Tie breakers are used in tournaments to distinguish between players finishing the tournament with the same score, for pairing or for seeding purposes. In general tournaments use more than one tiebreaker, this is because many tiebreakers don't break ties under all circumstances, or cannot be used. In cases where a tiebreaker doesn't break ties only players who tie in the top group of that tiebreaker are considered for the second tiebreaker and so on.
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In many cases, breaking ties is not required. There is often nothing wrong with simply having players share the same place. 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 only to get a final ordering for purpose of determining the official winner and sorting the published results.
In some cases however, sharing a place is not acceptable because the prize cannot be shared (a cup, a right to play another player, an invitation for a next tournament, a ticket, a clock) and the tie between the players must be broken. In general however it is seem more reasonable to divide the prize or give an extra prize. (For example if the prize is a free book from the book stall, give all players who tie for this place a book)
This list is not more than just a list of tiebreakers. Tiebreakers not mentioned are not necessarily better or worse than the methods mentioned. (they are only sadly missed do add them)
- Play-off: Breaks ties by having the players play extra rounds. Also known as Rematch. This is generally considered a good method, but its use is often not possible due to time constraints.
- Previous performance: breaking ties according to last years performance is used in the Honinbo, Kisei and Meijin leagues, other implementations (rating) are possible as well.
- Random tie-breaker: tie-breaking at random, a nice way to implement this is by Nigiri.
- Face to Face Result: In the case of two tied players, use the result of the game between them (if it was played)
- Direct Comparison: Generalization of Face to Face Result so it can be applied to tied groups of any size. Compares only the results of those games that tied players played against each other. Requires all in group games to have been played. Not widely implemented in software.
- Iterative Direct Comparison: Iterative application of Direct Comparison. It can sometimes break more ties of more than three players than non-iterative Direct Comparison.
- Direct Confrontation: Another generalization of Face to Face result, similar to Direct Comparison, but without the requirement that all in-group games have been played.
- Simplified Direct Confrontation: The same as Direct Comparison
- SOS: Sum of the Opponents Scores, also know as Buchholz or Solkoff in Chess. Measured average strength of the opponents. 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 SOS. Generally only used as a secondary tie breaker after SOS.
- Koya System: The number of points achieved against all opponents who have achieved 50 % or more.
- Extended / Reduced Koya System: The Koya System can be extended by including score groups with a lower score, or reduced step by excluding players who scored less than a higher scores.
- SODOS: Sum of the Defeated Opponents Scores, also known as SonnebornBerger in Chess. Is advised 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: Cumulative Sum of Scores. Expected average strength of the opponents, also known as Sum of Progressive Scores (or, simply Progress) in chess.
- Number of Board Wins (1 per board win, 1/2 per board jigo, 0 per board loss; added for all rounds)
- First Board Wins (board wins only on the first and strongest board, to be used when total Board Wins are even)
- SORP: Sum of Result Points (in a round, a team's SORP is the opposing team's negative SORP)
- Board wins And SOS Summed
- Meta-Tiebreaker: Breaks ties only if each listed tiebreaker orders alike.
- Pairing Tiebreaker: Measures how high the opponents' places in the opponents' score groups were.
- SACO: Score Against Common Opponents
- SOP: sum of placing of opponent (nickname suposition)
- SOR: sum of ranks OR sum of ratings
- LRC: Later Round Comparison
- Maximum Likelihood: a mathematical method to determine the player most likely to win, not easily calculated by hand.
Anonymous: Some tiebreakers are clearly worse than using none.
TMark: 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.
- the EGF Tournament System Rules contain some discussion of tie breaking systems but these are not accepted valid by the EGF executive.
- 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
- Why break ties?
- Order of finishing