of your games, even with perfect play.
Your argument is valid. I'm not going to make any
more arguments in this article because I just
responded to one from Patti B. on the same subject
and I have nothing more to add.
Please notice that I'm not arguing that there is
such a thing as perfect play/player, what percent
of the time a perfect play/player would win, etc.
There are a lot of conflicting arguments on some
issues in this newsgroup (some even coming from
the same people). I would like to see those get
sorted out. I'm trying to carry discussions in a
way that what I would like to say will somehow
come out of somebody else's mouth. Since some
people in this newsgroup appear to have developed
a mental block against anything I say, I thought
this may be a more productive approach...
MK
Patti Beadles
Murat Kalinyaprak <mu...@cyberport.net> wrote:
>Previously you had defended that any miniscule
>probability of winning a much underrated player
>may have against a highly rated one was based on
>the mistakes that the better player would make.
I don't *think* so. I realize that luck is a part of backgammon,
especially in the short term.
>Given your above example, the "almost perfect"
>player's chance of winning would depend rather
>on the "total idiot"s somehow messing up those
>rolls... :) I bet that there will be times the
>moves will be forced and the "total idiot" won't
>be able to mess up (even if he could)...
Nope. It would depend upon the total idiot making mistakes, and
on both of them rolling badly or well. If total idiot gets unlucky
and leaves a shot, there's no skill whatsoever in hitting it from the
bar.
>If the dice alone can beat an "almost perfect"
>player, then a real fancy formula claiming to
>measure skill would account for the probablity
>of that happening (i.e. the probabilities of
>winning/losing can't go above/below a certain
>percentage).
Have you looked at the FIBS formula? It calculates a probability of
winning based on the relative skill difference between the players,
and the length of the match involved. There's strong evidence that it
doesn't always do this perfectly, but in general it does a pretty
damned fine job.
-Patti
--
Patti Beadles |
pat...@netcom.com/pat...@gammon.com |
http://www.gammon.com/ | Try to relax
or just yell, "Hey, Patti!" | and enjoy the crisis
Murat Kalinyaprak
>I had been trying to avoid writing any more about FIBS ratings,
>because I don't think I have anything else to contribute. Here
>is one last post all the same. Apologies to everybody who is
>sick of this stuff :-)
Being sick of it doesn't prevent me from writing
more on the subject and without any apologies... :)
>Murphy McKalin writes:
>> Just to avoid any calculation errors I may make,
>> I just logged on to FIBS and was lucky enough to
>> spot 3 players with ratings of 1965, 1565 and
>> 1766 (close enough) all at once. The on-screen
>> calculator showed that my winning chances against
>> them were 43.49%, 54.95% and 49.18% respectively.
>> If I adjust the last one for 1765, I get 49.21%
>> while the average of first two is 49.22%...
>Unfortunately that's just a special case where the total
>probability IS roughly the average of the three parts
>(because your rating is very close to the median of a
>symmetric distribution). David is right: the probability
>against the average rating is not necessarily the same as
>the average probability against all ratings.
I must admit that I didn't know whether what I was
observing was real or due to rounding errors, etc.
Just to be safe, I had still left the two figures
as 49.21 and 49.22. A measuring stick with unequal
halves is beyond even my high (not:) expectations,
but I'll leave this for another day since it doesn't
really effect the essence of my argument which could
be made based on average or individual ratings.
> - my average probability of winning against the 1565 and
> 1965 players is 13.1%, but against the 1765 player is
> only 11.2%. They are NOT the same.
This is quite more drastic than the differences I
was observing based on 1 point matches. Thus far,
I had stuck to using 1 point matches as examples
just to keep out the square root baloney applied to
multi-point matches. If the percentage differences
mentioned above don't go beyond fractions with 1
point matches, then I could perhaps still use them
as equal/close enough for the sake of keeping the
arguments simple. I'll test some more sample cases
to see if the difference with 1 point matches reach
magnitudes of several percents, in which case I'll
have to reword my argument by making a highly rated
player play against each individual rating instead
of many times the same average rating (the point
made will still be the same).
>> If I have to accept this as true, then I would have
>> to argue that there is no such thing as "perfect"
>> or even anything close to it in bg. 75% is just too
>> far from it...
>There is such a thing as perfect -- perfection is never
>making any mistakes. (A precise definition of a perfect
>strategy is one that maximises your "security level" -- ie.
>a maximin strategy, one that maximises your minimum expected
>gain across all possible opponents.
If you want to shift the context to some sort of
perfection that is not directly visible in results,
that's fine. But still some questions may be asked.
What defines a move as a mistake? 50-ply roll-outs?
Statistics from N-billion games? What differentiates
errors from moves that may succesfully recycle a game
to a "new-beginnning" so to speak, for example...?
>Perhaps one issue that is causing confusion is that the idea
>of perfection in backgammon is somewhat abstract. (This is
>because we haven't reached perfection, and we don't always
>know what a mistake is.)
I agree. Do we even have any ideas about whether
"perfection" in bg is eventually possible?
>> Given this, the FIBS forfula can't be claimed to
>> rate "skill" either...
>Yes, it can. Skill is the ability to play without making
>mistakes. The more mistakes you make, the less matches you
>expect to win. If both players play without making any
>mistakes, then they each expect to win 50% of the matches.
>If only one player makes mistakes, then he expects to win
>less than 50%. The more (and costlier) mistakes he makes,
>the fewer matches he expects to win. You can view FIBS
>ratings as measuring skill, or the ability to play without
>making mistakes, or the rate of matches won -- they are all
>equivalent.
What you say would be true between "equal" players
but not between unequal players. Many arguments
made in these topics suffer from the same problem.
If N% of games are lost/won due to luck, this will
gradually overshadow the skill as probability of
winning decreases towards it and/or go below it...
>> So...? Their ratings will go up in ever smaller
>> increments (i.e. slower) but what would prevent
>> them from going much higher? Imagine a Martian
>> with a potential rating of 3000 lands on earth
>> and joins FIBS. Are you guys saying that even
>> after 20000, 50000, 100000 matches he will never
>> get past achieveing a rating of 2000-2100...?
>For one thing, it is impossible to have a potential rating of
>3000 (without cheating). My guess is that the best humans and
>computers in the world today make mistakes which would cost
>them at most an expected 0.4 points per game for money against
>a perfect player (that's including chequer play and cube decisions).
>This is only worth about 200 FIBS rating points. If we assume
>that the best current players could consistently maintain a rating
>of 2100 without cheating (which is very generous), then even a
>perfect player would have difficulty remaining above 2300. In
>truth it's very likely to be lower. The other players on FIBS
>simply do not make enough mistakes for anybody to be consistently
>rated higher than that, no matter how good they are.
When a potentially 2100 rated player joins FIBS,
he gets assigned a 1500 rating. Obviously FIBS'
assessment of this player is wrong until he
reaches his so-called "true rating" which would
be 2100 in this example, and that's how he gets
from 1500 to 2100 (i.e. by winning more often
than predicted and at the same time being overly
compensated for his "true rating"). If a player
with 2100 potential doesn't stop at 2000, why a
potentially 2500 or 3000 player would stop any
time before reaching their "true rating"...?
Another way of putting this may be as follows:
Eliminate all 1500+ rated players from FIBS.
Have a human/robot with a known/guessed rating
of 2100 (like SW) start as a new player at 1500.
What rating would that player eventually reach?
Actually, I'm not sure how this topic strayed in
this direction thus far. Initially I had argued
that even a small inaccuracy (this is the keyword)
in FIBS' precdicting winning chances would become
more visible potentially/expectedly in at least a
few players breaking away from the pack...
MK
Murat Kalinyaprak
>In <365DFE...@cyberport.net> Murat Kalinyaprak wrote:
>>> Please tell me how often you would expect a perfect player
>>> to beat a player rated 2 points below her.
>>100% of the time. If that's not what we are observing,
>>then we must be "measuring" something different than
>>just skill...
>Am I understanding correctly that what you want is a measure
>of skill level such that a player always beats a less skillful
>player, always wins against a more skillful player, and wins
>with 50% probability against a player of equal skill?
What I'm trying to get at is this: when talking about
equal players, what percentage of games are won/lost
due to luck doesn't matter because supposedly in the
long run both players will get equal luck and benefit
or suffer from it equally. But between unequal players
this is not so. A 2100 rated player doesn't need luck
to even equal out in the long run against a 1200 rated
player. I don't know what the actual number may be but
after the gap between the two players gets to a certain
amount, the lower rated player will no longer be able
win against the higher rated player with equal luck
anymore. If he wins at all it will be due to luck alone.
Some people already gave examples on how a "perfect"
player can still lose a game just beacuse of the dice.
The big question is: what percent of the time a perfect
player will lose to dice?
When I was experimenting against JF (before I played
those 100 + another 100 games) I was trying to break a
real or imaginary pattern in its dice by making some
"trick" (unexpected/against the pattern) moves. While
doing that, I had actually gone as far as playing
against it by making totally random moves, just to see
how much worse could anyone lose with supposedly zero
skill. I hadn't even come close to reaching any kind
of conclusion on that but it was fun/interesting doing
(I suggest you guys try it some day:)...
The point is that in order to lose at a rate below a
centain percentage, one may have to actually work to
lose. It would be completely idiotic to let two people
play for rating points, if there is a big enough gap
between their ratings that one's winning chances is
below (or even close to) that minimum percentage. I'm
questioning whether this is happening on FIBS...
MK
Murat Kalinyaprak
> On 27-nov-98 00:31:07, Murat Kalinyaprak wrote:
> MK> .....
> Then you are simply very ignorant but fail to recognize it.
> MK> .....
> You don't understand what you're talking about (again). limiller is
> absolutely right (no question at all) that the two statements are not
> equivalent. If you don't understand, do some study of your own instead
> of making all sorts of false claims and assumptions.
> MK> .....
> This is just plain nonsense and shows you don't understand at all what
> you're talking about (again). Do some self study, ask some questions if
> you wish but please stop making statements about things you don't
> understand, I think it's tiresome.
> MK> .....
> Just get a clue first maybe?
> MK> .....
> If you are so convinced of your own observations and conclusions, you'll
> probably never understand the formula. Just do some experimenting with a
> calculator or read some text about rating systems, then come back and we
> can have a sensible discussion instead of repeatedly tell you that
> you're wrong.
> MK> .....
>
> You're wrong.
> [more nonsense snipped]
> MK> .....
> It is a relative measure. Any absolute measure of bg skill is impossible
> (as of today and the near future at least) because we don't know what
> perfect play in all possible situations is.
I erased all except what you wrote so you can clearly
see what little came out of your mouth(?)... I think
the sound of horses farting in my pature would have
more content...
MK
Robert-Jan Veldhuizen
MK> What I'm trying to get at is this: when talking about
MK> equal players, what percentage of games are won/lost
MK> due to luck doesn't matter because supposedly in the
MK> long run both players will get equal luck and benefit
MK> or suffer from it equally.
Rather obvious, because this is why we say they have equal skill.
MK> But between unequal players
MK> this is not so. A 2100 rated player doesn't need luck
MK> to even equal out in the long run against a 1200 rated
MK> player. I don't know what the actual number may be but
MK> after the gap between the two players gets to a certain
MK> amount, the lower rated player will no longer be able
MK> win against the higher rated player with equal luck
MK> anymore.
You are again confusing all sorts of things here. There's no such thing
as "a certain amount" needed. It's all just very simple: with equal luck
against an equal opponent you will win 50% in the long run; if you are
better than your opponent this figure will rise, in practice to about
80% for a 1ptr between an expert and a pretty bad player.
You can also look at it "the other way": a better rated player can still
win 50% of his matches with less luck than his opponents.
MK> If he wins at all it will be due to luck alone.
No, it's always a combination in practice. Only if someone makes
completely random moves the luck factor gets to 100%.
MK> Some people already gave examples on how a "perfect"
MK> player can still lose a game just beacuse of the dice.
MK> The big question is: what percent of the time a perfect
MK> player will lose to dice?
That of course all depends on his opponent. Against nowadays experts, a
perfect player will very probably win less than 60% of games, personally
I think it would be around 55% but that's just a guess; we don't know
how close experts are to perfect play.
[snip]
MK> The point is that in order to lose at a rate below a
MK> centain percentage, one may have to actually work to
MK> lose.
Not sure what you mean here. If you're saying that it is difficult to
lose 90% of your games against JellyFish, you are right. That's just
because luck is an important factor in bg. You will always win some
games, even against a perfect player, if your moves are completely
random due to this.
MK> It would be completely idiotic to let two people
MK> play for rating points, if there is a big enough gap
MK> between their ratings that one's winning chances is
MK> below (or even close to) that minimum percentage.
No, there is no "minimum percentage". So your statements are false.
MK> I'm
MK> questioning whether this is happening on FIBS...
You really should try to get a better understanding of the nature of bg
and what "perfect play" means to judge about things like this.
--
Zorba/Robert-Jan
Robert-Jan Veldhuizen
[snip]
MK> Dice can't hurt a "total idiot" any more than an
MK> "almost perfect" player can hurt him by his skill
MK> but dice can hurt an "almost perfect" player much
MK> more than a "total idiot" could hurt him with his
MK> total lack of skill.
Not true. If you are more skilled than your opponent it means you will
win more games against him, *independent* of the dice.
This is pretty obvious I would think. One of the things that makes
someone a good player is to also win games when the dice are against
you.
MK> Allowing rated matches between
MK> "almost perfect" players and "total idiots" is one
MK> of the problems in the FIBS rating system...
Maybe, but not because of the arguments you give.
--
Zorba/Robert-Jan
Robert-Jan Veldhuizen
MK> In <wt7lwj7...@brigantine.CS.Arizona.EDU> Gary Wong wrote:
>>Murphy McKalin writes:
>>> Just to avoid any calculation errors I may make,
>>> I just logged on to FIBS and was lucky enough to
>>> spot 3 players with ratings of 1965, 1565 and
>>> 1766 (close enough) all at once. The on-screen
>>> calculator showed that my winning chances against
>>> them were 43.49%, 54.95% and 49.18% respectively.
>>> If I adjust the last one for 1765, I get 49.21%
>>> while the average of first two is 49.22%...
>>Unfortunately that's just a special case where the total
>>probability IS roughly the average of the three parts
>>(because your rating is very close to the median of a
>>symmetric distribution). David is right: the probability
>>against the average rating is not necessarily the same as
>>the average probability against all ratings.
MK> I must admit that I didn't know whether what I was
MK> observing was real or due to rounding errors, etc.
It was due to you picking a special case. Read again what Gary writes,
because you don't seem to understand the point he made. Better reading
in general would be good advice.
[snip]
>>Yes, it can. Skill is the ability to play without making
>>mistakes. The more mistakes you make, the less matches you
>>expect to win. If both players play without making any
>>mistakes, then they each expect to win 50% of the matches.
>>If only one player makes mistakes, then he expects to win
>>less than 50%. The more (and costlier) mistakes he makes,
>>the fewer matches he expects to win. You can view FIBS
>>ratings as measuring skill, or the ability to play without
>>making mistakes, or the rate of matches won -- they are all
>>equivalent.
MK> What you say would be true between "equal" players
MK> but not between unequal players.
*sigh* Why not use your brains more and your keyboard less?
MK> Many arguments
MK> made in these topics suffer from the same problem.
No, you suffer from lack of knowledge and understanding. Other people in
this thread know what they're talking about, you obviously don't. So you
can stop making your false claims now.
MK> If N% of games are lost/won due to luck, this will
MK> gradually overshadow the skill as probability of
MK> winning decreases towards it and/or go below it...
No. Study the subject some more.
MK> When a potentially 2100 rated player joins FIBS,
MK> he gets assigned a 1500 rating. Obviously FIBS'
MK> assessment of this player is wrong until he
MK> reaches his so-called "true rating" which would
MK> be 2100 in this example, and that's how he gets
MK> from 1500 to 2100 (i.e. by winning more often
MK> than predicted and at the same time being overly
MK> compensated for his "true rating"). If a player
MK> with 2100 potential doesn't stop at 2000, why a
MK> potentially 2500 or 3000 player would stop any
MK> time before reaching their "true rating"...?
They wouldn't. If you had actually read what Gary wrote, you would have
understood that he thinks there *are* no potentially 2500-3000 rated
players.
MK> Another way of putting this may be as follows:
MK> Eliminate all 1500+ rated players from FIBS.
MK> Have a human/robot with a known/guessed rating
MK> of 2100 (like SW) start as a new player at 1500.
MK> What rating would that player eventually reach?
That's an interesting question. It should probably be roughly the same,
i.e. 2100. In practice it might as well be lower (SW is *relatively*
better at beating strong opponents) or higher (SW is *relatively* better
at beating weak opponents).
MK> Actually, I'm not sure how this topic strayed in
MK> this direction thus far. Initially I had argued
MK> that even a small inaccuracy (this is the keyword)
MK> in FIBS' precdicting winning chances would become
MK> more visible potentially/expectedly in at least a
MK> few players breaking away from the pack...
Which is nonsense, something which you would have known by now if you
had done some study of the FIBS rating system.
The only thing that would make players stray away from the pack is
a very long lucky streak (statistically unlikely), but eventually that
will end too and by then, the highly overrated player will lose rating
points quickly after that. That's how the rating system is designed: to
maintain a higher rating, you have to win more.
--
Zorba/Robert-Jan
Robert-Jan Veldhuizen
MK> Robert-Jan Veldhuizen wrote:
MK>
>> MK> .....
>> MK> .....
>> MK> .....
>> MK> .....
MK> I erased all except what you wrote so you can clearly
MK> see what little came out of your mouth(?)...
Well, I was commenting on you, so maybe I had no choice. Is it so hard
to understand "You are wrong" when you are wrong? I guess it *is* for
you.............. Anyway, my statements above have more truth in them
than your statements on the ratings system, that's for sure.
MK> I think
MK> the sound of horses farting in my pature would have
MK> more content...
Really interesting. Nevertheless, my advice still stands strongly: get a
clue first what you're talking about before making any strong
(and mostly pretty ridiculous and plain false) statements.
--
Zorba/Robert-Jan
Michael J Zehr
Murat Kalinyaprak <mu...@cyberport.net> wrote:
>Actually, I'm not sure how this topic strayed in
>this direction thus far. Initially I had argued
>that even a small inaccuracy (this is the keyword)
>in FIBS' precdicting winning chances would become
>more visible potentially/expectedly in at least a
>few players breaking away from the pack...
So let's go back to that original question. The rating system is
designed so that one's rating will head for the point where one's actual
and predicted winning results match. If the FIBS rating predicts a
winning rate of 75% against players ranked 1500, and someone is actually
winning 78% against players ranked 1500, then the rating will move to a
number that predicts a winning rate of 78%. Once it reaches that
rating, there's no reason to assume that the person will suddenly start
winning 80% of the time against the same set of players.
Think of the FIBS rating as a distillation of all match results. If
someone is playing better or worse than they have in the past (or if
they haven't yet reached equilibrium), then their rating will change
until the actual and predicted results match. Note that actual
vs. predicted includes a reflection of who they play and the match
length. It is known (do an archive search on r.g.b) that one will have
a higher rating by playing only 1point matches than by playing longer
matches. So if someone has a rating of 1800 playing 7point matches and
then starts playing 1point matches only, the predited winning rate will
be lower than their actual winning rate. Their rating will slowly
changes, say to 1900, until predicted and actual are back in
equilibrium. If they then start playing 7point matches again, the
equilibrium will be lost until the rating lowers.
What about the possibility of someone getting a rating of 3000+? To
maintain such a rating they would need to win 95% of 7point matches
against players rated 2000, or win 95% of 3point matches against players
rated 1500. No one has been able to do that, or even come close to
doing that. It doesn't matter if their current rating predicts that
they will win 65% of the time in 7pt matches against players rated 2000
and they actually win 66% of the time. Since their actual win rate is
66%, they won't reach a rating of 3000. (If they keep playing 7pt
matches against opponents rated 2000 and win 66% of the time, their
equilibrium rating is 2218.)
What about if they win 75% of 7pt matches against 1500 players, and
50% of the time in 5pt matches against 2000 rated players? Turns out
there isn't a single equilibrium rating for this player -- they seem to
have a rating of 2000 against 2000 players and 1861 against 1500
players. Their actual rating will flucuate according to the frequency
of playing 1500 or 2000-rated players. When they play 2000-rated
players, their rating will move towards 2000. When they play 1500-rated
players, their rating will move towards 1861. Again, there's no
"breaking away from the pack" involved. The rating changes until the
actual and predicted values match, based on the lengths of the matches
and opponents being played. Unless you believe the same person will
play better or worse depending on their current FIBS rating, then there
will be an equilibrium rating, and their actual FIBS rating will head
towards it.
The FIBS rating _is_ a measure of actual match results, and hence can't
be out of synch with actual match results. It isn't based on "skill" in
the sense that we can't observe skill. We observe match results.
-Michael J. Zehr
David desJardins
> It's also the case that for a ratings difference of 4000 pts, fibs
> expects the better player to win 10/11% of 1 pt matches. I'd imagine
> everyone could agree that no player can win 99% of the time against an
> opponent who's trying (maybe even against an opponent who's not
> trying, too :-) ), so that expert will lose points on average. That's
> enough to show that no player's rating can increase without bound
> (which was what I was posting about originally).
It's easy to win 100% of the time against an opponent who's not trying
to win. (I double, you drop; I double, you drop; I double, you drop.
Or you just resign, resign, resign.) I believe that the FIBS rating
system does have the property that if I play an infinite sequence of
matches against 1500 players whom I always beat, then my rating will
not converge to a limit, but will grow without bound. So it's
theoretically possible to manipulate the system to achieve arbitrarily
high ratings. It takes more and more work, though.
> What I was really wanted to do is point out that there's a "true
> ratings difference" between 2 players (without considering skill
> improvement, of course). If the 2 players play each other in fixed
> length matchs ad infinitum, their average (expected) ratings after the
> ith game will converge, since it'd be a monotonically increasing
> bounded sequence.
Of course, the expected rating converges, but you can't actually measure
that, so it's not very interesting. Because the system counts new games
more than old games, the computed ratings difference (what you see) will
fluctuate randomly around the "true" value. It won't ever converge to a
limit (i.e., it will infinitely often be the case that the ratings
difference between the two players will be more than X points away from
the "true" difference, for some positive value of X; perhaps even for
all X?).
David desJardins
Murat Kalinyaprak
>On 02-dec-98 10:58:25, Murat Kalinyaprak wrote:
>> The point is that in order to lose at a rate below a
>> centain percentage, one may have to actually work to
>> lose.
>Not sure what you mean here. If you're saying that it is
>difficult to lose 90% of your games against JellyFish, you
>are right. That's just because luck is an important factor
>in bg. You will always win some games, even against a
>perfect player, if your moves are completely random due to this.
>> It would be completely idiotic to let two people
>> play for rating points, if there is a big enough gap
>> between their ratings that one's winning chances is
>> below (or even close to) that minimum percentage.
>No, there is no "minimum percentage". So your statements are
>false.
Another one who can't write two consecutive
paragraphs without contradicting himself...?
Read back what you wrote. Your first paragraph
amounts to saying that one can win 10% against
JF because of luck alone even one makes random
moves. That means nobody can win less than 10%
against JF (per your comments). This is that
"minimum percentage" I'm talking about. If one
plays against JF on FIBS and FIBS gives him less
than 10% chance of winning then FIBS would be
wrong, wouldn't it? Maybe you can't understand
me because of deficiencies in my expressing but
shouldn't you at least understand yourself...?
>> I'm questioning whether this is happening on FIBS...
>You really should try to get a better understanding of the
>nature of bg and what "perfect play" means to judge about
>things like this.
As you missed the main point, all other related
arguments you made were basicly off-mark/useless
and I skipped them. Maybe you should consider
taking your own advice here. If you are a good
examples of somebody who "understands" the FIBS
formula, etc. maybe I should consider myself
fortunate that I don't understand them...
MK
Murat Kalinyaprak
>In <742mvq$9kv$2...@news.chatlink.com> Murat Kalinyaprak wrote:
>>Previously you had defended that any miniscule
>>probability of winning a much underrated player
>>may have against a highly rated one was based on
>>the mistakes that the better player would make.
>I don't *think* so. I realize that luck is a part of backgammon,
>especially in the short term.
Ok, maybe it was somebody else. There are quite a
few people here who approach things from the point
of view of mistakes better players are supposedly
expected to make. Perhaps it was one of them...
>>Given your above example, the "almost perfect"
>>player's chance of winning would depend rather
>>on the "total idiot"s somehow messing up those
>>rolls... :) I bet that there will be times the
>>moves will be forced and the "total idiot" won't
>>be able to mess up (even if he could)...
>Nope. It would depend upon the total idiot making mistakes,
>and on both of them rolling badly or well. If total idiot gets
>unlucky and leaves a shot, there's no skill whatsoever in
>hitting it from the bar.
What I mean though, is that everything a "total
idiot" makes is a mistake to begin with... But,
it's very possible that the dice rolls will fall
in place so well and the moves will be forced so
that one can't lose even by trying to lose...
I think I remember seeing at a web site some bg
puzzles. Perhaps this can be added there (i.e.
find a sequence of dice rolls so that the player
who rolls them can't lose no matter how much he
tries to lose).
>>If the dice alone can beat an "almost perfect"
>>player, then a real fancy formula claiming to
>>measure skill would account for the probablity
>>of that happening (i.e. the probabilities of
>>winning/losing can't go above/below a certain
>>percentage).
>Have you looked at the FIBS formula? It calculates a probability
>of winning based on the relative skill difference between the
>players, and the length of the match involved. There's strong
>evidence that it doesn't always do this perfectly, but in general
>it does a pretty damned fine job.
I looked at the formula. I think you are missing
the point here. If a "total idiot" (i.e. *zero*
skill) can beat an "almost perfect" player N% of
the time due to complete luck, then no player's
winning chances can be said to be less than that
N%. I don't know what the value of "N" would be,
but based on the arguments made so far it must
have a certain value which would apparently be high
enough to be deemed "considerable". Maybe some of
our resident scientists here can tackle the task
of figuring out what that value may be...
In the meantime, just to clarify my argument, if
we use 5% as a sample value for "N", then nobody
should have less than 5% chance of winning, unless
there exists a level of "idiocy" below "total"...
I hope this will help you understand what I mean.
MK
Michael J Zehr
Let's suppose Kit Woolsey has a rating of 1950. (We could use any scale
we want, but we'll set the scale to KW=1950.)
We also know that Mary just beat Richard in a 5-point match. Joe has won
3 of 5 7-point matches against Alice but has lost 3 of 4 3-point matches
against John. (And by the way, John and Mary have played 2 1-point
matches, each of them winning once.)
What are each player's chances against Kit in a 9-point match?
-Michael J. Zehr
David desJardins
Mary 18.243%
John 18.243%
Richard 14.138%
Joe 13.637%
Alice 11.890%
David desJardins
Robert-Jan Veldhuizen
MK> In <2850.7640...@xs4all.nl> Robert-Jan Veldhuizen wrote:
>>On 02-dec-98 10:58:25, Murat Kalinyaprak wrote:
>>> The point is that in order to lose at a rate below a
>>> centain percentage, one may have to actually work to
>>> lose.
>>Not sure what you mean here. If you're saying that it is
>>difficult to lose 90% of your games against JellyFish, you
>>are right. That's just because luck is an important factor
>>in bg. You will always win some games, even against a
>>perfect player, if your moves are completely random due to this.
>>> It would be completely idiotic to let two people
>>> play for rating points, if there is a big enough gap
>>> between their ratings that one's winning chances is
>>> below (or even close to) that minimum percentage.
>>No, there is no "minimum percentage". So your statements are
>>false.
MK> Another one who can't write two consecutive
MK> paragraphs without contradicting himself...?
Just as you see conspiracies everywhere, you now start seeing
contradictions all over the place too? :-)
MK> Read back what you wrote. Your first paragraph
MK> amounts to saying that one can win 10% against
MK> JF because of luck alone even one makes random
MK> moves.
MK> That means nobody can win less than 10%
MK> against JF (per your comments).
Almost right so far. It's an estimate of course.
You forget however that random moves are not *worst* moves. We could
make a JF-like bot that searches for the *worst* moves (anyone...?). I
think in that case the real JF can win 99,9% against this
"worst-moves-ever" bot.
MK> This is that
MK> "minimum percentage" I'm talking about.
And which doesn't exist the way you describe it (modest as ever):
"completely idiotic" etc. As far as the rating system goes, there's
nothing idiotic about this, someone coould actually play worse than
random.
So, what's your point?
MK> If one
MK> plays against JF on FIBS and FIBS gives him less
MK> than 10% chance of winning
FIBS gives? What do you mean? FIBS only "gives" dice. Or do you mean the
rating difference *expects* (words are important) someone to win less
than 10%? You need a huge rating difference then. Have you studied the
formula FIBS uses? (Normally I wouldn't ask, but in your case...)
MK> then FIBS would be
MK> wrong, wouldn't it?
No. You are the one that's wrong for the umpteenth time.
MK> Maybe you can't understand
MK> me because of deficiencies in my expressing but
MK> shouldn't you at least understand yourself...?
I understand both myself and the rating system to a reasonable amount.
The only thing I understand about you is that you are discussing
things you clearly don't understand. In fact you remind me of
politicians, but that's another story.
>>> I'm questioning whether this is happening on FIBS...
>>You really should try to get a better understanding of the
>>nature of bg and what "perfect play" means to judge about
>>things like this.
MK> As you missed the main point, all other related
MK> arguments you made were basicly off-mark/useless
MK> and I skipped them.
I think -- or know by now -- you are just not up to a high-level
discussion.
MK> Maybe you should consider
MK> taking your own advice here. If you are a good
MK> examples of somebody who "understands" the FIBS
MK> formula, etc. maybe I should consider myself
MK> fortunate that I don't understand them...
Whatever justifies your own laziness.
--
Zorba/Robert-Jan
Robert-Jan Veldhuizen
MK> I looked at the formula. I think you are missing
MK> the point here.
I don't think *Patti* misses the point.
MK> If a "total idiot" (i.e. *zero*
MK> skill) can beat an "almost perfect" player N% of
MK> the time due to complete luck, then no player's
MK> winning chances can be said to be less than that
MK> N%. I don't know what the value of "N" would be,
MK> but based on the arguments made so far it must
MK> have a certain value which would apparently be high
MK> enough to be deemed "considerable".
I think the value is far less than 1%. That's not with *random* moves,
but with *worst* moves, mind you. There is a pretty big difference
between those two I think.
MK> Maybe some of
MK> our resident scientists here can tackle the task
MK> of figuring out what that value may be...
MK> In the meantime, just to clarify my argument, if
MK> we use 5% as a sample value for "N", then nobody
MK> should have less than 5% chance of winning, unless
MK> there exists a level of "idiocy" below "total"...
MK> I hope this will help you understand what I mean.
I think you mean the rating system shouldn't *expect* anyone to have a
winning chance against f.i. JF lower than 5%, or 0,1% which seems more
appropriate to me. Well, as this is the case, what's your problem?
--
Zorba/Robert-Jan
Vince Mounts
>I think you mean the rating system shouldn't *expect* anyone to have a
>winning chance against f.i. JF lower than 5%, or 0,1% which seems more
>appropriate to me. Well, as this is the case, what's your problem?
>
>--
>Zorba/Robert-Jan
There used to be a FIBS bot that might meet the total idiot requirement. I
cant remember its name though (robot?). Does anyone remember? I'd say it
would have to be extremely lucky to beat Jellyfish. .1% might be pushing it
(lol)
Me Again
> whois Program_bg
Information about Program_bg:
Last login: Tuesday, August 04 00:04 GMT from falcon.inetnebr.com
Last logout: Tuesday, August 04 00:15 GMT
Not logged in right now.
Rating: 566.23 Experience: 282
No email address.
Me Again
I don't think you can calculate this without making some HUGE
assumptions. I am going to guess that David assumed that the above
match results were each person's first ever games on FIBS. That's a big
assumption to make.
What if Mary is FME rated at 1901.32, and John is jkisssane rated at
1903.19, and Richard is heinrich rated at 1911.42, and Joe is Slotter
rated at 1905.69, and Alice is DeMented rated at 1907.72? OK, enough of
that, what if they aren't?
Assume that they are new to FIBS and have just had their ratings change
from the default 1500 by playing and winning or losing the above
matches. Their resulting ratings say NOTHING about their ultimate skill
level. I lost a fair number of my first matches because I played
players above my skill level and my rating dropped to ~1450 before I
found the right skill level players to play against and be neither bored
with their stupid moves (players far below me) nor blown away by their
brilliance (players far above me). Ultimately I ended up at
~1650-1700. The early results of my first matches created "a rating"
but that rating wasn't of any use in predicting the results of my match
play the next time I played someone.
jc
Robert-Jan Veldhuizen
Dd> Michael J Zehr <ta...@mit.edu> writes:
>> Let's suppose Kit Woolsey has a rating of 1950. (We could use any scale we
>> want, but we'll set the scale to KW=1950.)
>>
>> We also know that Mary just beat Richard in a 5-point match. Joe has won
>> 3 of 5 7-point matches against Alice but has lost 3 of 4 3-point matches
>> against John. (And by the way, John and Mary have played 2 1-point
>> matches, each of them winning once.)
>>
>> What are each player's chances against Kit in a 9-point match?
Dd> Mary 18.243%
Dd> John 18.243%
Dd> Richard 14.138%
Dd> Joe 13.637%
Dd> Alice 11.890%
LOL. You're probably a mathematician?
The only really good answer we don't know at all. Even with a result
from one of those five against KW we wouldn't really know much, but
without it we just know nothing (we're from Barcelona, so to speak).
--
Zorba/Robert-Jan
Julian Hayward
<vmo...@mindspring.com> writes
>
>There used to be a FIBS bot that might meet the total idiot requirement. I
>cant remember its name though (robot?). Does anyone remember? I'd say it
>would have to be extremely lucky to beat Jellyfish. .1% might be pushing it
>(lol)
>
-600. It moved truly worse than random - yet the jammy b*stard beat me
by chucking a few doubles in a running game. I never saw it beat anyone
else... with that sort of luck heaven knows how I manage to keep above
1730 8-( 8-( 8-(
---------------------------------------------------------------------------
Julian Hayward 'Booles' on FIBS jul...@ratbag.demon.co.uk
+44-1344-640656 http://www.ratbag.demon.co.uk/
---------------------------------------------------------------------------
"Any man can be 62, but it takes a bus to be 62A"
- Spike Milligan
---------------------------------------------------------------------------
Murat Kalinyaprak
>In <vohg1b4...@pizza.berkeley.edu> David desJardins wrote:
>> The formulas used by FIBS (and all other Elo-style rating
>> systems) are simply ad hoc choices with no particular
>> statistical justification except that they work reasonably well.
> You're correct. For some reason, I was thinking that the
> ratings formula was derived from some probability distribution,
> but that's not true.
From the formula itself, one can already see/conclude
that it's arbitrary but I had nevertheless kept asking
hoping to hear a validating answer from the creator(s)
of the formula (which is probably unlikely to happen).
So, I guess we can just take our own words for it...
>>> It's constructed so that if 2 people at their "true rating"
>>> play each other, the average number of fibs rating points each
>>> will win is zero.
>> There's no reason to believe that this is true, and lots of
>> reasons to believe that it's not true in general. It would
>> be quite a miracle if somehow the probability of winning a
>> match exactly followed the FIBS formula for all pairs of
>> players and all match lengths.
This is one of the points I had kept repeating and I
am glad to see David agree with me on this... :) The
fact that two players of equal strength will break
even over time has no value in constructing a rating
systems like FIBS'.
> ... Not too interesting, in general, but it's enough to show
> that continually playing someone who's just terrible won't
> keep increasing your rating. I believe this also shows that
> ratings angle players, newbie predators, and the like shouldn't
> expect their ratings to go up forever. Even if the inferior
> player's rating remains constant, the expected rating of the
> better player will still converge, since the fibs formula
> replies on ratings difference only.
However, nobody has to play against the "same" lower
rated player forever. It's very likely that a number
of players on FIBS may be abandoning their accounts
after dipping below 1500 and starting over with 1500
under new names. Thus, there may be (most likely is)
a constant supply of players overrated at 1500 to be
preyed on. Yes, even with this a player will reach a
high enough rating which eventually stop earning (or
earn very minute amounts of) points for him but that
rating would be well over 2000-2100's in my estimate
and (curiously enough) we are not seeing such higher
ratings on FIBS. It had been argued that some of the
highest rated players on FIBS may be as much as 400
overrated. That means a 1700 rated player can reach
2100 by being overrated by 400 points. Why couldn't
a 1900 player reach 2300 or 2100 rated player reach
2500 by being overrated by the same amount...? This
alone should be enough to keep a "reasonable" person
from arguing FIBS' system works "reasonably" well...
>> Clearly you understand this stuff far better than Murat, and
>> I don't disagree especially strongly with your explanation
>> of why it is the way it is. But it overstates the case to
>> describe it as perfect.
Anyone who thinks that *understanding* FIBS formula
will lead a person to believe it "works" (resonably
or unreasonably well...:) may have a bigger problem
than the ones who admit to not understand the basis
for that pretentious baloney. I see that even David
feels a need to take back with the other hand what
he had to give me with one hand on this subject. :)
MK
Patti Beadles
Murat Kalinyaprak <mu...@cyberport.net> wrote:
>I had nevertheless kept asking
>hoping to hear a validating answer from the creator(s)
>of the formula (which is probably unlikely to happen).
It's entirely likely that the reason you aren't getting an answer from
them is that the creators of the formula aren't readers of
rec.games.backgammon.
>It had been argued that some of the
>highest rated players on FIBS may be as much as 400
>overrated. That means a 1700 rated player can reach
>2100 by being overrated by 400 points. Why couldn't
>a 1900 player reach 2300 or 2100 rated player reach
>2500 by being overrated by the same amount...?
Because while there may be a continuous supply of massively overrated
1500 players on FIBS, the supply of similarly overrated 1900-level
players is much smaller. And one doesn't get an inflated 1900-rating
just by stumbling into a new account... you have to work at
manipulating the system in order to achieve it. People who do this
aren't likely to suddenly play like the idiots they are and give away
ratings points willy-nilly.
-Patti
--
Patti Beadles | Not just your average purple-haired
pat...@netcom.com/pat...@gammon.com | degenerate gambling adrenaline
http://www.gammon.com/ | junkie software geek leatherbyke
or just yell, "Hey, Patti!" | nethead biker.
Steve Mellen
Kalinyaprak) wrote:
>
> A "total idiot" can't make any worse than random
> moves because in order to do that he would have
> to know what bad/worse moves are and in order to
> know that he would have to know what good/better
> moves are. Take a logic class if you get a chance,
> it may do you good...
>
You suggest that the only way for a player to be worse than a completely
random player is to know which moves are good and bad, yet consciously
choose to make the bad moves. I disagree. For example, a player might
follow the strategy of making the ace point as soon as possible and
stacking more checkers on it whenever possible. Or a player might choose
to play each roll so as to leave as many blots as possible. I suspect
both of these strategies would lose in the long term to a strategy which
merely made random plays at every opportunity.
I also would like to point out, in my most Chuck Boweresque way, that it
really decreases the general level of civility on this newsgroup when
every point must be followed by a cheap shot at the intelligence/reasoning
ability of the original poster. 'nuff said :)
Steve Mellen (fnurt on FIBS)
Murat Kalinyaprak
>On 04-dec-98 09:27:02, Murat Kalinyaprak wrote:
> MK> I looked at the formula. I think you are missing
> MK> the point here.
>I don't think *Patti* misses the point.
Maybe you should think other things and let her
respond for herself...
> MK> If a "total idiot" (i.e. *zero*
> MK> skill) can beat an "almost perfect" player N% of
> MK> the time due to complete luck, then no player's
> MK> winning chances can be said to be less than that
> MK> N%. I don't know what the value of "N" would be,
> MK> but based on the arguments made so far it must
> MK> have a certain value which would apparently be high
> MK> enough to be deemed "considerable".
>I think the value is far less than 1%. That's not with
>*random* moves, but with *worst* moves, mind you. There
>is a pretty big difference between those two I think.
A "total idiot" can't make any worse than random
moves because in order to do that he would have
to know what bad/worse moves are and in order to
know that he would have to know what good/better
moves are. Take a logic class if you get a chance,
it may do you good...
> MK> Maybe some of
> MK> our resident scientists here can tackle the task
> MK> of figuring out what that value may be...
> MK> In the meantime, just to clarify my argument, if
> MK> we use 5% as a sample value for "N", then nobody
> MK> should have less than 5% chance of winning, unless
> MK> there exists a level of "idiocy" below "total"...
> MK> I hope this will help you understand what I mean.
>I think you mean the rating system shouldn't *expect*
>anyone to have a winning chance against f.i. JF lower
>than 5%, or 0,1% which seems more appropriate to me.
>Well, as this is the case, what's your problem?
I don't have a problem. I'm questioning what that
minimum chance may be and whether FIBS predicts
anybody having less chance than that. If you can't
provide any useful information or factual answers,
why do you bother with blabbering...?
MK
Murat Kalinyaprak
>Michael J Zehr <ta...@mit.edu> writes:
>> What are each player's chances against Kit in a 9-point match?
>Mary 18.243%
>John 18.243%
>Richard 14.138%
>Joe 13.637%
>Alice 11.890%
And to a degree of accuracy no less than 3 decimal
digits... :) You guys are funny...
MK
Murat Kalinyaprak
>On 04-dec-98 08:03:49, Murat Kalinyaprak wrote:
>>>Not sure what you mean here. If you're saying that it is
>>>difficult to lose 90% of your games against JellyFish, you
>>>are right. That's just because luck is an important factor
>>>in bg. You will always win some games, even against a
>>>perfect player, if your moves are completely random due to this.
>>>> It would be completely idiotic to let two people
>>>> play for rating points, if there is a big enough gap
>>>> between their ratings that one's winning chances is
>>>> below (or even close to) that minimum percentage.
>>>No, there is no "minimum percentage". So your statements are
>>>false.
> MK> Another one who can't write two consecutive
> MK> paragraphs without contradicting himself...?
>Just as you see conspiracies everywhere, you now start seeing
>contradictions all over the place too? :-)
And in this article I see that you are trying to
weasel out of the situation you put yourself into...
> MK> Read back what you wrote. Your first paragraph
> MK> amounts to saying that one can win 10% against
> MK> JF because of luck alone even one makes random
> MK> moves.
> MK> That means nobody can win less than 10%
> MK> against JF (per your comments).
>Almost right so far. It's an estimate of course.
Yes, it's taken as such (i.e. as an example).
>You forget however that random moves are not *worst* moves.
>We could make a JF-like bot that searches for the *worst*
>moves (anyone...?).
I'm not forgetting anything. Read the first paragraph
I quoted above. Didn't you write that...? Does it talk
about random moves or purposefully made worse moves
that your are now trying to switch to...?
And what would rewording yourself from random to worse
moves do you any good? I was questioning whether FIBS
was predicting winning chances below the said minimum.
Are you going to argue that there are people on FIBS
who make purposefully the worst moves they can and that
FIBS allows for that...? I may rub you the wrong way
but you shouldn't let it lead you to argue against me
just for the sake of arguing against me and at the
expense of making a fool out of yourself...
> MK> This is that
> MK> "minimum percentage" I'm talking about.
>And which doesn't exist the way you describe it (modest as
>ever): "completely idiotic" etc. As far as the rating system
>goes, there's nothing idiotic about this, someone coould
>actually play worse than random.
I'm sure they could and FIBS formula must be so deeply
thought-out that it probably includes this possibility
in predicting a player's winning chances... :) Thanks
for the joke...
>So, what's your point?
Sorry, I must not be capable of expressing myself any
more clearly than I tried in English. I may be able to
do better in my native language Turkish, but I doubt
that it will help you any better... :)
> MK> If one
> MK> plays against JF on FIBS and FIBS gives him less
> MK> than 10% chance of winning
>FIBS gives? What do you mean? FIBS only "gives" dice. Or
>do you mean the rating difference *expects* (words are
>important) someone to win less than 10%? You need a huge
>rating difference then. Have you studied the formula FIBS
>uses? (Normally I wouldn't ask, but in your case...)
If random moves alone can amount to 10% winning
chance, then nobody can loose less than that (of
course, unless they try to loose as you now say:)
and no rating difference can exist/result in order
to give anyone less than 10% chance of winning.
Is this really so hard to understand...?
> MK> then FIBS would be
> MK> wrong, wouldn't it?
>No. You are the one that's wrong for the umpteenth time.
Fine. If you're happy, I'm happy... :)
MK
Robert-Jan Veldhuizen
Murat, you're hopeless. It's no use explaining things to you if you just
can't or won't understand. So I'll just clear up some things that could
be ambigious, but I'm not gonna try to deny your weird twists of
arguments yes even conspiracies which you seem to have a patent on.
MK> In <3493.7642...@xs4all.nl> Robert-Jan Veldhuizen wrote:
>> MK> Read back what you wrote. Your first paragraph
>> MK> amounts to saying that one can win 10% against
>> MK> JF because of luck alone even one makes random
>> MK> moves.
>> MK> That means nobody can win less than 10%
>> MK> against JF (per your comments).
>>Almost right so far. It's an estimate of course.
MK> Yes, it's taken as such (i.e. as an example).
example <> estimate.
>>You forget however that random moves are not *worst* moves.
>>We could make a JF-like bot that searches for the *worst*
>>moves (anyone...?).
MK> I'm not forgetting anything. Read the first paragraph
MK> I quoted above. Didn't you write that...? Does it talk
MK> about random moves or purposefully made worse moves
MK> that your are now trying to switch to...?
I am just proving you wrong on "That means nobody can win less than 10%
against JF". For instance *I* could easily win less than 10% against JF,
so there is your answer.
MK> And what would rewording yourself from random to worse
MK> moves do you any good?
*yawn*....
MK> I was questioning whether FIBS
MK> was predicting winning chances below the said minimum.
MK> Are you going to argue that there are people on FIBS
MK> who make purposefully the worst moves they can and that
MK> FIBS allows for that...?
Yes! F.i. robot was very probably worse than random with a rating that
was -500 at a certain point in time.
MK> I may rub you the wrong way
MK> but you shouldn't let it lead you to argue against me
MK> just for the sake of arguing against me and at the
MK> expense of making a fool out of yourself...
You're really a funny guy. Sorry I misjudged your expertism at first.
>> MK> This is that
>> MK> "minimum percentage" I'm talking about.
>>And which doesn't exist the way you describe it (modest as
>>ever): "completely idiotic" etc. As far as the rating system
>>goes, there's nothing idiotic about this, someone coould
>>actually play worse than random.
MK> I'm sure they could and FIBS formula must be so deeply
MK> thought-out that it probably includes this possibility
MK> in predicting a player's winning chances... :) Thanks
MK> for the joke...
FIBS doesn't predict anything...
FIBS doesn't predict anything...
FIBS doesn't predict anything...
FIBS doesn't predict anything...
Do you get it already?
>>So, what's your point?
MK> Sorry, I must not be capable of expressing myself any
MK> more clearly than I tried in English. I may be able to
MK> do better in my native language Turkish, but I doubt
MK> that it will help you any better... :)
I suggest you be more careful when you write in a non-native language...
>> MK> If one
>> MK> plays against JF on FIBS and FIBS gives him less
>> MK> than 10% chance of winning
>>FIBS gives? What do you mean? FIBS only "gives" dice. Or
>>do you mean the rating difference *expects* (words are
>>important) someone to win less than 10%? You need a huge
>>rating difference then. Have you studied the formula FIBS
>>uses? (Normally I wouldn't ask, but in your case...)
MK> If random moves alone can amount to 10% winning
MK> chance, then nobody can loose less than that (of
MK> course, unless they try to loose as you now say:)
Or they think they play good but actually are worse than random...do I
see a similarity with discussion in rgb here...
MK> and no rating difference can exist/result in order
MK> to give anyone less than 10% chance of winning.
MK> Is this really so hard to understand...?
Not for me, but then again you are the one "complaining" about the
ratings, not me.
>> MK> then FIBS would be
>> MK> wrong, wouldn't it?
>>No. You are the one that's wrong for the umpteenth time.
MK> Fine. If you're happy, I'm happy... :)
Whatever it takes.
--
Zorba/Robert-Jan
Murat Kalinyaprak
Steve Mellen wrote in message ...
>In <74sbeg$8lj$2...@news.chatlink.com> Murat Kalinyaprak) wrote:
>> A "total idiot" can't make any worse than random
>> moves because in order to do that he would have
>> to know what bad/worse moves are and in order to
>> know that he would have to know what good/better
>> moves are. Take a logic class if you get a chance,
>> it may do you good...
>You suggest that the only way for a player to be worse than a
>completely random player is to know which moves are good
>and bad, yet consciously choose to make the bad moves.
I think "consciously choosing" is a key term here...
>I disagree. For example, a player might follow the strategy of
>making the ace point as soon as possible and stacking more
>checkers on it whenever possible. Or a player might choose
>to play each roll so as to leave as many blots as possible. I
>suspect both of these strategies would lose in the long term
>to a strategy which merely made random plays at every opportunity.
I suppose one could argue so but I'm not sure if it has any
value regarding the subject in hand. The key terms used in
my original argument were "pure luck (luck factor)" and "zero
skill"... The point was that FIBS or any other rating system
shouldn't give any player a less of a winning chance than what
luck alone would give him in the total absence of skill. Unless
one is willing to propose that rating systems should take into
consideration the possibility you argue for above, there is no
need to discuss it within the scope of this thread...
>I also would like to point out, in my most Chuck Boweresque
>way, that it really decreases the general level of civility on this
>newsgroup when every point must be followed by a cheap shot
>at the intelligence/reasoning ability of the original poster. 'nuff said:)
Who do you think the "original poster" who was attacked here...?
I realize two wrongs don't make a right, but when a writer starts
addressing me instead of the subject, I feel attacked and I guess
I'm not civilized enough to not respond in kind...
MK
Murat Kalinyaprak
>In <74rvb1$vgp$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>>I had nevertheless kept asking
>>hoping to hear a validating answer from the creator(s)
>>of the formula (which is probably unlikely to happen).
>It's entirely likely that the reason you aren't getting an answer from
>them is that the creators of the formula aren't readers of
>rec.games.backgammon.
Yes, very likely so and I wasn't insinuating anything else either...
>>It had been argued that some of the
>>highest rated players on FIBS may be as much as 400
>>overrated. That means a 1700 rated player can reach
>>2100 by being overrated by 400 points. Why couldn't
>>a 1900 player reach 2300 or 2100 rated player reach
>>2500 by being overrated by the same amount...?
>Because while there may be a continuous supply of massively overrated
>1500 players on FIBS, the supply of similarly overrated 1900-level
>players is much smaller. And one doesn't get an inflated 1900-rating
>just by stumbling into a new account... you have to work at
>manipulating the system in order to achieve it. People who do this
>aren't likely to suddenly play like the idiots they are and give away
>ratings points willy-nilly.
I wasn't talking about anybody preying on a 1900 rated player
but talking about 1700, 1900, 2100 rated players all preying on
1500 rated ones. Or you can look at those 3 ratings as of the
same player at different stages...
Keeping the figures constant for simplicity's sake, let me try to
illustrate my point. Let's say there is a steady supply of 1500
rated players who should be really rated at 1400. When a 1700
rated player wins against such a player, he earns 1.77 points
instead of 1.66 which he should be earning against a 1400
rated player, and wins more often then predicted. When his own
rating gets to 1800, 1900, 2000, he only earns 1.66, 1.55, 1.44
(and so on) points per 1-point match but he still earns a surplus
of points and still wins more often than predicted.
What happens when he reaches 2000...? Does he say "Ok,
this is enough now, I'll stop here"...? If he continues to prey
on overrated 1500 players, he will continue to earn points,
although at a slower and slower pace (because his winning
chances are constantly off). So why don't we see 2500 ratings?
Or is it a question of time before those "anglers" reach 2500...?
Once we accept the existance of overrated 1500 players, then
the above is bound to happen unintentionally with players who
accept invitations indiscriminately (like robots) also. If a human
player can achieve an overrating of 400 points in only a few
thousand games experince, robots with experiences in the
tens of thousands of games would end up having done the
same inadvertently simply because even if a fraction of their
experiences consist of games against overrated 1500 players,
those could/would easily add up to a few thousand...
Now let's say that at one time or another (especially when they
first join FIBS) all players end up with a few undeserved points
earned from overrated 1500 players. If most peoples ratings
were overinflated by 10 points at the time they played against
those robots, after tens of thousand of matches, those robots
would have earned a tiny little bit of undeserved points from each
of those players which can amount to a significant number...
So, why don't we see the expected accumulative effect of a flaw
that we know is there...? With a constant supply at the bottom,
it's got to bubble up but curiously somehow it doesn't happen...?
Leaving any other flaw in FIBS' rating system aside, this by itself
is enough to say that all ratings are irregularly (i.e. not all by 5%
or 10%) approximate by an amount of error unknown at best...
MK
Julian Haley
for all of those "over-rated" 1500 players... there are also "under-rated"
1500 players who have recently signed up... who's rating should be
considerably (upto 500 points) higher.
Even though there may be less of them on the server, the impact on the
rating of the higher rated played losing to one of these people should go
along way to offset the additional points gained by winning against the
over-rated players.
Julian
Murat Kalinyaprak
You bring up a good detail but I don't think it will have the impact
you propose. 1500 has been said to be the "average" rating on
FIBS and obviously there will be underrated/overrated players
above and below it. Those underrated/overrated players who
stick to their ratings and user-ID's can perhaps be assumed to
cancel each other out and I was ignoring them, focusing only on
the players who abondon a user-ID below 1500 to start over at
1500 with a new user-ID. I think those players would constitute
a "net surplus" of overrated players since I doubt there would be
too many players who would abadon a user-ID with a rating over
1500 in order to start again at 1500 with a new user-ID.
MK
Murat Kalinyaprak
>On 12-dec-98 01:28:14, Murat Kalinyaprak wrote:
> MK> In <3493.7642...@xs4all.nl> Robert-Jan Veldhuizen wrote:
>>> MK> Read back what you wrote. Your first paragraph
>>> MK> amounts to saying that one can win 10% against
>>> MK> JF because of luck alone even one makes random
>>> MK> moves.
>>> MK> That means nobody can win less than 10%
>>> MK> against JF (per your comments).
>>>Almost right so far. It's an estimate of course.
> MK> Yes, it's taken as such (i.e. as an example).
>example <> estimate.
I stand corrected:), but maybe at your expense. Taking it as an
example was being more lenient on you because an example
is a number one pulls out of the air as a temporary filler to be
replaced by whatever the real figure may happen to be. Often,
its unknown nature is indicated by using "N%" instead of any
number. An estimate is more real than an example. Now you
owe us an explanation as to how you had arrived at that 10%
figure as an estimate...?
Of course, these petty arguments won't effect the validity (or
invalidity) of the points I had made earlier, but I'm willing to
discuss whatever is important to you... :)
>>>You forget however that random moves are not *worst* moves.
>>>We could make a JF-like bot that searches for the *worst*
>>>moves (anyone...?).
> MK> I'm not forgetting anything. Read the first paragraph
> MK> I quoted above. Didn't you write that...? Does it talk
> MK> about random moves or purposefully made worse moves
> MK> that your are now trying to switch to...?
>I am just proving you wrong on "That means nobody can win less than 10%
>against JF". For instance *I* could easily win less than 10% against JF,
>so there is your answer.
If we need to get pedantic about this, then let's do. The object
of the game is "winning" not "loosing", and "win" means "win"
not "loose". Within this context, anybody having any intentions
of winning can't win any less than 10% (by your estimate:)... If
there is out there a widespread practice of playing bg to loose
and if you or somebody else argues that FIBS formula takes
this into consideration, then I'd be more than elated to declare
that FIBS formula must a very beautiful/perfect one indeed... :)
> MK> And what would rewording yourself from random to worse
> MK> moves do you any good?
>*yawn*....
Maybe you should withold from writing when you're sleepy...?
> MK> I was questioning whether FIBS
> MK> was predicting winning chances below the said minimum.
> MK> Are you going to argue that there are people on FIBS
> MK> who make purposefully the worst moves they can and that
> MK> FIBS allows for that...?
>Yes! F.i. robot was very probably worse than random with a rating that
>was -500 at a certain point in time.
Whether that robot was designed to loose or whatever it tried
to win ended up worse than making random moves, arguing
that FIBS formula is designed to intentionally provide for such
a possibility is laughable... A formula so throughly thought out
to even consider and measure "negative skill"...? :) Fine, you
can have it...
> MK> I'm sure they could and FIBS formula must be so deeply
> MK> thought-out that it probably includes this possibility
> MK> in predicting a player's winning chances... :) Thanks
> MK> for the joke...
>FIBS doesn't predict anything...
>FIBS doesn't predict anything...
>FIBS doesn't predict anything...
>FIBS doesn't predict anything...
>Do you get it already?
First, go visit some web pages and read old articles about the
FIBS rating system and count how many time the "experts" use
the word "predict" in describing what FIBS does. Then, come
back here and repeat "FIBS doesn't predict anything..." a few
hundred more times, perhaps shouting louder also by using
capital letters. After that, if I see that they get it, I'll get it too...
:)
>>>So, what's your point?
> MK> Sorry, I must not be capable of expressing myself any
> MK> more clearly than I tried in English. I may be able to
> MK> do better in my native language Turkish, but I doubt
> MK> that it will help you any better... :)
>I suggest you be more careful when you write in a non-native language...
Good advice, and I'm surprized that you understood what I
wrote here... If you really had/have problem understanding
my English, you shouldn't have tried responding to a posting
in some language you didn't understand in the first place or
maybe you will stop responding after now...
MK
Steve Mellen
<mu...@cyberport.net> wrote:
>
> I wasn't talking about anybody preying on a 1900 rated player
> but talking about 1700, 1900, 2100 rated players all preying on
> 1500 rated ones. Or you can look at those 3 ratings as of the
> same player at different stages...
>
> Keeping the figures constant for simplicity's sake, let me try to
> illustrate my point. Let's say there is a steady supply of 1500
> rated players who should be really rated at 1400. When a 1700
> rated player wins against such a player, he earns 1.77 points
> instead of 1.66 which he should be earning against a 1400
> rated player, and wins more often then predicted. When his own
> rating gets to 1800, 1900, 2000, he only earns 1.66, 1.55, 1.44
> (and so on) points per 1-point match but he still earns a surplus
> of points and still wins more often than predicted.
>
> What happens when he reaches 2000...? Does he say "Ok,
> this is enough now, I'll stop here"...? If he continues to prey
> on overrated 1500 players, he will continue to earn points,
> although at a slower and slower pace (because his winning
> chances are constantly off). So why don't we see 2500 ratings?
> Or is it a question of time before those "anglers" reach 2500...?
>
Let's think about this situation for a moment. We're postulating a
1700-rated "angler," taking advantage of all these 1500-rated people who
really should be rated only 1400. So our angler is going to beat them at
whatever the rate is for two players rated 300 points apart, except --
since they're actually rated only 200 points apart -- the angler is going
to gain more points than he should.
But what happens when the angler gets his rating up to 1800? Now HE is
overrated by 100 points, just like his opponents! The difference in their
true skill levels is 300 points (1700-1400) -- after all, the angler has
not become a better player by virtue of shooting this angle, he has merely
increased his rating. The difference between their ratings is also 300
points (1800-1500). So the angler will win at exactly the rate the server
predicts for him, and his rating will not keep moving upwards.
I hope this explains why the angler does not reach a 2500+ rating in the
long run.
Robert-Jan Veldhuizen
MK> Once we accept the existance of overrated 1500 players,
...you also have to accept the existence of underrated 1500 players!
Very good!
FYI: the average rating on FIBS has been *above* 1500 every time I
looked at it.
MK> So, why don't we see the expected accumulative effect of a flaw
MK> that we know is there...? With a constant supply at the bottom,
MK> it's got to bubble up but curiously somehow it doesn't happen...?
Very simple answer: because your line of reasoning is just plain wrong.
MK> Leaving any other flaw in FIBS' rating system aside, this by itself
MK> is enough to say that all ratings are irregularly (i.e. not all by 5%
MK> or 10%) approximate by an amount of error unknown at best...
No (again).
--
Zorba/Robert-Jan
Michael J Zehr
>
>>In <74rvb1$vgp$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>>>It had been argued that some of the
>>>highest rated players on FIBS may be as much as 400
>>>overrated. That means a 1700 rated player can reach
>>>2100 by being overrated by 400 points. Why couldn't
>>>a 1900 player reach 2300 or 2100 rated player reach
>>>2500 by being overrated by the same amount...?
Has anyone argued that this has happened without intentional rating
manipulation?
>>Because while there may be a continuous supply of massively overrated
>>1500 players on FIBS, the supply of similarly overrated 1900-level
>>players is much smaller. And one doesn't get an inflated 1900-rating
>>just by stumbling into a new account... you have to work at
>>manipulating the system in order to achieve it. People who do this
>>aren't likely to suddenly play like the idiots they are and give away
>>ratings points willy-nilly.
>
>I wasn't talking about anybody preying on a 1900 rated player
>but talking about 1700, 1900, 2100 rated players all preying on
>1500 rated ones. Or you can look at those 3 ratings as of the
>same player at different stages...
>
>Keeping the figures constant for simplicity's sake, let me try to
>illustrate my point. Let's say there is a steady supply of 1500
>rated players who should be really rated at 1400. When a 1700
>rated player wins against such a player, he earns 1.77 points
>instead of 1.66 which he should be earning against a 1400
>rated player, and wins more often then predicted. When his own
>rating gets to 1800, 1900, 2000, he only earns 1.66, 1.55, 1.44
>(and so on) points per 1-point match but he still earns a surplus
>of points and still wins more often than predicted.
Sorry, but this is where you misunderstand how the system works, and
probably the root cause of the beliefs that ratings can arbitrarily move
upwards. The one player has a rating of 1500 but should have a rating
of 1400. The other player (eventually) has a rating of 1800 but should
have a rating of 1700. FIBS thinks they are 300 points apart in
rating. They actually ARE 300 points apart in rating because both are
overrated by the same amount. There is no average gain.
With the rating boosted by 100 points, the manipulator now has to play
people who are overrated by 100 points on average just to maintain the
current rating. To become higher rated he has to find people overrated
by more than 100 points.
You even have the answer in your numbers:
>When his own
>rating gets to 1800, 1900, 2000, he only earns 1.66, 1.55, 1.44
>(and so on) points per 1-point match but he still earns a surplus
>of points and still wins more often than predicted.
>When a 1700
>rated player wins against such a player, he earns 1.77 points
>instead of 1.66 which he should be earning against a 1400
>rated player, and wins more often then predicted.
Where is the surplus if he "should" be winning 1.66 and is actually
winning 1.55? There is a deficit, causing him to drift back to be
overrated by the same amount as his opponents are (on average).
>What happens when he reaches 2000...? Does he say "Ok,
>this is enough now, I'll stop here"...? If he continues to prey
>on overrated 1500 players, he will continue to earn points,
>although at a slower and slower pace (because his winning
>chances are constantly off). So why don't we see 2500 ratings?
>Or is it a question of time before those "anglers" reach 2500...?
Nope -- as I pointed out above once he is also overrated by 100 points
he can't gain without finding 1500-rated players that ought to be rated
1300. Okay, so there are some of them, and he can climb from 1800 to
1900. But then he *does* stop... until he finds people overrated by
even more than 200 points, since he is overrated by more than 200
points.
[Actually it's a bit more complicated than this, because you end up
"splitting" the extra rating points. You really do need to keep on
finding fresh overrated people, because after you play them a few times
they aren't as overrated as they were to start with. In addition, if
you're postulating that there's a steady stream of 1400-rated people who
come on to the system, play a bit, then quit, then the average rating
slowly drifts upwards. (You can see this happening.) Everyone else
will be getting some of those extra rating points too, so the relative
ranking of that person won't go up by all that much. Furthermore if
anyone did manage to find a way to become top-rated without being all
that good, the people who really are good would keep trying to play that
person. That person would have to decline (their rating will only stay
high by playing overrated new players), and would very quickly get the
reputation as having cheated to get the rating.]
>Once we accept the existance of overrated 1500 players, then
>the above is bound to happen unintentionally with players who
>accept invitations indiscriminately (like robots) also. If a human
>player can achieve an overrating of 400 points in only a few
>thousand games experince, robots with experiences in the
>tens of thousands of games would end up having done the
>same inadvertently simply because even if a fraction of their
>experiences consist of games against overrated 1500 players,
>those could/would easily add up to a few thousand...
>
>Now let's say that at one time or another (especially when they
>first join FIBS) all players end up with a few undeserved points
>earned from overrated 1500 players. If most peoples ratings
>were overinflated by 10 points at the time they played against
>those robots, after tens of thousand of matches, those robots
>would have earned a tiny little bit of undeserved points from each
>of those players which can amount to a significant number...
No. If the average player were 10 points overrated then the robots
would become 10 points overrated.
The FIBS rating system is based on the difference in rating points. If
player A is 100 rating points above player B, but player A wins as
frequently as if they were 150 rating points above player B, then the
ratings will change until there is a 150 point difference. (B will lose
25, A will win 25.) Now there *is* a 150 point difference and A wins as
frequently as if there's a 150 point difference. Equilibrium has been
restored to the system. Player A doesn't gain rating points forever.
-Michael J. Zehr
Michael J Zehr
Murat Kalinyaprak <mu...@cyberport.net> wrote:
>You bring up a good detail but I don't think it will have the impact
>you propose. 1500 has been said to be the "average" rating on
>FIBS and obviously there will be underrated/overrated players
>above and below it. Those underrated/overrated players who
>stick to their ratings and user-ID's can perhaps be assumed to
>cancel each other out and I was ignoring them, focusing only on
>the players who abondon a user-ID below 1500 to start over at
>1500 with a new user-ID. I think those players would constitute
>a "net surplus" of overrated players since I doubt there would be
>too many players who would abadon a user-ID with a rating over
>1500 in order to start again at 1500 with a new user-ID.
If there's a constant stream of people who log in, lose some points, and
quit FIBS forever.... why do you think the average rating is 1500?
Perhaps it's "been said" but it isn't true. The starting rating is
still 1500, but the average of active players is higher because of
exactly the reason you mention.
There isn't a "net surplus" of overrated players, but there is a "net
surplus" of rating points, which end up being distributed more or less
evenly over all of FIBS. So everyone's rating slowly creeps upwards.
(Very slowly... probably only a point a month, if that.) If someone can
collect more than their fare share of those surplus point, they will
increase more than everyone else. But the more extra points they manage
to collect, the harder it is for them to get any more.
-Michael J. Zehr
Kit Woolsey
: Has anyone argued that this has happened without intentional rating
: manipulation?
When I first started playing on FIBS, the top rating was around 1900 and
most of the better players had ratings around 1800. 2000 was sort of a
utopian goal, something like the 4-minute mile was many years ago. Today
many players maintain an average rating over 1900, and the best bots
maintain an average rating over 2000. Yet, the initial rating given to
new players remains at 1500.
This type of "rating inflation" is quite common with Elo type rating
systems. We have seen it occur in chess over the years. It happens
without intentional manipulation.
A common occurrence would be for a new player who is an absolute beginner
at backgammon to join FIBS. This player starts off at 1500, but his real
rating should be lower. He loses more than he wins, and his rating drops
off. Eventually he loses interest in the game and stops playing on FIBS.
However, those matches he lost result in "underserved" rating point
increases for the players he played, and these players are continuing to
play on FIBS. Consequently these players are not rated a bit higher than
they "should" be, so when they play other players these slightly higher
ratings are passed off to their opponents. In this way, there is a very
slow increase in the average rating of active players. You won't notice
it over a short period of time, but over a period of several years the
cumulative effect is quite apparent.
Of course rating manipulation can have the same effect. If a player
plays against himself on another account, and the "loser" eventually
drops off FIBS while the cheater continues to play, it is just as though
the "loser" were one of those overrated beginning players who loses more
than he wins and eventually drops off FIBS.
Kit
prick...@my-dejanews.com
> : manipulation?
>
> When I first started playing on FIBS, the top rating was around 1900 and
> most of the better players had ratings around 1800. 2000 was sort of a
> utopian goal, something like the 4-minute mile was many years ago. Today
> many players maintain an average rating over 1900, and the best bots
> maintain an average rating over 2000. Yet, the initial rating given to
> new players remains at 1500.
>
> This type of "rating inflation" is quite common with Elo type rating
> systems. We have seen it occur in chess over the years. It happens
> without intentional manipulation.
>
> A common occurrence would be for a new player who is an absolute beginner
> at backgammon to join FIBS. This player starts off at 1500, but his real
> rating should be lower. He loses more than he wins, and his rating drops
> off. Eventually he loses interest in the game and stops playing on FIBS.
> However, those matches he lost result in "underserved" rating point
> increases for the players he played, and these players are continuing to
> play on FIBS. Consequently these players are not rated a bit higher than
> they "should" be, so when they play other players these slightly higher
> ratings are passed off to their opponents. In this way, there is a very
> slow increase in the average rating of active players. You won't notice
> it over a short period of time, but over a period of several years the
> cumulative effect is quite apparent.
The old FIBS ratings report site used to provide statistics based on
experience, such as average rating per how many exp. eg. >500, >1000, >5000
and so on. I remember the average rating for people with an experience
greater than 500 was usually around 1530. It's been a couple of years since
the old site stopped posting ratings reports. Since gamercafe started posting
ratings reports, they haven't provided such statistics. They also don't
archive old reports. It would be interesting to see if the average rating has
indeed increased.
PricklyPear
--
Luck happens when preparation meets opportunity.
-----------== Posted via Deja News, The Discussion Network ==----------
http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own
Alexander Nitschke
overrated newbies will not go on forever. The system is self-correcting
because the average rating may increase (now it is about 1530 I think),
but any newcomer is still rated at 1500. A newcomer is actually 30
points below average now, and there must be a point when the average
rating is right in respect to the starting rating and equilibrium of the
system is restored.
We must never forget that these ratings are (and can only be) relative
figures and are not absolute. Only the difference is which counts not
the number in itself.
This said I want to criticize the FIBS rating system in a minor point:
We know that backgammon is a very different game than chess because of
the huge luck element which is involved. In spite of this the ELO system
is adopted whit some minor changes involving the match length factor and
the experience points. Especially the K-factor, which determines how big
a rating change will be was not changed. This is an error, because the
resulting swings are way too big. I cannot take a rating system with the
following characteristics for serious: The rating range is from about
1100 to about 2000 and possible rating swings (which are fully luck
induced) can easily be +/- 100 points. These swings are too big to be
accepted for a rating system which intention is to produce correct
ratings.
A very easy to implement correction would be to lower the K-factor
further, which is now fixed after 400 experience points. I think luck
induced swings of +/- 25 points would be acceptable, so the factor
should be reduced until it is a quarter of the current value.
It is correct that playing strength induced rating changes would be much
slower than now, but then again now it is impossible to even recognize
playing strength induced rating changes.
If anyone wishes, I can produce an exact new formula for the FIBS
ratings, which wouldn't have big differences to the current one.
Alexander
Kit Woolsey wrote:
>
> Michael J Zehr (ta...@mit.edu) wrote:
>
> : Has anyone argued that this has happened without intentional rating
> : manipulation?
>
> When I first started playing on FIBS, the top rating was around 1900 and
> most of the better players had ratings around 1800. 2000 was sort of a
> utopian goal, something like the 4-minute mile was many years ago. Today
> many players maintain an average rating over 1900, and the best bots
> maintain an average rating over 2000. Yet, the initial rating given to
> new players remains at 1500.
>
> This type of "rating inflation" is quite common with Elo type rating
> systems. We have seen it occur in chess over the years. It happens
> without intentional manipulation.
>
> A common occurrence would be for a new player who is an absolute beginner
> at backgammon to join FIBS. This player starts off at 1500, but his real
> rating should be lower. He loses more than he wins, and his rating drops
> off. Eventually he loses interest in the game and stops playing on FIBS.
> However, those matches he lost result in "underserved" rating point
> increases for the players he played, and these players are continuing to
> play on FIBS. Consequently these players are not rated a bit higher than
> they "should" be, so when they play other players these slightly higher
> ratings are passed off to their opponents. In this way, there is a very
> slow increase in the average rating of active players. You won't notice
> it over a short period of time, but over a period of several years the
> cumulative effect is quite apparent.
>
Scott Perschke
>The old FIBS ratings report site used to provide statistics based on
>experience, such as average rating per how many exp. eg. >500, >1000, >5000
>and so on. I remember the average rating for people with an experience
>greater than 500 was usually around 1530. It's been a couple of years since
>the old site stopped posting ratings reports. Since gamercafe started posting
>ratings reports, they haven't provided such statistics. They also don't
>archive old reports. It would be interesting to see if the average rating has
>indeed increased.
As of December 1st, these are the numbers - use a fixed pitch font to
display the table properly. The percentages shown indicate what rating
you much achieve to be in a certain percentile of players. For
example, if your experience is 400 (an "established" player), you must
get to 1661 to be in the top 30% of players with similar experience.
Scott
===================================================================
Exp # Avg 10% 20% 30% 40% 50% 60% 70% 80%
---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----
50 7093 1520 1728 1645 1593 1551 1514 1479 1440 1395
400 3637 1577 1788 1714 1661 1615 1576 1538 1497 1451
800 2514 1606 1810 1742 1690 1644 1604 1566 1526 1480
1600 1633 1632 1831 1766 1717 1673 1633 1594 1554 1508
3200 918 1665 1854 1800 1753 1710 1660 1624 1582 1542
6400 387 1695 1873 1822 1796 1741 1705 1658 1608 1572
====================================================================
Murat Kalinyaprak
>In <751des$gp2$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>>... 500 with a new user-ID. I think those players would constitute
>>a "net surplus" of overrated players since I doubt there would be
>>too many players who would abadon a user-ID with a rating over
>>1500 in order to start again at 1500 with a new user-ID.
>If there's a constant stream of people who log in, lose some points,
>and quit FIBS forever.... why do you think the average rating is 1500?
I don't and I hadn't come up with that figure either. It had been said to
be that by many other writers here and I don't mind using it because
it is probably still not to far off from the real average (in the unique way
the term average is used regarding FIBS ratings, of course:)...
The real importance of 1500 is that it is the entry point for new users,
regardless of what the average rating is. If somebody wanted to prey
on overrated new users, that's the rating of targeted "victims". What
the actual average rating may be is unimportant (perhaps completely)
talking about this subject.
MK
Murat Kalinyaprak
>In <74vs78$7sn$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>>>>It had been argued that some of the
>>>>highest rated players on FIBS may be as much as 400
>>>>overrated. That means a 1700 rated player can reach
>>>>2100 by being overrated by 400 points. Why couldn't
>>>>a 1900 player reach 2300 or 2100 rated player reach
>>>>2500 by being overrated by the same amount...?
>Has anyone argued that this has happened without intentional rating
>manipulation?
I don't think so. I don't understan the intent of your question either.
>>I wasn't talking about anybody preying on a 1900 rated player
>>but talking about 1700, 1900, 2100 rated players all preying on
>>1500 rated ones. Or you can look at those 3 ratings as of the
>>same player at different stages...
>>Keeping the figures constant for simplicity's sake, let me try to
>>illustrate my point. Let's say there is a steady supply of 1500
>>rated players who should be really rated at 1400. When a 1700
>>rated player wins against such a player, he earns 1.77 points
>>instead of 1.66 which he should be earning against a 1400
>>rated player, and wins more often then predicted. When his own
>>rating gets to 1800, 1900, 2000, he only earns 1.66, 1.55, 1.44
>>(and so on) points per 1-point match but he still earns a surplus
>>of points and still wins more often than predicted.
>Where is the surplus if he "should" be winning 1.66 and is actually
>winning 1.55? There is a deficit, causing him to drift back to be
>overrated by the same amount as his opponents are (on average).
You are right. The three example ratings I mentioned would need
to belong to different players and can't be of the same player at
different stages. I guess I got a little carried away with it. :) Thanks
for noticing and correcting me on this.
>>What happens when he reaches 2000...? Does he say "Ok,
>>this is enough now, I'll stop here"...? If he continues to prey
>>on overrated 1500 players, he will continue to earn points,
>>although at a slower and slower pace (because his winning
>>chances are constantly off). So why don't we see 2500 ratings?
>>Or is it a question of time before those "anglers" reach 2500...?
>Nope -- as I pointed out above once he is also overrated by 100 points
>he can't gain without finding 1500-rated players that ought to be rated
>1300. Okay, so there are some of them, and he can climb from 1800 to
>1900. But then he *does* stop... until he finds people overrated by
>even more than 200 points, since he is overrated by more than 200
>points.
Your argument is correct in general. Basing my argument on 1400
(pulled out of the air as an example average true rating of overrated
1500 players) doesn't get me too far. At least personally, I have no
idea what the actual number may be. I had written earlier (see above)
that other people had asserted some top rated players' (I believe the
name BROHAM was often mentioned) ratings may be as overrated
as by 400 points. According to your argument, this would require them
to prey on 1500 rated players with true ratings of 1100. At the time, no
"expert" had objected to it by saying that this was unlikely. There is, of
course, the possibility that some players may be throwing games at
themselves from a second accound, in which case there would be no
need for preying on overrated 1500 players. One point of mine is that,
all related but conflicting arguments on a given subject in this group
need to be reconciled. If FIBS has been keeping track of final ratings
of all the players who had dropped off in the past, it would help us to
know what the actual amount/avearge of overrating is.
>[Actually it's a bit more complicated than this, because you end up
>"splitting" the extra rating points. You really do need to keep on
>finding fresh overrated people, because after you play them a few times
>they aren't as overrated as they were to start with.
You are right and I my guess is that there *is* such a steady supply.
Perhaps somebody from FIBS can shed more light on this by giving
some actual stats if they have them.
>In addition, if
>you're postulating that there's a steady stream of 1400-rated people who
>come on to the system, play a bit, then quit, then the average rating
>slowly drifts upwards. (You can see this happening.) Everyone else
>will be getting some of those extra rating points too, so the relative
>ranking of that person won't go up by all that much.
I disagree. If some players can achieve overratings in the order of
hundreds of points, everybody else's rating going up by a few points
would be comparatively very insignificant (to smooth out the sharp
edges)...
>Furthermore if
>anyone did manage to find a way to become top-rated without being all
>that good, the people who really are good would keep trying to play that
>person. That person would have to decline (their rating will only stay
>high by playing overrated new players), and would very quickly get the
>reputation as having cheated to get the rating.]
Yes, and by what I saw written on this subject in the past, it seemed
that this had happened, hadn't it...?
>>Now let's say that at one time or another (especially when they
>>first join FIBS) all players end up with a few undeserved points
>>earned from overrated 1500 players. If most peoples ratings
>>were overinflated by 10 points at the time they played against
>>those robots, after tens of thousand of matches, those robots
>>would have earned a tiny little bit of undeserved points from each
>>of those players which can amount to a significant number...
>No. If the average player were 10 points overrated then the robots
>would become 10 points overrated.
I have to rethink this more throughly. If the average rateing on FIBS
is ever incresing, what I said may be true to a smaller extent but I
won't insist on it since I'm not sure at this moment...
>The FIBS rating system is based on the difference in rating points. If
>player A is 100 rating points above player B, but player A wins as
>frequently as if they were 150 rating points above player B, then the
>ratings will change until there is a 150 point difference. (B will lose
>25, A will win 25.) Now there *is* a 150 point difference and A wins as
>frequently as if there's a 150 point difference. Equilibrium has been
>restored to the system. Player A doesn't gain rating points forever.
I believe all players will, but at a very very slow rate. The real issue
here is the possibility of a few very sharp peaks. I appreciate your
thoughtful, clearly expressed and informative response on this
subject. Hopefully, soon enough there won't be anybody left in this
newsgroup who understands the FIBS rating system any less than
I do... :)
MK
Patti Beadles
your experience increases. This suggests that there is indeed a
surplus of "unearned" rating points in the pool, and that all players'
ratings will increase slowly over time, even if their skill doesn't.
The fact that peak ratings have always increased over the years also
bears this out. When I started playing on FIBS about five years ago,
the top rating was around 1800.
-Patti
--
Patti Beadles |
pat...@netcom.com/pat...@gammon.com |
http://www.gammon.com/ | Try to relax
or just yell, "Hey, Patti!" | and enjoy the crisis
Michael J Zehr
Murat Kalinyaprak <mu...@cyberport.net> wrote:
>Michael J Zehr wrote in <752cbj$q...@senator-bedfellow.MIT.EDU>...
>
>>In <74vs78$7sn$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>
>
>>>>>It had been argued that some of the
>>>>>highest rated players on FIBS may be as much as 400
>>>>>overrated. That means a 1700 rated player can reach
>>>>>2100 by being overrated by 400 points. Why couldn't
>>>>>a 1900 player reach 2300 or 2100 rated player reach
>>>>>2500 by being overrated by the same amount...?
>
>>Has anyone argued that this has happened without intentional rating
>>manipulation?
>I don't think so. I don't understan the intent of your question either.
Here's the point:
The system _can_ be manipulated and we can't stop that, but it's not
because the system is bad, it's because there are some people that will
abuse any system.
The system cannot predict exactly the expected winning chance between
any pair of players for any length match (see my posting on a perfect
system) but I'm not trying to prove that it can. (Of course proving
that it *doesn't* predict winning chances accurately is also hard since
we don't know the correct winning chances -- all we can do is observe
the outcome of matches. If we flip a coin 100 times and get 53 heads
and 47 tails and we call heads winning, we don't know if the expected
winning percentage is 53 or not.)
The existence of grossly overrated people causing other people to
arbitrarily move up in rating without manipulating the system because
someone who _intentionally_ is overrated is doing something specific to
get that rating, and that means they aren't playing random games. They
will boost their rating and not play anyone else. The experts or the
bots don't win against them because the player who intentionally
manipulated their ratings don't accept matches from the experts or bots.
So... if you can show through random play that people become 400 points
for any length of time, then I will agree there's something wrong with
the system.
But in any case, if you're going to use someone else's assertion as a
building block in your own argument that there's a problem with the
rating system, you better be willing to adequately prove that they are
correct. Otherwise I'll just say "I heard on the street that the system
is fair" therefore it's fair. :-)
Here's another reason why we should distinguish between intentional
mainpulation and random fluctuations in rating:
The person who spends their time intentionally manipulating the system
is on FIBS for that reason -- that's what they are doing instead of
playing games more or less at random.
The expert who is currently (and accurately) rated 1900 is on FIBS to
play backgammon. They could stop playing backgammon in order to
manipulate the system, but that's a bit like arguing:
The legal system doesn't work to keep society functioning because there
are crimes. If someone can be a career crimnal stealing over and over,
then what's to stop a community leader from stealing over and over?
You're right that a 1900-rated person *could* intentionally manipulate
the system and get a higher rating, but they have to do that by stopping
playing backgammon. Then if they go back to simply playing lots of
backgammon, their unearned rating points will spread around.
Furthermore they created an underrated person by this mainpulation.
Either that is an account they created and then stopped using, in which
case they permanently upped the average rating on FIBS. But they
haven't changed the expected rankings after those unearned points are
spread around again.... Or they created an underrated person some other
way, but that account will start playing backgammon now, causing them to
spread their rating point deficit around.
There's nothing special about a rating of 2100, or 1900, or anything
else. In time the top ten ranked players on FIBS might have a rating in
the 2500's. They'll still be the top ten players, and they probably
aren't any better. FIBS doesn't measure actual skill (what's the unit
of skill anyway?) but measures skill differences. (At one point I was
in the top 10 with a ranking in the 1700's. I think the server was 1-2
years old at the time, so this wasn't just while people's ratings hadn't
yet stabilized.)
> I had written earlier (see above)
>that other people had asserted some top rated players' (I believe the
>name BROHAM was often mentioned) ratings may be as overrated
>as by 400 points. According to your argument, this would require them
>to prey on 1500 rated players with true ratings of 1100.
Yes, or do something else to manipulate the system. But just as the
occurence of a theft doesn't "prove" that the legal system is broken,
the fact that someone can manipulate the rating system doesn't mean it
doesn't work to predict winning chances between people that don't try to
mainpulate the system.
>One point of mine is that,
>all related but conflicting arguments on a given subject in this group
>need to be reconciled.
Sorry, but some of the arguments are wrong and I'm not going to try to
reconcile them. :-) I will reconcile my own statements with the
evidence we have from FIBS and other sources though.
>>Furthermore if
>>anyone did manage to find a way to become top-rated without being all
>>that good, the people who really are good would keep trying to play that
>>person. That person would have to decline (their rating will only stay
>>high by playing overrated new players), and would very quickly get the
>>reputation as having cheated to get the rating.]
>
>
>Yes, and by what I saw written on this subject in the past, it seemed
>that this had happened, hadn't it...?
Yes. Some people cheat. But for those that don't cheat,
the system works incredibly well at ranking people by skill.
-Michael J. Zehr
highlander
>There's a very clear trend here toward a higher average rating as
>your experience increases. This suggests that there is indeed a
>surplus of "unearned" rating points in the pool, and that all players'
>ratings will increase slowly over time, even if their skill doesn't.
there is no reason for an upper limit of the rating
for every new player who subsribes the "energy" of the fibs system will be
increased by 1500 points.
this energy will be spread over all players. therefore the average will
increase slightly with every player who subsribes. if after some losses the
player creates a new identity and abandons the "loser" these points will be
wasted. the average will be increased according to following formula.
(#players_ever_subscribed*1500/#players_subscribed_now)
thats a fact - nothing to do against
highlander
___
it doesn't matter if you win or lose, until you lose
highlander
>(#players_ever_subscribed*1500/#players_subscribed_now)
>
ok ok - there is a little bug in the formula ...
((#players_ever_subscribed*1500) - sum(abandoned_player(i)*(1500 -
rating_when_abandoned(i))))/#players_subscribed_now)
Robert-Jan Veldhuizen
MK> Michael J Zehr wrote in <752cbj$q...@senator-bedfellow.MIT.EDU>...
>>Nope -- as I pointed out above once he is also overrated by 100 points
>>he can't gain without finding 1500-rated players that ought to be rated
>>1300. Okay, so there are some of them, and he can climb from 1800 to
>>1900. But then he *does* stop... until he finds people overrated by
>>even more than 200 points, since he is overrated by more than 200
>>points.
MK> Your argument is correct in general. Basing my argument on 1400
MK> (pulled out of the air as an example average true rating of overrated
MK> 1500 players) doesn't get me too far. At least personally, I have no
MK> idea what the actual number may be. I had written earlier (see above)
MK> that other people had asserted some top rated players' (I believe the
MK> name BROHAM was often mentioned) ratings may be as overrated
MK> as by 400 points.
Those players are usually cheaters. If you just play on FIBS without any
intent of getting a mucher higher rating than you deserve, I guess you
won't get overrated by more than 200 points; of course exceptions are
always possible.
MK> According to your argument, this would require them
MK> to prey on 1500 rated players with true ratings of 1100.
That is cheating, because normally you wouldn't know if a newbie's
strength is around 1100 or lower.
None will argue with you if you say cheating is possible with FIBS'
rating system.
MK> At the time, no
MK> "expert" had objected to it by saying that this was unlikely.
I think you can remove those quotes there, there are certainly experts
around here. I guess most people figured you could work out yourself
that your ideas are unlikely or even practically impossible.
MK> There is,
MK> of course, the possibility that some players may be throwing games at
MK> themselves from a second accound, in which case there would be no need
MK> for preying on overrated 1500 players.
How do you "prey on overrated 1500 players" without cheating?
MK> One point of mine is that, all
MK> related but conflicting arguments on a given subject in this group need
MK> to be reconciled. If FIBS has been keeping track of final ratings of all
MK> the players who had dropped off in the past, it would help us to know
MK> what the actual amount/avearge of overrating is.
Read what others wrote. The effect is negligible.
>>[Actually it's a bit more complicated than this, because you end up
>>"splitting" the extra rating points. You really do need to keep on
>>finding fresh overrated people, because after you play them a few times
>>they aren't as overrated as they were to start with.
MK> You are right and I my guess is that there *is* such a steady
MK> supply.
There is a supply of newbies, and it seems likely that the better
players will continue to play on FIBS and the worse players will stop
after some matches. That accounts for a very slight average rating
increase. Note however that it normally doesn't change the *relative*
ratings of people: all will "benefit" from this effect.
MK> Perhaps somebody from FIBS can shed more light on this by giving
MK> some actual stats if they have them.
How about going to dejanews...
>>In addition, if
>>you're postulating that there's a steady stream of 1400-rated people who
>>come on to the system, play a bit, then quit, then the average rating slowly
>>drifts upwards. (You can see this happening.) Everyone else will be
>>getting some of those extra rating points too, so the relative ranking of
>>that person won't go up by all that much.
MK> I disagree. If some players can achieve overratings in the order of
MK> hundreds of points, everybody else's rating going up by a few points
MK> would be comparatively very insignificant (to smooth out the sharp
MK> edges)...
You disagree because you just don't understand the ratings system.
Michael is absolutely right. Your "opinion" is not interesting at
all because it just contradicts the facts.
>>Furthermore if
>>anyone did manage to find a way to become top-rated without being all
>>that good, the people who really are good would keep trying to play that
>>person. That person would have to decline (their rating will only stay high
>>by playing overrated new players), and would very quickly get the reputation
>>as having cheated to get the rating.]
MK> Yes, and by what I saw written on this subject in the past, it seemed
MK> that this had happened, hadn't it...?
Yes, so here's part of your answer why it's unlikely that we get an
overrated 2500 player. The higher your rating gets, the more you will be
noticed and then there's only two options: keep on cheating and probably
get kicked off or play with other players and watch your rating drop!
>>>Now let's say that at one time or another (especially when they
>>>first join FIBS) all players end up with a few undeserved points
>>>earned from overrated 1500 players. If most peoples ratings
>>>were overinflated by 10 points at the time they played against
>>>those robots, after tens of thousand of matches, those robots
>>>would have earned a tiny little bit of undeserved points from each
>>>of those players which can amount to a significant number...
>>No. If the average player were 10 points overrated then the robots
>>would become 10 points overrated.
MK> I have to rethink this more throughly.
That's always a good idea.
MK> If the average rateing on FIBS
MK> is ever incresing, what I said may be true to a smaller extent but I
MK> won't insist on it since I'm not sure at this moment...
AFAIK the average rating increased by only 5-6 rating points a
year...it's now somewhere around 1530.
[...]
MK> I believe all players will, but at a very very slow rate.
That's not really a believe, that's a fact which you might have read in
some other articles.
MK> The real issue
MK> here is the possibility of a few very sharp peaks.
Not likely because those "peakers" will be (very) overrated themselves.
It's like rolling boxcars ten times in a row. The more overrated you
get, the less likely it becomes to maintain or even increase your
rating; an essential part of the ratings formula.
--
Zorba/Robert-Jan
Chuck Bower
highlander <highl...@immortal.com> wrote:
>
>>There's a very clear trend here toward a higher average rating as
>>your experience increases. This suggests that there is indeed a
>>surplus of "unearned" rating points in the pool, and that all players'
>>ratings will increase slowly over time, even if their skill doesn't.
>
>
>there is no reason for an upper limit of the rating
>for every new player who subsribes the "energy" of the fibs system will be
>increased by 1500 points.
Whoa. There's a word (energy) that gets more than its share of abuse.
>this energy will be spread over all players. therefore the average will
>increase slightly with every player who subsribes. if after some losses the
>player creates a new identity and abandons the "loser" these points will be
>wasted. the average will be increased according to following formula.
>(#players_ever_subscribed*1500/#players_subscribed_now)
>
>thats a fact - nothing to do against
And even ANOTHER word (fact) that gets over(mis)used. Of course
if you say it loudly enough (how about shouting "FACT"), beat your
chest a few times, and glare at the person you're trying to convince
maybe it will work. Not here, though.
So let me get this straight. If the person joining really should
be rated at 1500, that will still drive up the ratings of the others?
And, also a new player who will eventually settle at 1800? Say "FACT"
a little louder, please. Some of us are having trouble being snowed.
Chuck
bo...@bigbang.astro.indiana.edu
c_ray on FIBS
OSMAN
Do you need to make a correction for those abandoners who are over 1500
rating?
--
Osman F. Guner
os...@prodigy.net
http://pages.prodigy.net/osman
OSMAN
[snip]
> We must never forget that these ratings are (and can only be) relative
> figures and are not absolute. Only the difference is which counts not
> the number in itself.
[snip]
> A very easy to implement correction would be to lower the K-factor
> further, which is now fixed after 400 experience points. I think luck
> induced swings of +/- 25 points would be acceptable, so the factor
> should be reduced until it is a quarter of the current value.
If you reduce the K factor by a quarter, would you not obtain exactly
the same rating order wrt the previous case, but only a bit tighter?
While you claim (and I fully agree) that what is important is the
relative ratings of the players, your modification does not change the
relative positions at all. Am I missing something?
David desJardins
> So let me get this straight. If the person joining really should
> be rated at 1500, that will still drive up the ratings of the others?
Yes. The effect doesn't depend on inaccuracy of the initial ratings,
although that's certainly a factor. Even if you could build a psychic
computer which always started each player off at that player's "true"
rating (based on the norms currently in effect, since this is
time-dependent), a player might subsequently happen to have a run of bad
luck, leading to a depressed rating. If that player then quits, and
rejoins at the "true" rating level once again, then excess rating points
have artificially been introduced into the system, which raises
everyone's "true" rating by a fraction of a point.
Conversely, if players with inaccurate *high* ratings quit, and rejoin
with a lower rating, then everyone's rating will go down. It's only
human nature that makes that happen less often.
Of course, some of the quitters are players created intentionally to
lose, and those players of course do join with a rating much higher than
their "true" rating. That would be true even if you started them at 0.
David desJardins
highlander
> And even ANOTHER word (fact) that gets over(mis)used. Of course
>if you say it loudly enough (how about shouting "FACT"), beat your
>chest a few times, and glare at the person you're trying to convince
>maybe it will work. Not here, though.
flaming people is a great thing, heh ....
but a fact remains a fact - if you like it or not ... sorry
but FACT remains a FACT
highlander
p.s. get a math book for beginners, skip the introduction, and start reading
highlander
OSMAN schrieb in Nachricht <367806...@prodigy.net>...
>Do you need to make a correction for those abandoners who are over 1500
>rating?
no - thats in the sum :-)
highlander
i want to prove that there is no upper limit.
- but i can not prove that, so i try to that there is in fact an upper limit
...
(proving the controverse, or something ;-) )
there is only 1 player "A" registered at fibs. his rating is 1600. the
average on fibs is therefore 1600
a new player "B" logs in and brings new 1500 points to the pot.
- the average drops to 1550 what a shame.
"B" is a bad player and loses most of his matches, his rating drops
somewhere at 1300. "A" has 1700 points.
the loser abandons his player "B". the average on fibs is now 1500 as long
as "B" is subscribed ! if "B" is deleted by the SYSOP the average will be
1700.
guess what comes now. "B" creates "C", drops to 1300, creates "D" drops to
1300 , and so on ...
"A"s rating will increase every time so there is no upper limit. the
average of course will increase as well as soon as a player is eliminated
(not only abandoned)
if a new 1500 player wins a match against a 1800 player. he will win more
points than the other loses ...
more ENERGY is created.
If he loses, he will lose less points than he could have won. the ENERGY is
not destroyed
----
bottom line
there is no upper limit on FIBS ! - chuck - i could shout, but thats an
email, so it won't do any good and
that's an other FACT
sorry
highlander
Alexander Nitschke
>
> > A very easy to implement correction would be to lower the K-factor
> > further, which is now fixed after 400 experience points. I think luck
> > induced swings of +/- 25 points would be acceptable, so the factor
> > should be reduced until it is a quarter of the current value.
>
> If you reduce the K factor by a quarter, would you not obtain exactly
> the same rating order wrt the previous case, but only a bit tighter?
> While you claim (and I fully agree) that what is important is the
> relative ratings of the players, your modification does not change the
> relative positions at all. Am I missing something?
>
(only the K-factor changes in my suggestion), the rating differences
have to be the same. Only the velocity of rating changes is slowing, and
so are the luck swings.
--
Alexander Nitschke
Murat Kalinyaprak
>In <756jej$ll9$1...@news.chatlink.com> Murat Kalinyaprak wrote:
>The system _can_ be manipulated and we can't stop that, but it's not
>because the system is bad, it's because there are some people that
>will abuse any system.
The system has other problems besides abuse by people. I think
we need to judge the system in terms of what it accomplishes. If
we want a system that provides an optimistic/utopic environment
based on an arbitrary "magic" formula, then everything is fine. But
if we want a system that provides resonably accurate ratings of bg
skill, than I would say that the current system is not fine.
>The system cannot predict exactly the expected winning chance between
>any pair of players for any length match (see my posting on a perfect
>system) but I'm not trying to prove that it can. (Of course proving
>that it *doesn't* predict winning chances accurately is also hard since
>we don't know the correct winning chances -- all we can do is observe
>the outcome of matches.
There are multiple problems with the current system and I'm coming
to believe more and more that the combined effect of all of which is
enough to render the resulting ratings mostly meaningles. More and
more people seem to be participating in these discussions and
realizing/making a variety of valid arguments on the deficiencies,
biases, etc. of the existing system.
For example, if two old buddies find each other on the Internet and
decide to play bg on FIBS as they used to in the old days of real life,
if they are of eaual stregth and let's say of 1800 "true rating", as long
they play exclusively against each other, 100 yeras from now FIBS
would tell us that they are both rated at 1500. I'm happy to see that
lately writers are wording their arguments more carefully/precisely
like saying "the system would work reasonably well if the majority
of players play against a good variety of opponents randomly", etc.
The problem is, the system doesn't incorporate any policy to ensure
such conditions are met and we have absolutely no idea who is who,
who joins or quits how many times over at what final rating, who is
playing against whom what kind of matches, etc. At the end of the
day, many people still argue that it works reasonably well despite it
all. What kind of teflon system is this that nothing sticks to it...?
We know that it's not a "measuring system" because it has no unit
of mesaure.
We also know that it's not a rating system as the concept/term would
be understood by the general population regarding rating systems
in general. Whether is brightness of light bulbs, horse-power of
engines, print speed of printers, people assume that 50 is half of 100.
For example two printers *rated* at 10 page per minute will output an
equal amount to two other printers rated at 12 and 8 pages per minute.
As it has been explained to me:), this is not the case with the FIBS
"rating" system. There are other cases where the term "rate" is used,
such as irregular tax or insurance rate tables and FIBS system may
be one such rate table at best.
In many cases, players are just ranked based on all playing the
same amount of games, winners simply winning points while
loosers don't loose points, etc. But I don't think FIBS rating system
can even be said to be an accurate ranking system.
So, the question becomes: what really is it and what does it do...?
>So... if you can show through random play that people become 400
>points for any length of time, then I will agree there's something
>wrong with the system.
I can't prove or demontrate it but at least I'm questioning and also
making a not so impossible suggestion that very large volume
players, like robots, could/would hit on overrated 1500 players
enough times that this could/would happen unintentionally as well.
Again, this is focusing on one of the many problems with it. Still,
even much less than 400 points may be unacceptable to some
people. What if some clusters of players were only overrated by
100 points? Would that be acceptable to you? Recently, other
writers in other threads wrote some pretty good stuff about many
possible biases, inluding such clustering of users, etc. If one
tries to consider them all at once, it looks like a tangled fishing
line. I don't think one could begin to even roughly estimate what
the combined effect of all of them may amount to...
>But in any case, if you're going to use someone else's assertion as a
>building block in your own argument that there's a problem with the
>rating system, you better be willing to adequately prove that they are
>correct. Otherwise I'll just say "I heard on the street that the system
>is fair" therefore it's fair. :-)
I'm not really trying to build an argument based on other people's
assertions but more likely trying to toss it all in the air to see where
they will all fall in place. For example, at one time I had argued
that the system was so complex that players needed an on-screen
winning-chances calculator to pick their opponents. At that time, I
was explained:) that it wouldn't matter which opponent a player
picked because the system was self-adjusting, self-correcting,
self-this, self-that, zero-sum, bla, bla... But we know very well that
it matters whom you play against, and we know this even better
after the very same people explained that one's winning chances
against two 1600 rated players are not the same as against one
1500 and one 1700 rated player...
Sometime I feel like all I have to do is to switch to arguing that
FIBS rating is perfect and works well, and let others argue/prove
back to me the opposite... :) If I have to admit, lately some of my
arguments have been bordering this strategy...
>.............
>Yes. Some people cheat. But for those that don't cheat,
>the system works incredibly well at ranking people by skill.
I skipped a lot of what you wrote because either I agree with them
or have nothing new to say about them. But it's interesting that at
the end it still comes to your saying this. Any arbitrary formula
based on the same philosophy as with the FIBS's formula will
self-fulfill. The question is whether its output will have a reasonably
close resemblance to reality. Never mind (if you wish) what I wrote
on the subject, but many other writers also made numerous valid
arguments that would make it difficult for anybody to insist that the
FIBS rating works incredibly well (at accomplishing anything). I
guess I may not be too far off when calling it a "teflon system"...
MK
Gary Wong
> We know that it's not a "measuring system" because it has no unit
> of mesaure.
Yes it is, and it does. It measures ratios between probabilities of
winning -- this makes a rating point just as valid a unit of measure
as the decibel. For one point matches, 200 rating points is 1 dB;
for 64 point matches, 25 points is 1 dB.
> We also know that it's not a rating system as the concept/term would
> be understood by the general population regarding rating systems
> in general. Whether is brightness of light bulbs, horse-power of
> engines, print speed of printers, people assume that 50 is half of 100.
> For example two printers *rated* at 10 page per minute will output an
> equal amount to two other printers rated at 12 and 8 pages per minute.
You're right that rating points do not behave like pages per minute.
Think in terms of ratios or logarithms or decibels -- two identical
amplifiers, one set to a gain of +8 dB and the other at +12 dB will
not produce the same total output as two at +10 dB each. (Incidentally,
brightness of light bulbs works in a similar way. The _luminance_, or
luminous intensity per unit area, of two identical light bulbs is
twice that of one light bulb; but the _brightness_, how much "light" a
human perceives, is not -- the first light bulb contributes far more
brightness than the second.)
Rating points behave like light bulb brightness and amplifier gain; they
do not behave like printer pages or light bulb luminance. Just because
it is nonlinear does not mean it is wrong :-)
Cheers,
Gary.
--
Gary Wong, Department of Computer Science, University of Arizona
ga...@cs.arizona.edu http://www.cs.arizona.edu/~gary/
Chuck Bower
highlander <highl...@immortal.com> wrote:
Well, I took your advice. I went and got that "beginner's" math
book, skipped the intro, and read the whole thing. Now I condiser myself
enlightened, although I'm sure that I'm still a long way from making
it to your level. I didn't find there where "fact" was defined. I did
find an interesting thing, though.
Start out with 1/2. Add to that 1/2 of 1/2. Sum = 3/4.
Add to that 1/2 of 1/2 of 1/2. Sum = 7/8.
Continue to do this until you get tired. The sum will ALWAYS increase
as long as you add more terms, but guess what. It never reaches 1.
(I'm not sure if that is a "fact" or not, though.)
Thus I learned in this elementary math book (and thanks again for
your recommendation) that something can increase forever, but still
not necessarily increase without bound.
So, which math book do you now recommend that will show me that
your above argument is a proof? (And even more important, a fact??)
David desJardins
>> there is no upper limit on FIBS ! - chuck - i could shout, but thats an
>> email, so it won't do any good and
>> that's an other FACT
>
> Add to that 1/2 of 1/2 of 1/2. Sum = 7/8.
>
> recommendation) that something can increase forever, but still not
> necessarily increase without bound.
Obviously "highlander" doesn't have a rigorous mathematical background,
and you can quibble with him forever, if it makes you feel good. But
the truth of the matter is obviously correct, and I can't believe you
aren't smart enough to see that already. So what's the point of the
quibbling?
THEOREM. Suppose that player A has rating ra, and player B has rating
rb. Set a "target rating" rt for player A. Then there is a finite
number N, depending on ra, rb, and rt, such that, if player A wins N
consecutive matches from player B, player A's rating will exceed rt.
PROOF of THEOREM. By conservation of rating points, if player A and B
always play one another, then when player A has rating x, player B will
have rating y such that x+y = ra+rb. Suppose that player A wins n
consecutive matches from player B, and that player A's rating never
exceeds rt. Then player B's rating never falls below ra+rb-rt, and the
rating difference between A and B never exceeds 2*rt-ra-rb.
In the FIBS rating system, if one player defeats another, then the first
player always gains a positive number of rating points. Furthermore,
the number gained is a monotone nonincreasing function of the rating
difference between the players. Let the number of rating points gained
when the rating difference is 2*rt-ra-2b be rg (for "gain"). Then, by
the hypothesis, player A gained at least rg points in each of n
matches. Therefore player A's rating is at least ra+n*rg.
Choose N such that ra+N*rg >= rt. Then player A's rating after N wins
must be at least rt. QED.
COROLLARY. Suppose that player A plays an infinite series of matches
against player B, always winning. Then player A's rating increases
without bound.
PROOF of COROLLARY. Suppose that player A's rating is bounded above by
an upper bound U. Apply the theorem above, with rt=U. Then after N
wins, player A's rating would exceed U, a contradiction. QED.
Was that really so hard?
David desJardins
Alexander Zamanian
>
> THEOREM. Suppose that player A has rating ra, and player B has rating
> rb. Set a "target rating" rt for player A. Then there is a finite
> number N, depending on ra, rb, and rt, such that, if player A wins N
> consecutive matches from player B, player A's rating will exceed rt.
>
> PROOF of THEOREM. By conservation of rating points, if player A and B
> always play one another, then when player A has rating x, player B will
> have rating y such that x+y = ra+rb. Suppose that player A wins n
> consecutive matches from player B, and that player A's rating never
> exceeds rt. Then player B's rating never falls below ra+rb-rt, and the
> rating difference between A and B never exceeds 2*rt-ra-rb.
>
> In the FIBS rating system, if one player defeats another, then the first
> player always gains a positive number of rating points. Furthermore,
> the number gained is a monotone nonincreasing function of the rating
> difference between the players. Let the number of rating points gained
> when the rating difference is 2*rt-ra-2b be rg (for "gain"). Then, by
> the hypothesis, player A gained at least rg points in each of n
> matches. Therefore player A's rating is at least ra+n*rg.
>
> Choose N such that ra+N*rg >= rt. Then player A's rating after N wins
> must be at least rt. QED.
>
I think see a flaw in this proof. rg is not a constant. As n increases
rg decreases. n*rg may have a maximum value, for instance:
If rg = 1/n, then the maximum value of n*rg is 1.
Therefore it may not be possible to "Choose N such that ra+N*rg >= rt"
>
> Was that really so hard?
>
It's probably not hard to prove or disprove your theorem, but I suspect
the proof must contain the FIBS rating formula, or a tighter description
of the FIBS rating formula -- I suspect that there are some rating
formulas that are nonincreasing functions of the rating difference, and
always give a positive number of rating points to the winner, but will
cause player A's rating to converge.
-Alex
--
Alex Zamanian
azam...@bbn.com
adz...@dartmouth.edu
A win an infinite sequence of consecutive matches against B in the condition
for the corollary to hold, because you seem mathematically inclined enough
to know that that requirement can't happen. I think that some people here
who are trying to think of ways that ratings can increase without bound might
overlook the condition.
Claim - If a player A plays against player B an infinite sequence of games,
and if player B wins each game with a non-zero probability, then player B
will eventually win a game
Proof - Suppose player A wins with probability Pa < 1. Let Pi denote the
probability that player A wins an infinite sequence of consecutive games, and
suppose Pi > 0. Then there is a number N such that Pa^N < Pi. Since games
are independent events (player B isn't getting so flustered at losing that he
completely loses it. :-) ), Probability (player A wins N consecutive games) =
Pa^N. Pi = Probability (player A wins N consecutive games) * Probability (A
wins the remaining games). Prob (A wins the remaining games) <= 1, so
Pi <= Pa^N * 1. But, Pa^N < Pi by our choice of N. Hence, Pi = 0.
Not that this shows that it's impossible to have a rating increase without bound;
I attempted to do that in an earlier post, based on how, in order for a rating
to increase without bound, a player must win with a probability approaching 1.
I'm not diligent enough to check up on replies about if there was anything
wrong with my argument there, though. But regardless, if every player's rating
is bounded, then so is the average; the average can never exceed the highest
player's rating.
Adzuki