Tie breakers are used in tournaments to distinguish between players finishing the tournament with the same score/number of wins. It is possible to have more than one tie breaker.
They can be used in McMahon Pairing or Swiss System tournaments.
Popular combinations are:
Note: Being popular says nothing about quality. Anyway, SOS/SOSOS is the most widely accepted combination.
Some tie breakers:
Anonymous: Some tiebreakers are clearly worse than using none. (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.
TMark?
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 satisfaying, 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)