Sum of Opponents' Scores (SOS) is a tie breaker often used in go tournaments. Chess players dub it Buchholz or Solkoff.
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SOS is the sum of the scores of all opponents that a player played against in a tournament. Its purpose is to give an indication of how strong the field of opponents you faced was. It is vulnerable to noise, especially by unlucky pairings in earlier rounds.
If you have to break ties and there is no option to play extra rounds or have a play-off between tied players, then SOS or variants thereof are among the recommended tiebreakers of organisations like the EGF, the Pandanet Tour, and AGA. SOS is also often the default tie breaker of many pairing programs.
Because a player's "score" will mean different things in different tournament formats, the instructions on exactly how to calculate SOS are on their own page.
Variants of SOS include:
- SOS-1 has two distinct variations
- drop the numerically smallest opponent's score from the sum. (Known to Chess as Buchholz Cut 1)
- drop the first round opponent's score from the sum. The first round differs from all following rounds in that first round is randomly paired. This method was used in the 1st World Mind Sports Games. source
- SOS-2 has two distinct variations which proceed directly from the definitions of SOS-1
- drop the numerically smallest and the next smallest opponents' scores from the sum. (Known to Chess as Buchholz Cut 2)
- drop the both the first and second round's opponents score from the sum.
- SOS-n has two distinct variations which proceed directly from the definitions of SOS-1
- drop the numerically smallest n scores from the sum.
- drop the both the first n round's opponents score from the sum.
In the EGF Tournament System Rules? the version where the smallest n scores are removed from the score is used.
- Median: drop the smallest and the largest opponents' scores from the sum.
- Modified Median: Order the opponents' scores like so: lost games (biggest score first), ties (biggest score first), won games (biggest score first). Drop the first and last score. Apply again if needed, but keep the number of dropped games smaller than the number of counted games. So if bad pairing luck gives an easy win, you must actually win that game in order to get that game canceled in the tie breaker. Similarly, if you get paired against a really strong opponent, then that SOS will not get canceled if you manage to actually win that game.
These methods are believed to reduce the effects of statistical noise, and pairing luck, with SOS-2 being more effective that SOS-1. SOS-1 and SOS-2 become more effective at reducing noise in tournaments with more rounds.
These variants are rarely used, as support for them in pairing programs is limited or non-existent.
Unplayed games will cause trouble with SOS. See the SOS calculation page for a more detailed explanation and recommended countermeasures.
SOS is highly sensitive to pairing decisions. In practice this means, that you can not consider criteria other than "fair SOS collecting possibilities" when you use SOS as a tie breaker, however desirable they may be (e.g. not pairing players from the same place, manually forcing certain pairings).