English Chess Forum

David Smerdon (Aussie GM) has a blog in which he describes how he used economic theory to develop an approach to chess tie breaks as part of the work required for his current course of study.
http://www.davidsmerdon.com/?p=944

An alternative and parallel method would be to use the recursion method or equivalent to compute ratings for all the players in a tournament using only the tournament results as the input. You then separate ties by which players had the higher relative performance. It has to be done on a computer naturally and only makes sense when you have a monster Swiss of multiple rounds.

It's an idea.

Tie breaks are one of those thing where, sadly, someone is going to find fault with whichever method, especially if it doesn't favour them!

Roger de Coverly wrote:David Smerdon (Aussie GM) has a blog in which he describes how he used economic theory to develop an approach to chess tie breaks as part of the work required for his current course of study.
http://www.davidsmerdon.com/?p=944

An alternative and parallel method would be to use the recursion method or equivalent to compute ratings for all the players in a tournament using only the tournament results as the input. You then separate ties by which players had the higher relative performance. It has to be done on a computer naturally and only makes sense when you have a monster Swiss of multiple rounds.

Smerdon's tie break method is designed to punish all draws by not counting them at all in the tie break score. The only way draws contribute, is being included in the total score, but it has no effect for tie break score. As such it doesn't matter if you draw or lose, there is no bonus for that whatsoever. Instead you get a bonus for each win, and a bonus for each indirect win, for instance if you win against a player and he wins against 3 players, you get 1 point for the direct win and 3 points for the indirect wins. The 3 points for indirect wins could be downsized with a constant, but I doubt that will improve the tie break to actually be as predictive as Buchholz and others.

Of course if you agree that we need to discourage any draw (like the football system) then this system makes some sense. It will obviously be biased against players like Anand that makes many draws and win few games. If that is fair then the Smerdon tie break could be considered as fair. However, I don't like this bias towards draws alltogether. Grandmaster draws is something to eradicate (I favor Sofia rules), but a draw is a natural outcome from a hard-fought game, and those I don't want to punish.

The problem here is that there is so many opinions about what is the fairest kind of tie break. It seems that each person has a different opinion.

I have been involved in discussions on the Australian ChessChat arbiter sub-forum about trying to measure the performance of a given tie break scientifically. Kevin Bonham came up with the amazingly simple idea that we could use already existing tournaments, and pretend the last round(s) wasn't played. The tie break score is calculated at round n-1 (n rounds in tourney) or n-2 or n-3, and then check if the tie score actually predicts who advances more in the last round(s). For example player A and B are tied on 6 points after 8 rounds. The tie break is calculated for each player. If player A and player B scores the same in the last round(s) then the result is not considered for the statistics of the tie break method, but if one of the players is ahead of the other in points, then it is checked whether that corresponds with that player having the highest tie break before the round(s). Then all players with equal points before the round(s) are compared to each other, and when there is a difference in score after last round, the result is included in the statistics.

This simple approach has given some surprising results compared to the current bias on tie break methods. For instance the official FIDE pages on tie breaks mention a lot of semi-dubious methods, but doesn't even mention Progressive (also called Cumulative). In the discussions before measuring tie break predictiveness, we all had some bias against Progressive, yet this turns out to be one of the most predictive tie breaks. In my opinion predictiveness is the best measurement of fairness, and in the end what we want is the fairest tie breaks possible. Punishing certain results is simply leading to worse predictiveness. For instance the Smerdon tie break is in some tournaments much worse than Buchholz or Progressive or even Berger (which actually performs surprisingly well in Swiss tournaments even if it is currently used much more in Round Robin). It is also noteworthy that Buchholz Cut 1 (throwing out 1 result) or Median Buchholz (throwing out 2 results), far from being fairer is simply lowering the predictiveness compared to full Buchholz.

Whether predictiveness is actually the only means to measure fairness, is of course a philosophical question.

I have made a program to measure tie break methods but I am missing one suggested tie break, what you mention, a tournament performance for each player without using anything else than the games in the tournament, and not considering the players current Elo. Do you have an idea how that could be calculated? I am willing to include it in my program if we can find a suitable formula. Your last comment that it only makes sense in a monster Swiss to use this tie break, seems unfounded to me. Why would it not work in small tournaments?

I think the basic maths are in the spreadsheet in this entry : http://www.ecforum.org.uk/viewtopic.php?f=4&t=1038 In this case the prior grading/ratings need setting to some equal arbitrary number.

Jesper Norgaard wrote: Your last comment that it only makes sense in a monster Swiss to use this tie break, seems unfounded to me. Why would it not work in small tournaments?

In a small tournament, players tying with the same score are more likely to have played the same opponents, thus making the same relative rating.

The ECF rating team got it into its heads a few years ago that all the English ratings were wrong. They therefore rebooted them using approaches as described by Brian Valentine. What you do is set every player to an equal arbitrary rating. You then rate the tournament. You then take these ratings and rate the tournament again. This is repeated until convergence. Where the rating method includes a cutoff for large rating differences, you have to be careful where players make extreme scores, although for tiebreak purposes only, this might not matter.

The first official version of Norgaard Tiebreak tool is out:

http://www.worldtimeexplorer.com/tiebreak.html

You can see the 47-page manual directly from this page, and downloading and installing should not be difficult. The program has an installer and uninstaller. It is a 2.9 Mb download, and it occupies 5.3 Mb on the harddisk.

Comments are welcome. It is possible to send comments in email to me (see manual) but perhaps the more relevant would be to post any comments here.

With this program you can calculate tie breaks for tournaments, and you can calculate predictiveness for the combinations of criteria you use.

I hope this will be useful for a lot of people. It is a free program, no strings attached, no spam, no viruses (I hope!).

If you have feedback to the philosophy of the program (calculating predictiveness of tiebreak methods) I am perfectly happy to discuss them here.

In the 2013 version of Arbiters_Manual_2013.pdf http://www.fide.com/images/stories/NEWS ... l_2013.pdf there is a paragraph about the Progressive tiebreak. This paragraph states that the Progressive tiebreak was deleted from the FIDE tournaments after the FIDE Congress 2009 in Kallithea, Greece. The main reasons given are:
1. if two players play the same opponents and achieve exactly the same results they don't have equal tiebreak score
2. it is not so easy to understand why there should be a difference in tiebreak score if one player has a win in round 5 and a draw in round 6, the other one a draw in round 5 and a win in round 6.

Ad (1) I tested this criteria in 2087 tournaments, and only came up with 3 examples of 2 players that had the same opponents with the same results. In 2 of those examples, there was no detriment to the Progressive score (since 3 draws were played in a 3 round tournament) and thus resulted in the same progressive scores for both players. Only the third example involved a different progressive score between the 2 players. It is therefore an extremely seldom occurrence that 2 players have exactly the same opponents in a Swiss tournament, especially if there are many rounds (7,8,9). In fact the examples may have been bogus because a 3-round tournament with 60 players looks extremely odd. In terms of the predictiveness, it is clear that in the vast majority of Swiss tournaments the predictiveness of Progressive score is actually better than Buchholz, IMHO showing that this tiebreak is on average beneficial to the players, not detrimental. Whether this tiebreak is unfair in a few cases can't be measured with the average predictiveness, but it is likely that whatever unfairness is given is countered by more fairness in other cases given the average has better predictiveness.

Compare this alleged unfairness of Progressive to other tiebreak unfairness. As an example take Buchholz. If a player's opponents score extremely badly in the rounds after having played their game against that specific player C, then C will have a bad Buchholz score even though he in theory played against strong opponents. Player C has no way to avoid this detriment to his Buchholz score. The progressive score however reflects only how many points he had (and therefore his opponents had) in the round where they were paired, and is therefore more adequately reflecting the actual pairing of player C.

Ad (2) it should be easy to understand why player A having a win in round 5 and a draw in round 6, will have better progressive tiebreak than player B having a draw in round 5 and a win in round 6. Suppose both players had won the first 4 games. They would on average both get an opponent with 4 points in round 5. Player A would then get an opponent with 5 points (on average) in round 6, while player B would get an opponent with 4½ points (on average) in round 6, thus a lower ranked player than A's opponent. That is why player A has better progressive score - he had 1 opponent who was better than B's opponent in that round.

Jesper Norgaard wrote: Ad (2) it should be easy to understand why player A having a win in round 5 and a draw in round 6, will have better progressive tiebreak than player B having a draw in round 5 and a win in round 6. Suppose both players had won the first 4 games. They would on average both get an opponent with 4 points in round 5. Player A would then get an opponent with 5 points (on average) in round 6, while player B would get an opponent with 4½ points (on average) in round 6, thus a lower ranked player than A's opponent. That is why player A has better progressive score - he had 1 opponent who was better than B's opponent in that round.

I was involved in a practical example where it could have mattered.
This was the 1993 Guernsey Open with the cross table at
http://www.guernseychessclub.org.gg/fes ... urnament=O

International Master Robert Bellin was clear winner with 6.5/7, but he had been held to a draw by a then young Simon Williams in round 2. Hubert Mossong and myself reached 4/4 against less testing opposition and played one another in round 5, a draw. As a consequence one of us had to play Bellin and I had the right colour sequence. Mossong won in round 6 and thus had to face Bellin in round 7. I won in round 7, so tied with Mossong for third place on 5.5 , IM David Cummings having got second with 6/7 without playing any of the other top three.

There was a qualification place for the British Championships, for which a tie break would have been decided by Sum of Progressive Scores. I won the place, Bellin and Cummings already being qualified as IMs, but I wouldn't have if Mossong were British. The difference in our tournament tie break being determined by the order in which we played and lost to Bellin. That in turn was more or less determined from our places in the initial seedings and the resulting colour sequences. In one of those other bizarre pairing quirks, I had the same grade as Simon Williams, but he got to meet and draw with Bellin in round 2 and Cummings in round 3.

Roger de Coverly wrote: There was a qualification place for the British Championships, for which a tie break would have been decided by Sum of Progressive Scores. I won the place, Bellin and Cummings already being qualified as IMs, but I wouldn't have if Mossong were British. The difference in our tournament tie break being determined by the order in which we played and lost to Bellin. That in turn was more or less determined from our places in the initial seedings and the resulting colour sequences. In one of those other bizarre pairing quirks, I had the same grade as Simon Williams, but he got to meet and draw with Bellin in round 2 and Cummings in round 3.

Thanks for this input! It is an interesting example.

It is true you were behind in Progressive tiebreak against Mossong (25½ vs. 24½) but even more so in Buchholz (35 vs. 29) and Sonneborn-Berger (25.75 vs. 19.75) so it is not true that you would have been disfavored only because of the progressive score. More likely because of your low rating in the tournament (2008) compared to Mossong (2280) he simply got better opponents from the start. In that sense there is always negative bias towards low ratings in the Swiss system pairings.
In fact you only had 2 opponents in common with Mossong 3 (Bellin) and 22 (Goudswaard) the rest were different.

In the end it is always possible to show an example where a particular tiebreak is somewhat unfair (I'm not sure this is a relevant example though). More important is how often and how severely that unfairness happens in the given tiebreak system. I don't agree that the reasons for deleting the Progressive tiebreak from FIDE in 2009 are well argumented.

Rather than the two reasons given in the Arbiter Manual, I agree that sometimes an unfairness can occur in Progressive when two players alternate between meeting the eventual tournament winner, both losing. However, the example was not convincing because of the huge differences in Buchholz and SB. The more likely scenario for a Swiss pairing is that the lower rated player plays the top seed, and the higher rated player plays a player floating up. Of course different dynamics are prevalent in a tournament with 300 players instead of 84. All in all I think statistical evaluations of tiebreak systems are more convincing than very specific examples. I don't have any measure of how "unfair" a tiebreak system can be to a single player, rather than the average performance.