Author: Roger D Davis
Date: 20:41:38 12/25/00
Go up one level in this thread
On December 25, 2000 at 01:28:38, Steve wrote: >On December 25, 2000 at 01:07:23, Bruce Moreland wrote: > >>On December 24, 2000 at 22:08:30, Steve wrote: >> >>>On December 24, 2000 at 17:44:30, Roger D Davis wrote: >>> >>>>They should play a set number of games, say 5 or ten. At the end of that >>>>tournament, if the results are not statistically significant, they should play >>>>on until the results ARE statistically significant. If you look at all past >>>>world champions, it appears that there have seldom been enough games played to >>>>make a statistically significant champion. Sad, but true. The world championship >>>>is rather like Junior 6 v. Shredder and one program coming out on top by one >>>>game. We all know that proves nothing. >>>> >>>>I do not mind there being someone called "world champion," but I think there >>>>should also be a "statistically significant champion." Only the statistically >>>>significant champion can be the real champion. >>>> >>>>Roger >>> >>>What exactly would be a "statistically significant" number of games between >>>closely matched players? 20? 50? 500? Who would sponsor such a match, and who >>>would pay to see it? >> >>Statistical significance has something to do with the number of games played, >>but not everything. If you are trying to prove that someone is the better >>player, it will take a lot of games if the score is nearly even, and not as many >>if the score is close. There is no single answer, it depends upon the score. >> >>bruce > >Thank you for the information. I thought that might be the case, which is why I >asked about closely matched players. You have answered my real question above, >by pointing out that in such a case, the match could stretch out to a completely >unmanageable length. And, as you also note, there is simply no reason to >require a "statistically significant" result. A score of 3.5-0.5 may not be >statistically significant, but as a practical matter it tells most chessplayers >a lot about the relative strength of Anand and Shirov at this point. Actually, statistical significance is a function of sample size and effect size. Sample size is number of persons in a study, for example, or the number of times a particular value in an experiment was recorded. The effect size is regarded as the true difference between the means of the samples on the relevant variable(s). Statistical significance is always a function of sample size AND effect size. If the effect size is large, as with a large difference of ability between two players, then fewer games will be needed to determine who is the significant winner (as opposed to just the winner, which may be statistically meaningless). Conversely, it is certainly possible that the match could stretch out forever between evenly matched opponents. Obviously, this statement is tautological, since that's what it means to be evenly matched in the first place...it is trivially true. One way of dealing with this possibility is to set a minimum and maximum number of games. If players reach the maximum number of games without a statistically significant result, then the tie could go to the old champion, or there could be no champion. Alternately, a draw could be agreed unless both players wanted to play on, in which the match could continue another ten games or whatever. There are many ways of constructing it that I would consider interesting. Obviously, Bruce has another opinion. Roger
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