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Topic: 2012 World Championship (Read 9100 times) |
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aaaa
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Re: 2012 World Championship
« Reply #45 on: Feb 5th, 2012, 10:21am » |
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on Jan 29th, 2012, 5:27pm, Fritzlein wrote:Oh, yeah, now I remember that I actually proposed pairing principle 10 myself. I didn't understand what the consequences would be, but now that I see it in action I realize that it is wrong. It should be split like this:
10. Minimize the sum of the squares of the differences in rank among paired players with different number of losses.
11. Maximize the sum of the squares of the differences in rank among paired players with equal number of losses.
That is to say, they shouldn't be combined in one formula; the difference in border crossings should be minimized first, and only then should be players within each category be optimally paired.
Obviously we shouldn't change the algorithm for this year's tournament (as much as I would like to avoid chessandgo this round  ), but I propose we change it for 2013. |
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I don't see why the preference to maximize the differences in ranks of pairings within a loss bracket should have less weight than the one to minimize the rank differences between players in different brackets; from a fairness point of view they seem to be of equal desirability.
A strict hierarchy of priorities involving more than one formula like that would be a pain to implement. In order to have each rule strictly overrule all those below it, the scheduler goes through each rule in ascending order of priority, determining an upper bound of the complete range of possible total weights so far, so that the penalty given will be high enough so as to prevent there ever being a schedule that's so ideal according to the lower priorities that it would be best preferred at the expense of a higher priority. For a function with a large "resolution" (like the proposed rule 10) to come on top of another such function (rule 11) would mean that between each pair of possible outputs a penalty must be assigned that covers the entire range of values the lower rule can output. In conjunction with all the other priorities, this could lead to severe overflow problems.
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ocmiente
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Re: 2012 World Championship
« Reply #46 on: Feb 5th, 2012, 12:16pm » |
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In my particular case, the pairings for this tournament were not as fair as they could have been. The specific reason why I state this is that in round two I was paired outside of my loss bracket (I had one loss and my opponent had none), and again in round four (I had two losses and my opponent had one). Once would be OK, and understandable. Twice in four rounds is not. Especially when there were five people in my loss bracket in round four from which to choose.
If a player has been paired outside of their loss bracket before, that should be taken into account. This applies when paired above and below their loss bracket. It should be tracked as byes are tracked.
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| « Last Edit: Feb 5th, 2012, 12:17pm by ocmiente » |
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Sconibulus
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Re: 2012 World Championship
« Reply #47 on: Feb 5th, 2012, 9:20pm » |
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Yeah, actually, as it stands, the scheduler seems to prefer pairing people outside their loss bracket multiple times. Seeing as the tiebreaker for ranking within brackets is based on opponent wins, having an opponent with one fewer wins or one more win than others within your bracket will tend to keep you in the high or low position.
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omar
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Re: 2012 World Championship
« Reply #48 on: Feb 7th, 2012, 9:39pm » |
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To break ties without additional games I would suggest just using the pre-tournament ranks. I think players are more in favor of breaking ties using game additional games, but I didn't want to extend the tournament longer.
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Fritzlein
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Re: 2012 World Championship
« Reply #49 on: Feb 8th, 2012, 7:33am » |
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on Feb 7th, 2012, 9:39pm, omar wrote:| To break ties without additional games I would suggest just using the pre-tournament ranks. |
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Well, maybe that would encourage hanzack not to sandbag: he's certainly going to lose any tiebreak this year, as he is the lowest-seeded player remaining.
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Nombril
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Re: 2012 World Championship
« Reply #50 on: Feb 8th, 2012, 11:59pm » |
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Regarding fairness of the pairings (and a PS about places of the finalists):
In the context of winner take all tournament where we just crown 1st place finisher with no distinction between the rest: fairness doesn't matter very much. To get to the top you need to be able to win most of your games.
In the context of a "high" entry fee tournament where you get a payout based on how many games you win, it seems we should do a better job of having a fair schedule. For how complex and convoluted the rules are, it seems there were a number of instances of intuitively unfair pairings.
Ocmiente's schedule is a good example, another lesser example was my round 2 game against C&G. If there are no upsets in the top few players, why should the 1 and 3 seed play each other already in the 2nd round, especially since the 2nd see has the bye?
I don't have any suggestions for how to improve the algorithm, because I must admit I don't have the motivation to decipher it to understand it in the first place. But I would suggest for next year:
a. Update the format to have a clear 1, 2, 3 place finish.
b. Update the algorithm to be more "fair" to address these issues, or just get rid of all the convolutions and use some straightforward transparent mechanism.
(PS: And yes, I don't see how we can recognize 2nd and/or 3rd place this year. I'm with Fritz that the rules should not be changed unless there are dire consequences of inaction.)
(PPS: If I manage to get that close to the top - I'd be happy to play a "casual" game at an announced time to settle matters  )
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Fritzlein
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Re: 2012 World Championship
« Reply #51 on: Feb 9th, 2012, 10:45am » |
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on Feb 8th, 2012, 11:59pm, Nombril wrote:Regarding fairness of the pairings (and a PS about places of the finalists):
In the context of winner take all tournament where we just crown 1st place finisher with no distinction between the rest: fairness doesn't matter very much. To get to the top you need to be able to win most of your games. |
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I actually think fairness matters whether or not it is winner-take-all. It is true that if you win every game, you are guaranteed to be champion, so everyone controls his own destiny, but that isn't enough to ensure fairness, as we learned in 2007.
Quote:| For how complex and convoluted the rules are, it seems there were a number of instances of intuitively unfair pairings. |
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The current convolutions are a result of the last time FXE was used in the human World Championship, namely 2007. If you look at the six players who were still standing by round five, http://arimaa.com/arimaa/wc/2007/showGames.cgi and compare the four games they each played to get there, I had by far the easiest path. I had faced none of the other "finalists", but they all had had to play against each other before we even got to that point: omar, 99of9, and robinson once; PMertens twice; and chessandgo three times! Fortunately chessandgo took control of his own destiny and won the tournament, but the unfairness rankled enough anyway that we changed the format.
The problem was that we set up pairing to reward higher seeds (as is appropriate) but the rewards kept on coming in later rounds until they seemed excessive. After getting super-easy games the first two rounds as the top seed, I was rewarded with a bye for being undefeated, then rewarded again with another easy game in round 4. This has been addressed by aaaa's clever idea of replacing pre-tournament seed by performance as the tournament progresses, thus spreading out the rewards of byes and easier pairings among people who earn them in-tournament rather than showering them all on the top seed.
Quote:| If there are no upsets in the top few players, why should the 1 and 3 seed play each other already in the 2nd round, especially since the 2nd see has the bye? |
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In that case the top seed was being punished for his bye the first round. You are right that an innocent bystander (you) got an undeservedly tough pairing as a result, but this seems to have sort of evened out for you. In fact, looking at the current top five in the standings, you are the only one to have just one pairing within the group. Adanac, hanzack, and I have each had two, while chessandgo has had three! (Will we see a repeat of the 2007 comeback?) The only way your schedule has been tougher than ours is that you haven't had a bye yet, and if you get the bye in round 6 then the rest of us will rise to three and four pairings against each other while you stay stuck on one.
Quote:| Ocmiente's schedule is a good example |
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I see this as more of a fairness problem, because it didn't seem to even out across rounds for him in the way things evened out across the rounds for you. Having a tougher pairing than the average of his group one round didn't translate into having an easier pairing than the average of his group the next round.
Quote:| b. Update the algorithm to be more "fair" to address these issues, or just get rid of all the convolutions and use some straightforward transparent mechanism. |
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I'm all ears. What straightforward transparent mechanism did you have in mind? The whole motivation behind floating elimination was to address the great unfairness in the typical (transparent and straightforward) fixed-bracket double-elimination tournament, where a first round loser has to win twice as many games from then on to win the tournament as a first-round winner would. At least in FXE we have a system wherein each player needs the same number of wins for the title (perhaps minus one for a bye) so it is only pairing fairness that we are still disputing.
As for adding further tweaks to the convoluted system, I wouldn't mind that either. I think the FXE is much more fair than it was in 2007, but there is still room for improvement.
The source of the unfairness seems to come from pairing winners against winners and losers against losers. That is the opposite principle from rewarding good performance with an easier pairing. Yet pairing winners with winners isn't a principle we want to discard lightly; the alternative seems to be giving the top three seeds a round-robin against the bottom three seeds during the first three rounds while the middle seeds are having to fight for their lives against each other. That returns to over-emphasizing the importance of pre-tournament seed relative to in-tournament performance.
The issue is what to do about edge-effects, where players who are from different score groups have to meet. From Swiss tournaments I am conditioned to think that the lowest from the higher group should play the highest from the lower group. But this is an artifact of a different fairness condition, namely giving players a good shot at tiebreaker points. In FXE we have different issues.
Perhaps we should revisit the possibility (from the first incarnation of FXE) that the highest player in the higher group should play the lowest player in the lower group. Of course we should still avoid cross-score pairings when possible, but when they inevitably happen, this may be the fairest way to deal with it. The objection would be that the top seed is getting too much reward, as in 2007, but because there is now a mechanism for performance to replace seeds over time, it will tend to even out in way that the current cross-score pairing rule (witness ocmiente) doesn't even out.
In short, we changed two things from 2007 when perhaps it would have been fairer to only change one of them. We could make a one word change to the current pairing rules:
"10. Based on a ranking of the non-eliminated players primarily by least number of losses, secondarily by tournament performance rating and thirdly by seed, maximize the sum of the squares of the differences in rank among paired players with equal number of losses plus the sum of the squares of the differences in rank among paired players with different number of losses."
Yes, I realize this is the opposite of what I proposed earlier in this thread. I reserve the right to change my mind again. 
When someone at the top of a group gets to play down against the bottom of the next-lower score group, it will work like a mini-bye for him; the next round he will not be at the top of his score group. Meanwhile the lower player who got rocked with a hard game will probably lose but will be compensated with an easier pairing next round as he will have risen within his score group thanks to relative performance rating.
Does this theory seem reasonable?
Quote:| (PPS: If I manage to get that close to the top - I'd be happy to play a "casual" game at an announced time to settle matters ) |
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Me too! If we tie for second/third or third/fourth, consider this the handshake. 
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ocmiente
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Re: 2012 World Championship
« Reply #52 on: Feb 9th, 2012, 1:01pm » |
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on Feb 9th, 2012, 10:45am, Fritzlein wrote:
"10. Based on a ranking of the non-eliminated players primarily by least number of losses, secondarily by tournament performance rating and thirdly by seed, maximize the sum of the squares of the differences in rank among paired players with equal number of losses plus the sum of the squares of the differences in rank among paired players with different number of losses."
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Does this theory seem reasonable?
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Maybe. The two concerns that come to mind are
- Let's say a player ends up playing someone in a higher win/loss bracket, and that the next round every win/loss bracket has an even number of players. In that next round, the two bottom players of the win/loss bracket might end up paired together because of the effect of the lowest rated player playing a highly rated player.
- How would this affect the final rankings? This is not as much of a concern to me, but I do think it's worth mentioning. On the WC 2012 wiki, my final rank matches my initial seed. I did not play harren or Simon during the tournament, so the whole final rank is questionable at best, but I do think that given the information of the games played during the tournament along with the initial seed, the relative ranking of ocmiente, harren and Simon makes sense. I would have preferred to have played a game against at least one of them to make the Rank mean more, but it is what it is.
Anyway... my concern is whether having the lowest ranked player in a lower win/loss bracket playing the highest ranked player in a higher win/loss bracket might cause the lower seeded player to end up ranked higher than a higher seeded player, especially if they end up with the same win/loss record.
I think that tracking the times a player was paired outside of his win/loss bracket may be better (leaving everything else the same) than changing criteria 10 - but I also think that simulations need to be run to validate or disprove our beliefs about how these things will work in practice.
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Nombril
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Re: 2012 World Championship
« Reply #53 on: Feb 9th, 2012, 1:45pm » |
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Is there an absolute requirement that we pair outside of the brackets, provided there are more then x players left in each bracket? If crossing boundaries is the issue, is giving 2 (or more?) byes in a round feasible?
I certainly agree that my overall schedule has ended up relatively easy. My point is that round 1 and 2 can be the most easily predicted for pairings, and if already in round 2 we have pairings that don't make sense... well...
Maybe the weight of the bye can be adjusted somehow?
I certainly appreciate the goal of minimizing the influence of initial seed. But is in-tournament performance significant, with so few games played going into the number? I don't like my opponents future performance having a strong affect on my results.
But as I admitted to start with, I don't understand the algorithm and don't have any experience with designing tournaments...I wish I had some concrete suggestion to offer.
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Hippo
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pairing rules
« Reply #54 on: Feb 9th, 2012, 2:50pm » |
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At the first sight maximizing the square difference in standings while minimizing the number of boundary crosses while giving bye to highest standing player among the players with minimal number of byes while minimizing the number of repeated pairings ... sounds well for me .
May be the question is why square in the standings difference and not in the value on which the standing is based. ... (equals the difference 1 in almost tied players to difference 1 on bracket boundaries? )
(Standings are given by minimal number of loses, maximal strength of schedule and maximal preturnament WHR in lexicographical order ... how to translate it well to one real number?).
Seems pairng across boundaries naturaly compensates in the SOS and therefore in future pairings. Of course I would prefer winnig to having better SOS after the third loss;).
I hope this is very close to the pairing proposed by Fritzlein.
OK I have finally read the current rules ... I dont like bye assignment done after minimizing the cross boundaries. So I would shift rule 6 just before the rule 10.
And I like the simplified rule 10 with sum in all cases.
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| « Last Edit: Feb 9th, 2012, 3:08pm by Hippo » |
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Fritzlein
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Re: 2012 World Championship
« Reply #55 on: Feb 9th, 2012, 3:40pm » |
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on Feb 9th, 2012, 1:01pm, ocmiente wrote:| but I also think that simulations need to be run to validate or disprove our beliefs about how these things will work in practice. |
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Yes, I also think we have to try things out to see how they work. The difficult thing is not running simulations so much as it is coming up with some accurate measure for how "fair" an algorithm was in a given run. If we could encapsulate fairness in a formula, we might design a better algorithm even before the simulations start.
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Fritzlein
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Re: 2012 World Championship
« Reply #56 on: Feb 9th, 2012, 3:48pm » |
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on Feb 9th, 2012, 1:45pm, Nombril wrote:I certainly agree that my overall schedule has ended up relatively easy. My point is that round 1 and 2 can be the most easily predicted for pairings, and if already in round 2 we have pairings that don't make sense... well...
Maybe the weight of the bye can be adjusted somehow? |
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I wonder what the effect would be of eliminating the concept of seed entirely in favor of in-tournament performance, whereby performance is calculated from a extremely weak prior, say 0.1 draws against a player of one's pre-tournament rating. For the first round there would be no effect; the second round a bye might not drop a player all the way to the bottom of the winner group. The size of the drop might be related to the weakness of the prior. Also it might be related to the dispersion of the field; playing someone rated 1200 points lower should be considered almost like having a bye.
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Adanac
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Re: 2012 World Championship
« Reply #58 on: Feb 13th, 2012, 6:40am » |
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Sorry to keep asking the same question over and over but this time it's important for my round 7 scheduling:
What will the next pairings be in the 4 possible scenarios from round 6? Monday, February 27th is by far the most convenient day for me to play in round 7 but if my possible opponents can't play that day I'll have to move my schedule around in advance. Thanks
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Fritzlein
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Re: 2012 World Championship
« Reply #59 on: Feb 13th, 2012, 7:21am » |
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Hanzack, yes it is OK with me to move our game time 24 hours later. I will make slot 89 my only top preference.
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