Assigning Player Order in Tournaments
Mountain Mike^^
Ron205 wrote in message <19991105023256...@ng-cd1.aol.com>...
yes........hm.........ok.........right.........sounds
good..............nice........pretty fair............
MM^^<--gettin' back on drugs.
Ron205
comment too. Some time ago we were discussing tournament charts, and I said
that I thought that some tournaments might benefit from using something other
than a "random" order of player assignmants. I've thought about this a little
more, and here is what I've come up with. There are 3 different player
assignment orders described below.
1) Random Order: This is appropriate for larger tournaments where all
participants are considered "equal".
2) Seeded Order: This is appropriate when some players are supposed to be
rewarded in some sense for prior performance. One example of this might be a
playoff tournament, where the player (or team) assignments is based on the
season rankings.
3) Group Order: This is where two or more players can sign up and be assured
that they will meet each other as late as possible in the elimination
procedure. For example, a father and son could enter a tournament, and they
would know that one of them would be in the top part of the bracket, and the
other would be in the bottom bracket.
For Random Order assignment, the usual way to assign player positions is by a
blind drawing. Most pool tournaments use a pill bottle, or they shuffle
numbered cards. Spreadsheets usually have some kind of RAND() function that
can be used to generate random permutations.
For Seeded Order assignment, the higher ranked players are rewarded by being
paired with lower ranked players. Here is a recursive way of determining the
appropriate order for any number of players. Start with two players, the
trivial case.
S2: 1, 2
Now, the four player order is determined by splitting the two-player order,
(1,*,2,*), and filling in the opponents in reverse order, with the highest
players being paired with the lowest players.
S4: 1, 4, 2, 3
The eight player chart is generated the same way, splitting the four-player
order, and filling in the opponents in reverse ranking order.
S8: 1, 8, 4, 5, 2, 7, 3, 6
Note that the sum of the ranks of the two first-round opponents is always equal
to the number of players plus 1. This makes the fill-in simple. It is
straightforward to generate the order for any number of players this way. If
the number of players is not a power of 2, then byes are assigned to the last
slots. For example, with 6 players, players 7 and 8 in the above S8 chart are
replaced by byes.
For Group Order assignment, the algorithm is similar. Start first with the
trivial two-player order. The four-player order starts by splitting the
two-player chart (1,*,2,*) as before, but the fill-in is done a little
differently. The four player order is
G4: 1, 3, 2, 4
The order is different from the Seeded Order because player 3 should be
separated as far as possible from the adjacent player 2. The eight-player
order is
G8: 1, 5, 3, 7, 2, 6, 4, 8
The goal with the fill-in is to separate adjacent players as far as possible.
Notice in this order that the difference (not the sum) of the player numbers in
the first round are all the same (4 in the G8 order). In the general case,
this difference is given by the number of players divided by 2.
If "m" players sign up together, then their relative order should be assigned
randomly, and then they should fill in the chart based based on the above
algorithm. That is, they should not be allowed to choose which branch of the
chart they go in, but rather they only can be assured that they will play
against other players in their subgroup as late as possible in the tournament.
Similarly, individual players (subgroups of 1) should be assigned as randomly
as possible. This seems pretty simple to me if the subgroups are only 1 or 2
players big, but if you have several larger subgroups (say several
father-mother-son-daughter subgroups), it seems like it gets complicated. One
method for assigning these might be to assign players in the large groups
first, then the smaller groups, and finally the individual players (m=1
subgroups).
Of course, it should be made known ahead of time that the TD will allow this
kind of grouping of players. That is the point, it should be regarded as an
advantage to players who are "partners" of some kind. I have seen it happen
often, for example, that a father and son are paired in the first round of the
tournament. They sometimes feel that they could have just stayed home and
played on their home table instead of driving to the tournament and paying two
entry fees, since one of them must be eliminated after the first match.
The above recursive algorithms are pretty straightforward, but it would be
simpler if there were some closed-form expressions that would give the player
orders. These things look like perfect-shuffle algorithms that sometimes show
up in, for example, fourier transforms, but I don't know if these algorithms
are any easier to use than the above recursive algorithm.
I would appreciate any comments and suggestions on these player orders. Are
there better ways to achieve these goals? Does the process seem fair? In the
Group Order case, do you think this would be enough of an improvement over
random order to attract father-son or husband-wife players to tournaments in
which they might not enter with random order?
$.02 -Ron Shepard
MIKE JANIS
explain, while many tournaments are open and anyone can play it is almost
always assumed that there will be a few top players that are better than the
rest of the crowd and not all players are equal. Here is a format for
seeding players in this situation: (assuming there is a Calcutta), you take
the top picks in the Calcutta and seed only them into different parts of the
tournament bracket, then you do the draw for the rest of the players. This
usually makes for some awesome final rounds for spectators, unfortunately
for the other players (the majority of the crowd) this isn't fair, because
the chances are the best players will almost always meet in the end.
I myself prefer the luck of the draw. There is nothing like the two top
players at a tournament facing off first.
MJ
Ron205 <ron...@aol.comNOSPAM> wrote in message
news:19991105023256...@ng-cd1.aol.com...
Ninebal310
Hustlin' Hank
greg miller
Ron205 wrote:
[...]
> 1) Random Order: This is appropriate for larger tournaments where all
> participants are considered "equal".
> 2) Seeded Order: This is appropriate when some players are supposed
to be
> rewarded in some sense for prior performance. One example of this
might be a
> playoff tournament, where the player (or team) assignments is based
on the
> season rankings.
I know you are talking about 'equal' in the sense that there is no
special consideration given to any individual as to where to position
him in the first round. But how about the case of a handicapped
tournament, where all the entrants are really equal by way of their
ratings? Is there a difference here if they are placed randomly as
opposed to being arranged in some order? I have always thought that
any arrangement would be fair. I have a weekly SE handicapped
tournament in which the byes are evenly distributed and then the
players are seeded top to bottom by skill level. This insures one of
the finalists to be from the lower half of the skill pool. Maybe it's
not fair. I don't know.
[...]
> For Group Order assignment, the algorithm is similar. Start first
with the
> trivial two-player order. The four-player order starts by splitting
the
> two-player chart (1,*,2,*) as before, but the fill-in is done a
little
> differently. The four player order is
>
> G4: 1, 3, 2, 4
>
> The order is different from the Seeded Order because player 3 should
be
> separated as far as possible from the adjacent player 2. The
eight-player
> order is
>
> G8: 1, 5, 3, 7, 2, 6, 4, 8
>
> The goal with the fill-in is to separate adjacent players as far as
possible.
> Notice in this order that the difference (not the sum) of the player
numbers in
> the first round are all the same (4 in the G8 order). In the general
case,
> this difference is given by the number of players divided by 2.
This can be used for a seeding arrangement also. The above seeding
method matches the top half against an inverted bottom half, this
method matches the top half against the bottom half evenly.
Ron205
>Hustlin' Hank
Would you explain why you believe this?
Also, do you not see any possible advantage (as far as attracting participants
to a tournament) to being able to play in a tournament with your wife, son, or
daughter, and know that you will not be paired up first round?
$.02 -Ron Shepard
FBrent1972
wrote:
I can see both sides. Looking at it from the lesser player's view, why would
they have to pay the same to enter a tournament and the other player get an
advantage? The lesser wants a chance at the money also. But, I don't have the
answer, just a question. Do you want more players in a tournament or better
players in the tournament?
Frank Brent
Ron205
I have seen this done, and I have never really understood what was the purpose
as far as tournament participation. Is it to attract stronger players from
longer distances (since they know they will have a weaker opponent first
round)? Is it to ensure that the weaker players get a better chance to play a
big-name player? Since you did it with the calcutta players, is it to
encourage participation in the calcutta auction (since they know that the
players they bid on will be "protected" from each other in early rounds)?
BTW, the Group Order method could be used to seed these players too. The goal
is the same, namely, to separate players in the subgroup as far as possible
from each other in the chart.
There was a discussion a while back regarding an Earl Strickland interview. He
was complaining about the pros having to play young/unknown opponents first
round, and he thought that pros should be given byes in early round matches to
"protect" them. I did not follow his reasoning. Other than protecting his own
self-interest, and giving him personally a better chance to cash in the
tournament, I don't see how this practice would help tournament participation
or add to spectator excitement. I can see why this is done in some other
sports, where early round injuries could hurt the pro's career more than the
amateurs, but this argument does not apply to pool; there aren't THAT many
injuries resulting from a pool match.
$.02 -Ron Shepard
Ron205
include both single-elimination and double-elimination tournaments. Is there a
reason to treat the two differently with respect to nonrandom player orders?
$.02 -Ron Shepard
Bob Jewett
: Blind Draw is the ONLY fair way to do it.
It is certainly fair in the sense of treating all players equally, but there
are several other points.
In tennis, do you really want to see the top four seeds in the same
starting group of four? Well, maybe you do if you have tickets to the
first rounds of play, but the promoter and sponsors and TV (if any)
would much prefer the top players to meet in the finals.
If a pool tournament is a "put your $20 in to play for, and the only
spectators are the people you drove up with" kind of event, then I
agree that blind draw is the best way to go.
You will also often get an argument from the top players that they have
spent so much more time and effort perfecting their games than the
average player that they deserve not to be paired against other top
players in the first round. And I would agree with them (but not for
those exact reasons, which are often false) in a tennis-like situation,
as in the first point above. If it's a little local tournament, I say
let them take their chances. In that situation, it is the weak players
who are supporting the better players, and if you guarantee that the
weak players can never advance by getting a lucky draw, you may lose
them.
Bob Jewett
Ron205
>I can see both sides. Looking at it from the lesser player's view, why would
>they have to pay the same to enter a tournament and the other player get
>an
>advantage? The lesser wants a chance at the money also. But, I don't have
>the
>answer, just a question. Do you want more players in a tournament or better
>players in the tournament?
Good question. Partial seeding and Group orders could also be applied to tour
points, or, in a local tournament, simply to the number of times a player has
entered. In this situation, the partial seeding would give such players an
advantage (although perhaps only a slight one in this case), but at the same
time it would be an incentive for players to enter the tournament more often in
order to accumulate the points and to earn that advantage.
In a handicapped tournament, I would rather play stronger players than weaker
players. If the chances of losing are the same (meaning a fair handicap), I'd
rather play a good player than a bad one. The victory is sweeter and the loss
is easier on the ego. I sometimes don't even like it when I draw a bye; I'd
rather play and lose now, than wait an hour, and then play and lose, and I'd
rather play and win than sit and wait. Of course, not all players think the
same way about this. I only compete in tournaments once a week (with a few
exceptions here and there), so I don't want to waste any time while I'm there;
other players get to play every night, so, compared to me, they are more
focused on the prize money than the playing.
$.02 -Ron Shepard
Ninebal310
Any player who complains about the "draw" they get in a blind draw tourny is a
cry baby. If the 2 top seeded have to play each other, so be it. If the weakest
has to play the strongest, so be it. The weaker MAY learn something. I almost
entered teh latest Viking 9ball tourny that Mike Janis had here in Columbus
Ohio. I would have loved to draw the strongest so that I could learn and get
some experience. Most people are not like me and they actually think they could
compete with the big boys. I do understand that it wouldn't be fun if I went to
a tourny and had to play my best friend, but that's the way it goes! The
"cream" will rise to the surface in the later rounds and some of the "cream"
will get lost in the process. Nobody wins them all. JMO
Hustlin' Hank
Ninebal310
>
>Would you explain why you believe this?
>
>Also, do you not see any possible advantage (as far as attracting
>participants
>to a tournament) to being able to play in a tournament with your wife, son,
>or
>daughter, and know that you will not be paired up first round?
>
>$.02 -Ron Shepard
>
Funny that you should mention family members. I have been in tournaments and
had to play my wife and my daughter. These were little local tournys, race to 1
and I have lost to both. I just can't see why any other way would be justified
even in the Pro tournys. Should Corey Duel (when he was an unknown) have to
play all the stronger players early in the tourny? If Corey drew Earl in the
first round out in Tulsa, the spectators that only went the first day would be
the lucky ones. So therefore, it is equal for the fans too!
Hustlin' Hank
Ed Mercier
your discussion. I will add a little to it. One other reason to "non-randomly"
place people on a tournament chart is due to time restrictions. For the Master's
division at the Milwaukee Journal Sentinel Sports show, some players start on
Thursday, and some players start on Friday. Almost no players have to play both
days the way it is set up. When I send out the tournament announcements, I tell
the players if they can't play on Thursday they should let me know with their
sign-up sheet. Then when I'm ready to do the tournament draw, I randomly draw the
Friday Only players into random Friday starting spots. Then I draw every spot left
(both Thursday and Friday starts) for the remaining players.
I found the discussion from Mike Janis very interesting. Seeding the top players
from the calcutta into different parts of the chart would have a significant impact
on the value of those players. I would think it would make the logical bid amount
of those players markedly higher. This is something that should always be done
above board, if the bidders were not aware this was happening it would be
dishonest.
As I have said previously, I don't agree too much with seeding based on ability.
The stronger players in most tournaments already have a marked advantage, it is not
necessary to give them a bigger advantage. In fact, to the extent that it may
discourage weaker players from playing in the event, thus keeping the ultimate
payout smaller, if the stronger players were smart they would probably be against
it too.
I don't have as much of a problem with rewarding players who are at the top of
your point list, possibly because they play in many events, by awarding them byes.
We don't do it, but it would be fair as I see it.
If you were to promise to keep players who came together apart in the tournament, I
think it would take possibly two events before the stronger players agree to meet
in the parking lot before walking in to the event, walking in together, and then
saying they came together. In effect they would be able to implement their own
'seeding' system by this tactic.
One aspect of having these more complicated draws is that it introduces more ways
to make mistakes, and it could possibly add a little bit of time it takes to get a
tournament started. Overall these ideas are worth thinking about, but I haven't
found a really compelling need for them either.
Ed Mercier
President
http://playpool.com
Ron205
>and
>had to play my wife and my daughter. These were little local tournys, race
>to 1
>and I have lost to both. I just can't see why any other way would be justified
>even in the Pro tournys.
For this "Group Order" option, I had in mind smaller local tournaments. The
goal would be to encourage participation, particularly by family groups and
"significant others" and so on.
I had one bad experience like this. One of the better shooters in my 8-ball
league had never played in a tournament. I had been encouraging him to get his
feet wet and try it. Anyway, after a year or so he decided to try one. We
went to the room together, but I had intended to set out and just watch. He
talked me into playing, I think just so I wouldn't make him nervous or
something. This was a 16-player SE tournament, handicapped 8-ball, and as luck
would have it, we drew each other first round. He played well, but I made a
hard shot and got out in the last game. From his point of view, we payed two
entry fees and played one match. He said we could have just rented a table for
the same price and played all night. I admit that his heart might not have
been in it with me as his opponent, and I thought about dumping the match to
give him a chance, but all these things are just excuses. The real problem is
that there was no way in that tournament to ask to be put in different brackets
because the TD only did blind draws because he thought it was the most "fair".
I think it would have been better if we had had the option of going into
separate brackets, and I'm willing to give other players in similar situations
the same option (it is "golden rule" fair).
I don't think this Group Order option should apply to all tournaments; In
particular the Pro tournaments, which have more players than slots already,
couldn't really benefit from this as much as smaller local tournaments, which
generally need all the players they can get.
I think what I proposed in the Group Order option is both fair and still solves
this problem. Of course, it should be known ahead of time that this is done;
if it isn't advertised, then it seems not only unfair, but it can't take
advantage of its main benefit, namely to attract family groups and friends to
tournament competition. However, I'm not sure that my proposal is the best, or
simplest, way to achieve this goal. That's why I posted the method for
discussion.
$.02 -Ron Shepard
Smorgass Bored
I just LOVE your tournament chart idea with random & seeded pairings
(though I stopped reading half way through).
Please print me some charts for EVERY example from 10 players up to 256
players in each of the three catagories (and HURRY).
I'll pick them up at Planet 9-Ball.
thanks,
Doug W.
~>*)))>< Big fish eat Little fish ><(((*<~
greg miller
Ron205 wrote:
[...]
> For Group Order assignment,
The four player order is
>
> G4: 1, 3, 2, 4
>
> The goal with the fill-in is to separate adjacent players as far as
possible.
> Of course, it should be made known ahead of time that the TD will
allow this
> kind of grouping of players. That is the point, it should be
regarded as an
> advantage to players who are "partners" of some kind. I have seen it
happen
> often, for example, that a father and son are paired in the first
round of the
> tournament. They sometimes feel that they could have just stayed
home and
> played on their home table instead of driving to the tournament and
paying two
> entry fees, since one of them must be eliminated after the first
match.
Does the process seem fair? In the
> Group Order case, do you think this would be enough of an improvement
over
> random order to attract father-son or husband-wife players to
tournaments in
> which they might not enter with random order?
Suppose all players have an equal chance to win a given match, and two
players decide to be "brothers" and split any winnings. Also suppose
the entry fee was $1 and first place paid $4
In the G4 case, the expected returns for each of those players
(.5)*(2)-(.5)*(1)= .5
would be higher than the expected returns for each of the independent
players.
(.25)*(4)-(.75)*(1)= .25
(There's GOT to be a mistake in there somewhere.)
So it would be an advantage to pair up and split the winnings.
Gotta go.
White,Eric
algorithms. Clearly random assignment is fair. Clearly seeding is
appropriate for certain situations.
The group order, however, is somewhat impractical, IMO. First, you run
the risk of not being able to provide every individual with the same
consideration. For example, you have a tournament with a small number
of large groups. It would be impossible to guarantee that every person
gets to play somebody outside their group in the first round. Secondly,
it opens the door for suspicions of favoritism. If you cannot guarantee
everybody the same treatment, you will run into this problem. I do not
see how you protect yourself against this, without knowing ahead of time
that there will be no groups too large to fairly split up.
Additionally, if you enter a tournament, I think it is a fair
expectation to think that you could be playing anybody who entered,
including a friend or family member.
By the way, what is wrong with recursion?
JMO
-Eric White
John (Kent, WA)
seeded tournament. That is if I understand how it is done.
In a seeded tournament he will almost always get to play another amateur in
the second match (Assuming he lost his first match). If the tournament is
not seeded its possible he could play 2 pros in his first 2 matches.
If he is a seasoned amateur and would like to say he got pretty far in an
open tournament with a lot of pros entered, then I would think he could get
lucky in a blind draw and play only amateurs all the way to the money
rounds.
IMHO
I would expect the pro and new amateur to like the seeded tournament. The
seasoned amateur to like the blind draw.
FBrent1972 <fbren...@aol.com> wrote in message
news:19991105131042...@ng-fo1.aol.com...
> >ron...@aol.comNOSPAM (Ron205)
> wrote:
>
> I can see both sides. Looking at it from the lesser player's view, why
would
> they have to pay the same to enter a tournament and the other player get
an
> advantage? The lesser wants a chance at the money also. But, I don't have
the
> answer, just a question. Do you want more players in a tournament or
better
> players in the tournament?
>
> Frank Brent
Ron205
>The group order, however, is somewhat impractical, IMO. First, you run
>the risk of not being able to provide every individual with the same
>consideration. For example, you have a tournament with a small number
>of large groups.
Yes, this is the hard case. That's why I said that subgroups of one or two
players were pretty easy, but larger groups might be harder to squeeze together
fairly. Perhaps a TD could just allow up to two-player groups? That case
alone would take care of the vast majority of the problem situations.
>It would be impossible to guarantee that every person
>gets to play somebody outside their group in the first round.
Actually, this works out alright provided the subgroup is N/2 or less in size.
For example, with 8 players, groups of 4 or smaller can be accomodated so that
none of them play each other first round. The order is
G8: 1, 5, 3, 7, 2, 6, 4, 8
If you look at any sequence of four consecutive numbers (i.e. (1,2,3,4),
(2,3,4,5), etc.), they all avoid each other first round. Furthermore, there
are 5 possible positions for this group within the field, and it is easy to
enumerate them and choose them with equal frequency.
But, suppose you have a group of 4, a group of 3, and a single player. Now
there are fewer possible ways to squeeze them together, and I don't know a
simple method to enumerate them so that they are all choosen with equal
frequency (which I think is as "fair" as possible, given the group constraint).
In this simple case they are 1:3:4, 1:4:3, 3:1:4, 3:4:1, 4:1:3, and 4:3:1, but
with larger fields, it seems harder to choose each possible order with the same
frequency.
In mathematics, there is a similar problem called the "backpack" problem. It
is a well-known problem that is believed to be "Np-complete", meaning that the
only solution is to try all possible combinations, and then choose among them.
This Group Order problem might be Np-complete in the same way, I don't know.
However, in a practical sense, this may not be necessary. As long as the
method does not allow itself to be manipulated by the players, it may still
qualify as "fair", or at least fair enough to satisfy the participants. BTW,
the TD at the Sunday afternoon 9-ball tournament at Chris's used to allow
players to split into different brackets. Stu didn't have a real "algorithm"
for the draw, but whatever he did was fair enough so that no one complained.
What I'm suggesting is a slight generalization of this, along with trying to
find a good way to spread the groups out to be as fair as possible to everyone.
>Additionally, if you enter a tournament, I think it is a fair
>expectation to think that you could be playing anybody who entered,
>including a friend or family member.
Yes, this seems to be the common perception, but I think that is just because
everyone thinks a blind draw is the only practical option. I'm not sure this
is really the case. I think the group option has some practical advantages,
especially if you want to encourage family groups to participate.
$.02 -Ron Shepard
John (Kent, WA)
seeded tournament. That is if I understand how it is done.
In a seeded tournament he will almost always get to play another amateur in
the second match (Assuming he lost his first match). If the tournament is
not seeded its possible he could play 2 pros in his first 2 matches.
If he is a seasoned amateur and would like to say he got pretty far in an
open tournament with a lot of pros entered, then I would think he could get
lucky in a blind draw and play only amateurs all the way to the money
rounds.
IMHO
I would expect the pro and new amateur to like the seeded tournament. The
seasoned amateur to like the blind draw.
This paragraph has nothing to do with pool. I originally replied to this
thread yesterday evening. It never showed on my ISP's server. I am curious
if anyone sees this message twice.
Jtiche
meniton of pairing stronger players against weaker players in the opening round
as a way of rewarding the stronger players. I have to take issue with this. If
you are going to do this than you discriminate against a lot of locals and
discourage them from playing in the tournaments. You need more players, not
less. If I draw the toughest guy there, no problem if I drew him at random.
Occasionally I should draw a weaker player and have a chance to at least win a
match or two. Give me a break.
MarkO
John (Kent, WA) <joh...@foxinternet.net> wrote in message
news:3824...@news2.foxinternet.net...
greg miller
greg miller wrote:
> Suppose all players have an equal chance to win a given match, and
two
> players decide to be "brothers" and split any winnings. Also suppose
> the entry fee was $1 and first place paid $4
> In the G4 case, the expected returns for each of those players
>
> (.5)*(2)-(.5)*(1)= .5
>
> would be higher than the expected returns for each of the independent
> players.
>
> (.25)*(4)-(.75)*(1)= .25
>
> (There's GOT to be a mistake in there somewhere.)
>
> So it would be an advantage to pair up and split the winnings.
I spread incorrect information again. Since posting this, I've been
going to school about expected returns. The above equations are wrong.
The mistake is in not recognizing that losing the $1 entry fee is a
certainty. So the equations should be:
for each paired player
(.25+.25)*(4/2)-(1)*(1)= 0
and for each independent player
(.25)*(4)-(1)*(1)= 0
So there is no advantage to anybody.
Now if these are wrong, I'm going to be *really* embarrassed.
Gregory