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Topic: 2013 World Championship Format (Read 31145 times) |
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Marty
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Re: 2013 World Championship Format
« Reply #120 on: May 7th, 2012, 2:59am » |
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on May 6th, 2012, 10:08pm, Fritzlein wrote:
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That makes one loss and ten wins. Now to win the tournament I need two more against the winner of the winners' bracket, i.e. a total of twelve straight wins.
Am I doing the math correctly? |
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your proof is convincing, but i believe i have an counter example. (the actual pairing would be probably arranged as fold pairing instead of adjacent pairing. that shouldn't change anything)
am i missing anything?
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hyperpape
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Re: 2013 World Championship Format
« Reply #121 on: May 7th, 2012, 6:32am » |
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Forget rounds. Schedule the consolation bracket whenever there are enough players available.
This does create the issue that you have to break ties: if there are n/2 - 1 players eliminated after some week, and n/2 + 1 eliminated the next week, you'll have to decide which player gets seeded into the following round of the consolation bracket.
(Maybe that's what you meant by "floating pairing", if so, then yay: agreement).
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Fritzlein
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Re: 2013 World Championship Format
« Reply #122 on: May 7th, 2012, 10:17am » |
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on May 7th, 2012, 6:32am, hyperpape wrote:| Forget rounds. Schedule the consolation bracket whenever there are enough players available. |
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What do you mean by enough players? If 8 players are eliminated in the third round of a 64-player triple-elimination, there are enough players to play 4 games in the consolation bracket. So should they play? If not, what are they waiting for, and why?
Before I was confused as to what you are trying to achieve, and I still am, but now I am also confused as to what you are proposing to do, never mind what it accomplishes.
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Fritzlein
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Re: 2013 World Championship Format
« Reply #123 on: May 7th, 2012, 10:31am » |
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on May 7th, 2012, 2:59am, Marty wrote:| your proof is convincing, but i believe i have an counter example. (the actual pairing would be probably arranged as fold pairing instead of adjacent pairing. that shouldn't change anything) |
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If I am reading your diagram correctly, you are having everyone who is still alive play every round. This is exactly what a traditional double-elimination bracket doesn't do, because the traditional double-elimination wants to maintain equal powers of two.
The difference between floating double-elimination and the bracket you propose is only in the pairing within score groups, but both have this structure:
After 1 round there are 32 winners and 32 losers
After 2 rounds there are 16 winners and 32 losers
After 3 rounds there are 8 winners and 24 losers
After 4 rounds there are 4 winners and 16 losers
After 5 rounds there are 2 winners and 10 losers
After 6 rounds there are 1 winners and 6 losers
In round 7 someone has to get a bye.
This is unlike traditional fixed-bracket double-elimination, which tries to keep 2^n players in both the winners' bracket and the losers' bracket, which requires the losers' bracket to play extra rounds.
In short, we're in agreement about everyone playing an equal number of games. 
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Nombril
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Re: 2013 World Championship Format
« Reply #124 on: May 7th, 2012, 9:42pm » |
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on May 7th, 2012, 10:17am, Fritzlein wrote:| What do you mean by enough players? If 8 players are eliminated in the third round of a 64-player triple-elimination, there are enough players to play 4 games in the consolation bracket. So should they play? If not, what are they waiting for, and why? |
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Wow, I took a break for school and I'm very confused now.
My original suggestion (which I thought was being discussed, and as voiced again by aaaa and others) of having the 2nd place and 3rd place bracket seems not to be clear at all. Of course those 8 players would play. The only reason to ever wait would be if there was only a single player in the bracket. Since those brackets continue to play, I don't see how the second place bracket can ever go more then 1 week past the championship, and the 3rd place bracket could ever go one week past that. To have reached those brackets, you are already one loss from getting knocked out of that bracket... and so on. So there is no way for those brackets to be larger or have players with fewer of losses then those that are still playing for the top spot.
I think the focus is too much on the number of wins. The number of wins to me is NOT relevant to who is the better player. What is relevant is who did they beat.
For example, this year I placed 4th. But towards the end, I had only one loss, while everyone remaining (but hanzack) had 2. By the metric of just "wins" I was in second place. But I had not yet beaten anyone that ended up in the top 3, since after a tough 2nd round game I had a relatively easy schedule, not getting paired against the top couple of players. But in the meantime, Fritz was paired twice against Jean, plus against hanzack and Adanac... and knocked out of the triple elimination before we had played each other. To me, it would have been much more fair had Fritz been "waiting" in the consolation bracket to have a chance to play against the other people that had lost to the same people he had. (In this case, it would have been for the difference between 4th and 5th place... but had there been one less person above us then the 3rd place bracket would have been in effect...but he would have had a rematch with Adanac, and then Jean would have played the remaining player to decide 2nd place...etc...)
I see it as a way to provide better differentiation for 2nd and 3rd place, while not changing the triple elimination tournament that was designed to most effectively designate the top player.
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Fritzlein
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Re: 2013 World Championship Format
« Reply #125 on: May 7th, 2012, 11:30pm » |
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on May 7th, 2012, 9:42pm, Nombril wrote:| My original suggestion (which I thought was being discussed, and as voiced again by aaaa and others) of having the 2nd place and 3rd place bracket seems not to be clear at all. Of course those 8 players would play. The only reason to ever wait would be if there was only a single player in the bracket. Since those brackets continue to play, I don't see how the second place bracket can ever go more then 1 week past the championship, and the 3rd place bracket could ever go one week past that. To have reached those brackets, you are already one loss from getting knocked out of that bracket... and so on. So there is no way for those brackets to be larger or have players with fewer of losses then those that are still playing for the top spot. |
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OK, we obviously need to play through an example to make this clear. The consolation brackets will be bigger than the top tier, and the tournament will extend more than two weeks past the time the champion is decided. How much more depends on byes and on the dominance of the top player; I am just going to assume the top player wins undefeated for the purpose of illustration. The table shows how many people there are after each round with 0, 1, 2, 3, 4, and 5 losses. Those with 5 losses are out; those with 4 losses can only play each other (for 3rd place) and those with three losses can only play each other (for 2nd place) until they lose and drop down a bracket. Players with two losses or fewer can only play each other until getting a third loss.
round 0L 1L 2L 3L 4L 5L
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0 64
1 32 32
2 16 32 16
3 8 24 24 8
4 4 16 24 16 8
5 2 10 20 20 10 2
6 1 6 15 20 15 7
7 1 3 10 18 18 14
8 1 1 7 14 18 23
9 1 0 5 10 16 32
10 1 0 2 8 13 40
11 1 0 1 5 11 46
12 1 0 0 4 8 51
Champion is decided
13 1 0 0 2 6 55
14 1 0 0 1 4 58
Second place is decided
15 1 0 0 1 2 60
16 1 0 0 1 1 61
Third place is decided
I hope this makes it clear that nothing strange has to happen for the extra brackets to have extra people; on the contrary, that is the natural evolution of the tournament. It might be possible to construct a scenario in which the extra two brackets only extend the tournament by two weeks, but it is also possible to construct a scenario in which (thanks to byes in the lower brackets) it takes five extra weeks to finish up.
Quote:I think the focus is too much on the number of wins. The number of wins to me is NOT relevant to who is the better player. What is relevant is who did they beat.
For example, this year I placed 4th. But towards the end, I had only one loss, while everyone remaining (but hanzack) had 2. By the metric of just "wins" I was in second place. But I had not yet beaten anyone that ended up in the top 3, since after a tough 2nd round game I had a relatively easy schedule, not getting paired against the top couple of players. But in the meantime, Fritz was paired twice against Jean, plus against hanzack and Adanac... and knocked out of the triple elimination before we had played each other. To me, it would have been much more fair had Fritz been "waiting" in the consolation bracket to have a chance to play against the other people that had lost to the same people he had. (In this case, it would have been for the difference between 4th and 5th place... but had there been one less person above us then the 3rd place bracket would have been in effect...but he would have had a rematch with Adanac, and then Jean would have played the remaining player to decide 2nd place...etc...)
I see it as a way to provide better differentiation for 2nd and 3rd place, while not changing the triple elimination tournament that was designed to most effectively designate the top player. |
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I understand the problem that you are trying to address, but I believe your proposal is an inefficient means of addressing it. If you are going to extend the tournament by four weeks because everyone (except the champion) plays until losing five times, then it would be better not to separate out the consolation brackets.
Consider exactly the scenario you proposed, where I have three losses and you have only two and you have never been forced to play me. Under your proposal, we would not be allowed to play each other, because I would be in the second-place bracket and you would still be in the winners' bracket. But if you don't split off this extra bracket, we could still play.
I personally don't think it is worth extending the tournament by four weeks to get a better reading on who is in second and third place. Typically it has only taken one additional game each year. For the 2012 tournament, first and second place were quite obvious, whereas third place only required one more game to clear up. If the fact that you finished fourth and I finished fifth instead of the reverse was not warranted by the actual games played, so be it. We were both clearly behind Adanac in third place, and an exact ordering of lower places don't matter much to me, or to the people who voted to stop playing after three losses.
However, IF we are going to extend the tournament another four weeks, the best use of the extra time would be to keep everyone in the same division, even if we crowned the champ well before tournament end. Then pairings that haven't happened yet will happen freely, and other even-out pairing mechanisms can work better too.
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| « Last Edit: May 7th, 2012, 11:34pm by Fritzlein » |
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aaaa
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Re: 2013 World Championship Format
« Reply #126 on: May 9th, 2012, 8:15am » |
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What is gnawing at me is that there are a multitude of ways to rank the losers of a championship and that any choice of using them to determine playoff spots or outright final ranks would be almost hopelessly arbitrary. Just considering the main tournament alone, I see number of wins, round reached and performance rating. Add in a consolation section and you get another dimension of which section these values pertain to, if not their combined result, not to mention that if you do account for consolation games, number of losses could also become useful as a differentiating tiebreaker.
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| « Last Edit: May 9th, 2012, 8:15am by aaaa » |
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Fritzlein
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Re: 2013 World Championship Format
« Reply #127 on: May 9th, 2012, 4:01pm » |
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on May 9th, 2012, 8:15am, aaaa wrote:| What is gnawing at me is that there are a multitude of ways to rank the losers of a championship and that any choice of using them to determine playoff spots or outright final ranks would be almost hopelessly arbitrary. Just considering the main tournament alone, I see number of wins, round reached and performance rating. Add in a consolation section and you get another dimension of which section these values pertain to, if not their combined result, not to mention that if you do account for consolation games, number of losses could also become useful as a differentiating tiebreaker. |
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I have to agree that our format isn't perfect at distinguishing second from third and is even less perfect at distinguishing third from fourth. But the format isn't terrible at it either. Indeed, I think that the rankings of 2-3-4 are good enough by tournament end that I would be satisfied with any of the three ordering methods you listed, although only the performance rating doesn't need a further tiebreak. So we could do
* Wins + performance rating
* Wins + single tiebreak game
* Order of elimination + performance rating
* Order of elimination + single tiebreak game
* Performance rating
Sure, the choice between these is somewhat arbitrary, but even the worst of them is not a bad choice. I guess my current preference is for the first one or the last one, because then we never have to extend an already-long tournament by an extra week. There may be some cases in which wins-then-rating isn't clearly 100% fair, but then no tournament format is ever clearly 100% fair. Sometimes taking extra measures to make a tournament more fair is not worth the fuss and bother.
In a situation where there are several rather good options, we can pick one and be happy that it is good, even if it isn't perfect.
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Nombril
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Re: 2013 World Championship Format
« Reply #128 on: May 9th, 2012, 10:18pm » |
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Thanks for charting it out for 64 people... it does seem pretty clear... but...
on May 7th, 2012, 11:30pm, Fritzlein wrote:| It might be possible to construct a scenario in which the extra two brackets only extend the tournament by two weeks, but it is also possible to construct a scenario in which (thanks to byes in the lower brackets) it takes five extra weeks to finish up... |
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It seems the "odds" of having an odd number and a bye occurring in either side of the dividing line should be the same? But I don't have any math backing me up here 
Also, I wasn't "constructing" a scenario, I was just looking at what happened this year. The 2nd place consolation brackets this year would have kept up with the 1st place bracket, with only 1 more game to be played after the final for the remaining player in the 2nd place bracket to play whoever was knocked out of the 1st place bracket. Was there something odd that happened this year? Or is that just due to the smaller number of players?
Maybe all it takes is one loss by the top player to give the 2nd place bracket a chance to "catch up"? (Hmm, nope, just tried that with your 64 player bracket...) I *guess* you could have some break point for starting the consolation brackets (such as you must have won at least 2 games, assuming good turn out). But I would shy away from making things complicated.
I definitely agree that it is unreasonable to extend a tournament 4 weeks to differentiate between 2-3-4.
Maybe I just need to give into the fact that this is a still a "short" tournament, and luck will have to play a factor, and the only way to finish at the top is to win the games you play. 
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Fritzlein
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Re: 2013 World Championship Format
« Reply #129 on: May 10th, 2012, 1:50pm » |
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on May 9th, 2012, 10:18pm, Nombril wrote:| It seems the "odds" of having an odd number and a bye occurring in either side of the dividing line should be the same? But I don't have any math backing me up here |
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Sure, the byes could be on either side, which could either lengthen or shorten the extension caused by having extra brackets. But the "default" with 64 players and minimal byes was not a two-round extension, but a four-round extension.
Quote:| Also, I wasn't "constructing" a scenario, I was just looking at what happened this year. The 2nd place consolation brackets this year would have kept up with the 1st place bracket, with only 1 more game to be played after the final for the remaining player in the 2nd place bracket to play whoever was knocked out of the 1st place bracket. Was there something odd that happened this year? Or is that just due to the smaller number of players? |
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Nothing strange happened; it was just due to the small number of players. The people in the consolation bracket didn't have time to "pile up" like they would in a larger tournament. But let me point out that even so, your proposal would have extended the tournament three weeks, not two, because the third-place bracket would not have kept up:
round 0L 1L 2L 3L 4L 5L
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0 11
1 6 5
2 4 4 3
3 3 2 5 1
4 2 2 3 4
5 1 3 1 4 2
6 1 1 3 2 3 1
7 1 0 3 2 3 2
8 1 0 1 3 3 3
9 0 1 1 2 3 4
10 0 1 0 2 3 5
Champion is decided
11 0 1 0 1 3 6
Second place is decided
12 0 1 0 1 2 7
13 0 1 0 1 1 8
Third place is decided
Quote:| Maybe all it takes is one loss by the top player to give the 2nd place bracket a chance to "catch up"? (Hmm, nope, just tried that with your 64 player bracket...) |
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Yes, losses by the top player don't allow the lower brackets to "catch up" unless those losses occur at the very end. Here is 64 players with the higher player always losing when "paired down" against someone with more losses, and in particular with the top player losing twice before securing the crown:
round 0L 1L 2L 3L 4L 5L
----- -- -- -- -- -- --
0 64
1 32 32
2 16 32 16
3 8 24 24 8
4 4 16 24 16 8
5 2 10 20 20 10 2
6 1 6 15 20 15 7
7 0 4 11 17 18 14
8 0 2 8 14 17 23
9 0 1 5 11 16 31
10 0 0 4 8 13 39
11 0 0 2 6 11 45
12 0 0 1 4 9 50
Champion is decided
13 0 0 1 2 7 54
14 0 0 1 1 5 57
Second place is decided
15 0 0 1 1 3 59
16 0 0 1 1 2 60
17 0 0 1 1 1 61
Third place is decided
Note that the two consolation brackets now take five rounds to finish instead of only four. So it is not just whether the top player loses that influences the length of the extension, but when he loses. And, to repeat, the extra weeks are mostly a function of the tournament size.
Quote:| I definitely agree that it is unreasonable to extend a tournament 4 weeks to differentiate between 2-3-4. |
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I'm glad we're generally in agreement that there is a tradeoff between effort and result. It is just too long a tournament extension to be justified.
Quote:| Maybe I just need to give into the fact that this is a still a "short" tournament, and luck will have to play a factor, and the only way to finish at the top is to win the games you play. |
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I agree: No matter how we decide to distinguish 3rd place from 4th place, the player who got the short end of the tiebreak method must know that he had a chance to place higher (three chances, in fact) by winning a game that he lost. I didn't waste time this year bemoaning the fact that I finished in 5th place behind you due to my having to play a tougher schedule than you had to. Instead I spent all my regret over losing the three games that I lost. If I had won any one of those three...
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mistre
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Re: 2013 World Championship Format
« Reply #130 on: May 10th, 2012, 3:01pm » |
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on May 9th, 2012, 4:01pm, Fritzlein wrote:
* Wins + performance rating
* Wins + single tiebreak game
* Order of elimination + performance rating
* Order of elimination + single tiebreak game
* Performance rating
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Or my idea which was if wins are tied, take the two players with the highest performance ratings and have them play a single tie-break game. This tie-break game can take place the same week as the final game so no need to extend the tournament.
To me this is a sufficient means of determining 2nd from 3rd or 3rd from 4th. I don't want to see any format in which there are consolation games being played weeks after the final has been finished and a champion crowned...
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| « Last Edit: May 10th, 2012, 3:02pm by mistre » |
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Fritzlein
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Re: 2013 World Championship Format
« Reply #131 on: May 13th, 2012, 10:11am » |
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on May 10th, 2012, 3:01pm, mistre wrote:
Or my idea which was if wins are tied, take the two players with the highest performance ratings and have them play a single tie-break game. This tie-break game can take place the same week as the final game so no need to extend the tournament.
To me this is a sufficient means of determining 2nd from 3rd or 3rd from 4th. I don't want to see any format in which there are consolation games being played weeks after the final has been finished and a champion crowned...
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That seems like a very reasonable scheme. Rank first by wins and then by a single playoff game. We haven't yet had a three-way tie for wins, but it could happen, so I like the clarification that if there are more than two tied, only the top two by performance rating get to be in the playoff game.
The 3rd-4th tiebreak game can take place while the top two are still playing, so there is no tournament extension in that case. When there is a tie in number of wins for 2nd-3rd, though (due to unequal byes) the playoff game would still have to be the week after crowning the champion. I am not sure how to balance my desire for a head-to-head tiebreaker with my desire not to extend the tournament. Would it be too arbitrary to say that if 2nd and 3rd tie on wins, we revert to performance rating to break the tie with no playoff game? Now that I think about it, many tournaments have a 3rd-4th game before the championship, but I can't think of any tournament in any sport that plays a 2nd-3rd game after the champion has been determined. Is it just too anti-climactic?
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| « Last Edit: May 13th, 2012, 10:14am by Fritzlein » |
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aaaa
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Re: 2013 World Championship Format
« Reply #132 on: May 13th, 2012, 12:20pm » |
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mistre's proposal to have one playoff game at the most is pretty much a codification of how we already have been doing things and I don't remember much of a fuss when a game to determine third place in the 2008 championship took place when the winner was already known for a week. The question is whether to assign a monetary award to winning any playoff game.
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Fritzlein
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Re: 2013 World Championship Format
« Reply #133 on: May 13th, 2012, 1:26pm » |
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on May 13th, 2012, 12:20pm, aaaa wrote:| mistre's proposal to have one playoff game at the most is pretty much a codification of how we already have been doing things and I don't remember much of a fuss when a game to determine third place in the 2008 championship took place when the winner was already known for a week. The question is whether to assign a monetary award to winning any playoff game. |
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Good question. I believe the standard in chess tournaments is to not break ties when it come to prize money. The prizes for the tied places are pooled and then evenly divided. But for ranking (i.e. glory) some tiebreaker such as strength of schedule is used. It makes sense to me to have our single playoff game not affect prize money and only affect recognition on the page http://arimaa.com/arimaa/wc/
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Hippo
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Re: 2013 World Championship Format
« Reply #134 on: May 19th, 2012, 3:06pm » |
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Uff, I have finally finished the reading . I like the idea of consolidation bracket for the 4th loss, but I don't think bracket for fifth loss is needed.
Even when players are eliminated from this 4elimination turnament they could be paired till the guaranted (say 6) rounds are played.
I would let 2nd place for the last eliminated player. I like the idea of the third place to be decided by game among the players in the 3 loss bracket with best performance rating. But there is the problem when to let them play.
... Best 2 players could play several games while others are eliminated and in that case fighting in 3 loss bracket could continue.
One option is to decide 3rd place in a round when first time winner could be decided. Another option is to wait to round when winner must be decided or in the case the winner was decided faster than needed play one additional round.
Both choices seems to be feasible for me.
BTW: There could be problems with performance ratings when forfeits in 3 loses bracket and or first 6 rounds appear but this would not be that big issue as when this was chosen as a criterion for the top 8 players cut-off.
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| « Last Edit: May 19th, 2012, 3:10pm by Hippo » |
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