Author: Roger D Davis
Date: 19:24:00 12/26/00
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On December 26, 2000 at 14:28:15, Bruce Moreland wrote: >On December 26, 2000 at 09:59:45, Uri Blass wrote: > >>It seems that there are more draws between humans. >> >>If you look at the match between kramnik and kasparov there were 13 draws out of >>15. >> >>If you assume probability of 25% for the winner,5% for the loser and 70% draws >>then the standard deviation is smaller and you need less games to get >>significant result. > >If the draw percentage is 70%, you are right. 75 points should win that one out >about 87% of the time. > >But Kasparov should have been about to get 7.5 out of 15.0 93% of the time, and >win it outright 82% of the time. > >How many did he get, 6.5? He should have gotten that score 0.5% of the time. > >But I don't think you can assume these huge draw percentages are "normal" >either. GM games are usually in some larger context. They achieve a winning >advantage in a match or tournament, then force draws to maintain this margin. > >>Another point is that the games are not independent events. > >Yes, I'm sure this messes everything up, but note that I'm not arguing for >statistical accuracy when choosing champions, either. > >I think it's more powerful for *us* if we apply it to computer chess, where >there is much less match strategy. > >bruce > > >>The first match between kasparov and karpov demonstrated it when karpov was >>leading 5-0 and decided to quit the match when he was leading 5-3 because he was >>tired. >> >>The reason that he decided to quit is that he knew that he was tired and that >>kasparov has bettter chances if the match continues. >> >>Karpov did not think about the games as independent events(otherwise he could >>prefer to continue and be almost sure of winning even if kasparov is slightly >>better). >> >>Even if you assume that the probability for kasparov to win a game is 0.2 and >>the probability of karpov to win a game is 0.1(I ignored white and black for >>doing the problem more simple) karpov had probability of 19/27 to win but karpov >>understood that the situation is worse than that and starting a new match from >>0-0 result is better for him. >> >>Uri Another problem for your argument is that ELOs are based on play across a pool of players. Match play is often (but not always) much different. If the two players reached some arbitrary large number of games with no statistical difference between the results, then there would simply be no statistically-significant champion, only a match winner. The fact that the winner is awarded the title of champion does not void the fact that there is no statistically significant difference between the two players, no matter how much you might like it to. What is at stake is simply whether the statistical equality of the two players is recognized (my point), or whether it remains obscure (your position). Roger
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