FIBS ratings formula
Albert Steg (Winsor)
I've been trying to get a feel for how ratings points are awarded or
deducted in various matches. I'm not enough of a mathematician to
"understand" the formula --I can read it and plug in the numbers, but I
don't have a feel for how it works. I know it takes into account the
players' ratings, experience, and the lengthg of the match. . .
. . .but the resul6ts always seem a bit mysterious to me. Today I got tired
nudging up and down by 5-10 points playing 3 or 5 point matches against
people with ratings within 50 pts. of my own (1570 at the time). So I
decided to play a 7-pointer against a player rated over 1700. I won and got
. . . 9 points. My opponent lost 10 points. I though I would be more
heavily rewarded for besting a more highly-rated opponent in a somewhat
longer match.
. . .Next I was invited to a 3-pointer by a player rated around 1480. I won
th match and got something like 4 points --and he got whacked for 10 points!
Golly! A player rated 100 points below me got raked for the same amount in a
3-point match as a player 150 points *higher* than me lost for losing a
7-point match! This seemed intuitively peculiar to me.
I'm not complaining! I'm sure the formula makes good sense, and it
works the same for everybody. I'm just wondering what my best "strategy"
for improving my rating is, in terms of the opponents and match lengths I
play. Many short matches against peers at my level? Bigger mnatches
against highly-rated players (assuming that my standard of play is, indeed
on a par with theirs --for the sake of argument)?
I'd appreciate any insights.
Albert
--
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Kit Woolsey
for newer players. One of the ideas behind the ratings formula is to
move the inexperienced players ratings faster, so they find their level
more quickly. Once a player has 400 experience, the multiplier is 1 so
that doesn't matter. No doubt the 1400 player you beat had low
experience, which explains why he lost so many ratings points. If both
you and your opponent have over 400 experience points you will win what
he loses or vice versa, and that will be determined by the match length
and the difference between your ratings as described in the formula.
Kit
Patti Beadles
the experience level of each player, the current rating of both
players, and whether the higher-rated or lower-rated player wins.
Experience figures into this in an interesting way. For players with
400 or more experience points, there's no influence. For players with
less than 400, the experience turns into a simple multiplier. Your
experience affects your rating change only, not that of your opponent.
Here are a couple of tables showing the ratings change for various
match lengths and ratings differences. Note that you need to use a
different table depending upon whether the higher-rated or lower-rated
player wins.
Ratings change when higher-rated player wins,
assuming 400+ experience.*
diff 1 3 5 7 9 11
---- -------- -------- -------- -------- -------- --------
100 1.884998 3.119854 3.899648 4.491772 4.974016 5.381994
200 1.770753 2.782339 3.345620 3.727760 4.006327 4.216725
300 1.658005 2.457773 2.826207 3.029076 3.142692 3.201313
400 1.547453 2.151421 2.353534 2.415209 2.409120 2.366478
Ratings change when lower-rated player wins,
assuming 400+ experience.*
diff 1 3 5 7 9 11
---- -------- -------- -------- -------- -------- --------
100 2.115002 3.808349 5.044624 6.091233 7.025984 7.884505
200 2.229247 4.145864 5.598652 6.855246 7.993673 9.049774
300 2.341995 4.470430 6.118065 7.553929 8.857308 10.065186
400 2.452547 4.776783 6.590738 8.167797 9.590880 10.900022
* For a player with lesser experience, multiply the number in the
table by -experience/100+5, e.g. for 200 experience, 3.
So if a 1500 player beats a 1700 player in a 3-point match, I would
look in the table and find that for a 3-point match, lower player
wins, 200 difference, the change is 4.15 (rounded.) If the 1700
player won, the change for both players is 2.78.
-Patti
--
Patti Beadles |
pat...@netcom.com | Most of my friends are
pat...@ichips.intel.com | aristophrenic lexiphanes.
or just yell, "Hey, Patti!" |
Ellen Savyon
[new players factor explanation deleted]
: If both
: you and your opponent have over 400 experience points you will win what
: he loses or vice versa, [...]
That is correct, but it contradicts with the 'help formula' text .
In the formula, P is the probability that underdog wins, and
although it is calculated (try 'toggle ratings'), it is not
factored into the real results . That way, winning a 1400 player
or a 1800 player gives the same increment in rating .
For all of you who asked me why I don't include ratings based
statistics in my lists, this is one (quite heavy) reason .
- muni . mu...@cibadiag.com
Stephen Turner
|> Kit Woolsey (kwoo...@netcom.com) wrote:
|> : If both
|> : you and your opponent have over 400 experience points you will win what
|> : he loses or vice versa, [...]
|>
|> That is correct, but it contradicts with the 'help formula' text .
|> In the formula, P is the probability that underdog wins, and
|> although it is calculated (try 'toggle ratings'), it is not
|> factored into the real results . That way, winning a 1400 player
|> or a 1800 player gives the same increment in rating .
|>
Sorry, muni, this is just not true. If both players have over 400
experience, the amount lost by the loser is the same as that gained
by the winner. But if a low player beats a high player, more is
exchanged than if the high player beats a lower player. That's how
P gets into it.
Stephen Turner
Stochastic Networks Group, Statistical Laboratory,
University of Cambridge, CB2 1SB, England
e-mail: S.R.E....@statslab.cam.ac.uk
Stephen Turner
I have been meaning to ask. I guess it's aimed mainly at the mathematicians
in the group.
Suppose that two players had a certain fixes ability, and only ever played
each other, and we let their ratings settle down. Suppose also that
all their matches were always the same length (all 5 points, for
example). Then the formula will guarantee that when they play, each will
have a change of points that has zero expectation.
Now suppose they play a longer match. Presumably the better player is
more likely to win than in the shorter match, because there is less
statistical effect in a longer match, but where does the formula
P_upset = 1/(10^(D*sqrt(n)/2000)+1)
(as a function of n) come from. Is there any basis for it? If it's not
right, then the expected number of points exchanged is not zero in the
longer match, and the two players will care about what length match
they play.
Another question is, is the formula correct as a function of D? This
is important if we have a server with more than two players!
Ellen Savyon
: In article <33921g$r...@sundog.tiac.net>, El...@max.tiac.net (Ellen Savyon) writes:
: |> That is correct, but it contradicts with the 'help formula' text .
: |> In the formula, P is the probability that underdog wins, and
: |> although it is calculated (try 'toggle ratings'), it is not
: |> factored into the real results . That way, winning a 1400 player
: |> or a 1800 player gives the same increment in rating .
: |>
: |> - muni . mu...@cibadiag.com
: Sorry, muni, this is just not true. If both players have over 400
: experience, the amount lost by the loser is the same as that gained
: by the winner. But if a low player beats a high player, more is
: exchanged than if the high player beats a lower player. That's how
: P gets into it.
Of course I was wrong - silly me . And I could swear that
one player had P and the other 1-P ...
Thanks, Stephen, for pointing this out .
- muni . mu...@cibadiag.com
Jason Lee
>
>I've been trying to get a feel for how ratings points are awarded or
>deducted in various matches. I'm not enough of a mathematician to
>"understand" the formula --I can read it and plug in the numbers, but I
>don't have a feel for how it works. I know it takes into account the
>players' ratings, experience, and the lengthg of the match. . .
The formula is strikingly similar to the formula used by the USCF (United
States Chess Federation) in computing their ratings. That system is
generally credited to Arpad Elo, and thus you will occasionally hear chess
players and see chess literature refer to "Elo rating".
There is actually strong mathematical reasoning behind the formula, although
offhand I don't know exactly how it works.
Apologies for bringing up chess in a backgammon newsgroup.
JLee
--
| Jason Lee jp...@galaxy.csc.calpoly.edu |
| |
| "If you don't play to win, why keep score?" |
| Vernon Law, Pittsburgh Pirates pitcher |
Ed Rybak x84336
Stephen Turner <sr...@statslab.cam.ac.uk> wrote:
> P_upset = 1/(10^(D*sqrt(n)/2000)+1)
>(as a function of n) come from. Is there any basis for it? If it's not
>right, then the expected number of points exchanged is not zero in the
>longer match, and the two players will care about what length match
>they play.
>
>Another question is, is the formula correct as a function of D? This
>is important if we have a server with more than two players!
The FIBS ratings have a Gaussian distribution...this is obstensibly because
the the above formula maintains them that way but I haven't taken a close
look (i.e. tried to rediscover Math. Stat. II ;-) Incidently the mean
rating several weeks back was roughly 1525. I attributed the drift from
the expected value of 1500 as bias created from users being evicted after
100 days of non-use. I reasoned that more than not these users were low
ranking.
Ed Rybak
Sequent Computer Systems
15450 SW Koll Parkway
Beaverton, OR 97006
phone: (503) 578-4336
fax: (503) 578-3811
ry...@sequent.sequent.com
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