Tie-Breaks in Swiss Tournaments

Tie-Breaks are used to rank players within point groups. In other words to break ties among players on the same score.

There are many different tie-break systems, some of them popular, some rather obscure. Confusion has been caused by the terminology as same systems are known under different names in different countries. This document attempts to document all tie-break systems recommended by FIDE and USCF.


Tie-break systems classified by their basic principle



PRINCIPLE: Sum of Opposition's Scores

Buchholz (FIDE) or Solkoff (USCF)

This is the sum of opponents' scores. The idea is that the same score is more valuable if achieved against players with better performances in a given tournament. Looks like an ideal tie-breaking method and has been used since the Swiss system was invented. However it has some weaknesses which are addressed by other methods (see Median-Buchholz, Progress, Berger).

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Median-Buchholz (FIDE) or Median (USCF) or Harkness (USCF)

Same as above but discarding the highest and the lowest opposition's scores.

Its idea is to eliminate distortions in Buchholz values caused by taking into account games against run-away winners and bottom placed players.

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Modified Median (USCF)

Same as Median-Buchholz "for players who tie with even scores but modified for other scores to disregard the only the lest significant opponent's scores. The lowest scoring opponent is discarded for tied players with plus scores and the highest scoring for tied players with minus scores.

For tournaments of nine or more rounds, the top two and bottom two scores are discarded for even score ties, the bottom two scores for plus score ties, and the top two scores for minus score ties." (USCF Rules)

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PRINCIPLE: Player's Progressive Score

Progress (FIDE) or Cumulative (USCF)

Calculated by adding points from a progress table eg if your scores were: Win, Loss, Win, Draw then your progressive scores are 1, 1, 2, 2.5 and your Progress tie-break value is 6.5

This is an attempt to put a higher value on scores which were achieved by scoring better in the initial rounds than by finishing from behind. It is common knowledge that the latter is usually much easier to achieve.

The problem is that the order of the Progress tie-breaks is known before the last round (last round scores will change the actual value but not the order within a point group). This may encourage some undesirable tournament "tactics" in the last round.

Interestingly the USCF Official Rules of Chess considers the above feature of the system an advantage on the grounds that it "avoids the problem, comon in Median and Solkoff, of having to wait for a lengthy last-round game between two non-contenders to end for top prizes to be decided".

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Cumulative Scores of Opposition (USCF)

"The cumulative tie-break points of each opponent are calculated as in Cumulative and these are added together." (USCF Rules)

An attempt to marry Cumulative with Solkoff. Rather strange.

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PRINCIPLE: Opposition's Weighted Scores

Berger or Sonneborn-Berger (FIDE, USCF)

This is calculated by adding scores of the opponets who were beaten by a given player and half the scores of the opponents who she drew with. This has been adopted from round-robin tournaments and is usually used as a secondary method.

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PRINCIPLE: Number of Wins

Number of Wins (FIDE)

Calculated by adding a point for a win and nothing for a loss or a draw. Intended to discourage making quick draws. Popular in 70's and early 80's (particularly in round-robins). In modern Swiss tournaments hardly justified.

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Kashdan (USCF)

Similarly to the "Number of Wins" method rewards agressive play. A player receives 4 tie-break points for a win, 2 for a draw, 1 for a loss and 0 for an unplayed game. If there are no unplayed games this system reduces the "Number of Wins".

Interestingly Kashdan can be used to calculate main scores rather than just tie-breaks. In virtually all football (soccer) competitions in Europe teams receive 3 points for a win, 1 for a draw and 0 for a loss.

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PRINCIPLE: Opposition's Ratings

Opposition's Rating Sum (FIDE)

Sum of the opponents' ratings. Uses the ratings ie presumed pre-tournament strength of the opponents rather than their performance in a given tournament. Also has the same problem with the last round as 'Progress'.

This is obviously an ill-conceived method. Ratings have been invented for other purposes.

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Average Opposition (USCF)

Averages the ratings of player's opponents. Effectively identical to FIDE's Opposition's Rating Sum

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Opposition's Performance (USCF)

The concept a bit better than Opposition's Ratings but same comment applies.

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Result Between Tied Players (USCF)

Obvious if two tie but the USCF's interpretation of the situation where more than two tie is interesting:

If more than two tie, all results among tied players should be considered, with rank according to plus or minus, not percentage (3-1) beats (1-0).

This means that you can apply this tie-break even if not all tied players played each other.

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Most Blacks (USCF)

Number of games played with Black.

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Copyright Robert Rozycki. All rights reserved.
Revised: 12 April 1997.