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SOS / Discussion
Sub-page of SOS
RobertJasiek 2003-10-04: For a single player, greater SOS for him than smaller SOS for him could be interpreted as greater strength of his opponents during the tournament. For any two players, a meaningful comparison is hardly possible because it is unclear
Some argue that SOS would be fair on average over many tournaments but this is refuted by the law of great numbers. It requires an infinite number of tournaments to allow that conclusion while no player ever can play an infinite number of tournaments. Even worse, specific titles are issued only once per year, tournament conditions and a player's development change. To summarize, SOS can be used to help a program to make its pairings but SOS ought never to be used as a tie-breaker in the final tournament results ordering, where it behaves like a random variable. I agree with some of Robert's points but not all of them. It is good if the organiser uses SOS when pairing to attempt to make sure that all players on the same score have equally difficult opponents. IF this happens then SOS is less useful as a tiebreaker. However, this is rarely done in my experience. SOS does not behave like a random variable. It is never worse than a random variable for resolving ties and sometimes much better. SOS is a rough measure of how strong your opponents have been. Normally if you lose early in a tournament you get to play others who have also lost early, who will typically turn out to be weaker (and finish with fewer points) than others who win their first few games. Losing early is sometimes known as "the Swiss gambit" as without tiebreakers it can be advantageous to lose early, play weaker opponents and reach the final rounds fresher than other players who have won consistently and thus played harder opponents. In general, SOS performs poorly at the extreme ends of a tournament. It is close to random in deciding first place. In the middle of the tournament it works quite well at ordering players who have finished on the same number of wins. Normally there is no need to order players in the middle of a tournament, and tiebreakers are most needed to decide first place. :( RobertJasiek 2003-10-08: We agree that SOS can be used as a means to assist a program to make pairings during the tournament, although there is no consensus which pairing strategy should be considered the best. - You claim that SOS does not behave like a random variable. I disagree. It behaves differently from coin tossing, sure. However, there is no general description yet that would explain that difference, there are only empirical tests. With more empirical tests observations could differ. To get a general statement about the difference between SOS and coin tossing, one needs more than empirical tests: One needs probability theory that is not only some theory but also explains what one observes. - You claim that SOS is never worse than a random variable. I think you mean "coin tossing" as a concept for a random variable. I disagree: Suppose a 1 round Swiss tournament with 2 participants A and B of known equal strength and the game result A beats B. Then we always, i.e. also on average over many tournaments, have SOS(A) = 0 and SOS(B) = 1. For coin tossing it could be either Coin(A) = 1 and Coin(B) = 0 or Coin(A) = 0 and Coin(B) = 1, each with 50% probability. On average we get Coin(A) = 0.5 and Coin(B) = 0.5. Since we assumed equal strengths of both players, the tie-breaker Coin is much better than SOS in this tournament. Hence SOS can be much worse than coin tossing. - Concerning the early rounds of a tournament, one cannot assess a tie-breaker fairly since it is random how strong every player's opponent (among the pool of available opponents) is. The WAGC is a good (since extreme) example of that: There are, say, 3 very strong participants (Korean, China, Japan) and many weaker participants from intermediate to very weak. The 3 very strong players should win all their games until they meet each other. For the games before, SOS is not fair since very weak opponents will make fewer wins than intermediate opponents. Even a modified SOS is not fair (only slightly better on average); e.g., SOS-1 that throws out the weakest opponent or SOS-round1 that throws out the first round. Such does not solve the principle problem that even after eliminating extremes the remaining probabilistic expectations for one's opponents are not the same. - You claim that tiebreakers were the most needed to decide the first place. For which purposes? To distinguish final results that cannot be distinguished sufficiently meaningfully? The number of wins determines the strongest player, then tiebreakers make some of them luckier by giving titles, prizes, and honour only to them while Go was supposed to be a game of greater skill and not of greater luck. LordOfPi: It seems there is a little mistake in that argumentation. If player A and player B are of equal strenght then the average SOS over many such tournaments will converge to 0.5 for both because both will win half of the games and lose half of them. RobertJasiek: You are referring to my trivial example tournament? There is not a mistake in it. The tournament is defined so that it is player A that wins. (Maybe we could say that player A knows how to beat player B's style, even though generally they are of equal strength.) We can invent another example: Like that example, but the win is given due to a 50% winning probability of the player A in each one-game tournament. Then after an infinite number of such tournaments, SOS converges to 0.5 for each player. With a still finite number of such tournaments, however, often either player A or player B would win more. Say, player A wins more. Then SOS(A)<=0.5 and SOS(B)>=0.5. The tie-breaker Coin is not the game result coin but is still 0.5 for each player; it is thrown only as a tournament final result list tie-breaker. Interpret that type of tournament as you like... kokiri i find it slightly odd agreeing with Robert Jasiek, but here goes anyway: I can understand why people would think of using this as a tie breaker, but is there any real substance behind it? mgoetze: What do you mean, substance? The idea is simply that when two people achieve the same result, the one who did it despite tougher opponents deserves a slightly better placing. But this is an idea and not a substance... kokiri...so does SOS tell you who beat the tougher opponents? really? I admit that I haven't thought it through completely, but I have my doubts. I'll give it some thought and get back to you... mgoetze: No, it tells you who played against the tougher opponents. If you want to know who beat tougher opponents, you're looking for SODOS. However, SOS is usually prefered because most people also consider a loss to be somewhat worse if it was against a weaker player. ("Tougher" in this case is defined as "having done better in the tournament".) kokiri sorry, yes, played. I'm still not convince that, although intuitively it seems reasonable, this isn't a big red herring. Who would you rather play, a 5 dan who's lost 5 games vs 5 dans, or a 1 kyu who's beaten 5 1 kyus? SOS would rate the latter as a harder opponant, no? IanDavis For SOS to be used as a tiebreaker it must show who has played on average the more successful opponent. If A and B tie and A has played the person who finished 12th 4th and 13th whilst B has played 4th 5th and 6th it should show A to have done better. On face value it seems to be doing this to me. This is a copy of the living page "SOS / Discussion" at Sensei's Library. ![]() |