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On Tournament Formats - December 1991

Another Congress has passed; with the usual amount of argument about the tournament draw. Why do people get upset about the draw? We need to think about why people play in go tournaments and what they want out of them. Everybody probably has different wishes in a go tournament but the most common are probably:

  • To play challenging games.
  • To meet players from other clubs.
  • To win a prize.
  • To get WAGC points.

On the surface it seems easy to design a tournament system which satisfies all these. The winning of prizes and WAGC points does, however, require an additional criterion of fairness. Fairness is hard to define but ideally the tournament should result in the players being ordered by "tournament form". I define "tournament form" as the relative ability of the players as measured by their win/loss record (and the strengths of the people they played) in the tournament.

Some tournament structures are better than others at measuring tournament form. Unfortunately there is always a trade-off between this and the first two criteria on the list above. Some tournament formats are:

  • Knockout: Everybody keeps playing until they lose a game. There are also variants where players may be given extra lives. This may suit professional tournaments as it results in an exciting climax but is bad at ordering people after the first position. Even first place may be too random for us.

  • Handicap: The normal handicap tournament satisfies the first criterion very well and allows everybody a fair crack at a prize. With some changes it could satisfy all 4 criteria very well. If at each round pairings are made to keep the size of the handicaps as small as possible and ratings are adjusted during the tournament, the WAGC points could go to the highest rated people after the tournament. Prizes would still go to those with the greatest improvement in their rating (or most wins). This leaves the possibility of people manipulating their rating before the tournament to improve their chances. Also people seem to prefer to play even games.

  • Round Robin: Everybody plays everybody else. The tournament needs to be broken up into small groups (6 people for a 5 round tournament). This is best achieved by using a qualifying tournament. The number of games played in the qualifying tournament added to those in the round robin may be too many for most people. If no qualifying tournament is held but players are separated by rating there is no way of comparing tournament form of people in different groups.

  • Swiss: The tournament most used for Chess. It has many forms but the most "standard" form has players ordered by rating initially, and the top half is paired against the bottom. In subsequent rounds players are grouped by number of wins (draws counting half) and within each group the top half is paired against the bottom. At the end of the tournament players are ordered by number of wins and within that by SOS (Sum of Opponents Scores). The number of variants shows that there are problems with that, even for chess. The main problem for go in NZ is the difference in strength of the participants. Typically the top half meeting the bottom half means that 4 dans play 6 kyus and 6 kyus play 35 kyus.

  • MacMahon: A development of the Swiss where the first round (or two) is presumed to have been played with no upsets. In practice groups are split at a convenient level of rating. This is better than dividing into separate tournaments as the top of one group may be close to (or overlap) the bottom or the next. The problem occurs in finding a winner of groups other than the top one. The early leaders of a group get to play (presumably stronger) people from the next group higher. They thus tend to end up on the same score as the people they have earlier beaten. SOS has to be used to separate them and is quite an accurate indicator of tournament form for this case.

It seems that the MacMahon format suits us best (which is why we have been using it for 15 years). The problems come from still having games between players of very different strengths and when players miss prizes or points because of an "unfair" draw.

In all tournaments above people are never drawn to play the same opponent twice. It may be better to relax this rule to avoid mismatches in the final rounds when people run out of reasonable opponents. This should be made clear to participants beforehand.

The unfairness of the draw is a difficult question and is often used to excuse a poor performance. Where people are matched against others on the same MacMahon score it doesn't matter how they are paired. Using ratings to reduce mismatches is reasonable as is the practice of avoiding pairings between family members or members of a club. The problem comes when there is an odd number of people on a score and people have to be selected to play "down" (and "up"). If the lowest rated player in a group is chosen to play the highest rated player from the next group down it guarantees the closest games but it can lead to a systematic bias which is disadvantagous to some people. (If one person found themselves the highest rated of an odd number in a score group more than once they may justifiably feel aggrieved at having to play more "hard" games than the others on the same score.)

The fairest way to choose who plays down or up is to attempt to even out SOS. This is straightforward but involves so many calculations that it can only be achieved by a computer. The player with the highest SOS in a group gets to play down against the player from the group below with the lowest SOS. (This is unlikely to be the closest possible pairing.) If no computer is available an approximation to this can be achieved by adding up the player numbers (in rating order) of the opponents (SOP). This is easier to calculate and does indicate something of the strength of the person's opposition so far. It may be inaccurate if the initial ranking is incorrect. To avoid any systematic bias without any calculations it is best to choose the middle rated player from a group to play up or down. This is used in some chess tournaments.

The simplest method to avoid systematic bias is to draw pairings randomly within a score group, and to randomly select who plays up or down. This has the advantage that the tournament result is determined solely by what happens during the tournament. It is obviously unsatisfactory for someone to be able to trace their position in a tournament to the outcome of a game played a week before it started. The disadvantage of random draws is the possible increased number of mismatches.

Kami Kazi believes that using ratings to decide pairings within a score group is reasonable but ratings should not be used to decide who plays up or down. The most preferred method for this is to even out SOS if a computer program can be written for this. Otherwise it is best to do all selections randomly. If people still prefer to use ratings then the middle rated person should be chosen to play up or down. Whatever system we use, it should be consistent from congress to congress (and also for other tournaments) The best way to ensure consistency would be a computer program. Can all tournament directors be expected to have access to a computer? MacIntosh or IBM Compatible? Who will write such a program?

©2004 Leon Phease