Tie breaker
Tie breakers are used in tournaments to distinguish between players finishing the tournament with the same score. It is possible to have more than one tie breaker. Used regularly in McMahon, Swiss or Round Robin tournaments
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When to break ties
In many cases, breaking ties is not required. There is often nothing wrong with simply having players share the same place. In some cases however, sharing a place is not acceptable and a tie between players must be broken. Examples of such situations include determining the tournament winner or determining the player to receive a prize that cannot be shared.
Both the EGF and the AGA recommend that tournament organisers divide prize-money (or other shareable prizes) equally between players that finish with the same score. Many tournaments do use a tie breaker to get a final ordering for purpose of determining the official winner and sorting the published results.
List of Possible Tie Breakers
- Rematch: Breaks ties by having the players play extra rounds. Also known as play-off. This is generally considered a good method, but its use is often not possible due to time constraints.
- Direct Comparison: Often used in a tie between only two players, considering the match between these players as a substitute for a play-off. Called "Face to Face Result" by the AGA. Not widely implemented in software.
- SOS: sum of the opponents scores, also know as Buchholz or Solkoff in Chess. Several variants exist which attempt to eliminate noise by discarding some results (eg: SOS-1, SOS-2, Median or Modified Median). Does not work for round robin.
- SOSOS: sum of the opponents of the opponents scores. Generally only used as a secondary tie breaker after SOS.
- SODOS: sum of the defeated opponents scores, also known as SonnebornBerger in Chess. Is adviced against in McMahon tournaments, because players with the same score do not necessarily have the same number of wins. Often used in round robin tournaments.
- CUSS: expected average strength of the opponents, also known as Sum of Progressive Scores (or, simply Progress) in chess
- ROS: expected average strength of the opponents with extra bonus for winning more games
- IROS?: inverse ROS, see ROS-Page
- SOP: (theoretical) sum of placing of opponent (nickname suposition)
- SOR: (theoretical) sum or ranks
- Maximum Likelihood: a mathematical method to determine the player most likely to win, not easily calculated by hand.
- Random tie-breaker: tie-breaking at random, used as a last resort.
- OOF: Order of Finishing
Popular combinations of tie breakers:
Note: Being popular does not necessarily indicate anything about quality. The above combinations are often chosen for their easy availability in pairing software.
AGA Ordered List of Tie Breakers
The following list is from the AGA Guide How to Run a Tournament (effective as of 1997).
- SOS
- SODOS
- Face to Face Result (Known as Direct Comparison by the EGF)
- Random Procedure (Known as Lottery by the EGF)
EGF Order List of Tie Breakers
The following list is from the EGF Tournament System Rules (effective as of July 2007).
- Number of Board Wins (team tournaments only)
- Direct Comparison
- SOS-2, SOS-1 or SOS In that order of preference, but only one can be used.
- Rating or other Previous Order?
- Lottery
- Other
See also
- the
EGF Tournament System Rules contain some discussion of tiebreaking systems.
- the AGA on
How to Run a Tournament
- a discussion of tie breaking methods at
SwissPerfect
- General Aspects of Tournament Systems and Tiebreakers
-
Tie breaker evaluation (pdf) by Tuomo Salo
- /Testing Tiebreakers
Anonymous: Some tiebreakers are clearly worse than using none.
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wms - I disagree with the implications of having this point standing on its own. At worst, most tiebreakers use random luck to decide the final winner. Luck is part of any tournament - who are you paired against? etc. - so using luck to break ties is not "clearly worse" than using nothing to break the ties.
Christoph Gerlach: your point is valid in the case of most tie breakers. At least with CUSS there are examples that prove it's worse than using no tie breaker.
These days, when computers are routinely used for pairing tournaments - more sophisticated methods are available. These are called Maximum Likelihood or ML methods.
My own preferred option was given in a set of Hints for Tournament Organisers, many years ago;
The tie-break order should be Nigiri, SODOS, SOS.
Anonymous: Speaking of tiebreakers, isn't it incorrect to take the arithmetic mean of schedule strength? Shouldn't it be the geometric mean? You should calculate the estimated probability of losing each game, and multiply them together. For example, two players play the exact same opponents, except the second plays an extra game against a weak player (with the other getting a bye). The opponent strength should be equal, but average strength favors the player with one fewer game. Or consider each player plays two games, where one player plays a top pro and a beginner; the other plays two intermediate players. Who had the tougher opponents? This problem is particularly notable in college football, where teams play a different number of games and different opponents.
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PAG?: If the reward is to be given to the "strongest player", why not sticking to the swiss system for qualifications only (4 to 8 groups), then Quarter finals, Semi finals and final. Wouldn't it make sense to have a stronger player winning rather than a 25kyu actually playing as a 15 kyu, winning all his/her games and being lucky enough to get a good SOS? That of course implies that the Tournament's Board wants to reward the strongest players. "Best performers compared to current rank" could then be evaluated separately. That would restrict the use of tie breakers, and would increase the need for separate Kyu tournaments of course. Am I missing something? Go is intellectually satisfying, because luck has little say in the game. Why not keep it to the minimum, at least for the few last games (more important because of Price for winners)
Dieter: The 15 kyu will not win if the tournament is organized with the McMahon method, which in some other cases also leads to unfair results.
Can someone make a nice summary of this discussion?
RobertJasiek: It is being the most actively performed...!