Author: Peter Fendrich
Date: 02:08:35 08/26/02
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On August 25, 2002 at 21:19:45, Kerry McDermott wrote: >Peter, > >Why a trinomial distribution instead of binomial? Because of the three possible >results... win, loss, draw? Right, the binomial distribution will also be an approximation of the Trin by counting a draw as a half win/loss. >I was actually thinking of this more in terms of a >t-test. I can't quite figure out the draw aspect of it though. Suggestions? The t-test is also relying on the normal distribution with the same need for enough number of games. By assuming a binomial distr. as above, you haven't really solved the "number of games problem" anyway. The main problem is that the Normal Distr. is a continous function and both Bin and Trin are not. We need enough number of games to make them "look" continuos. > >Are you saying that the results are so subject to random factors that even a >score of say 7.5-2.5 would be suspect? What would the probability be that the >lower rated computer would have the 7.5? The score isn't suspect but applying the Normal distribution is. I once did some work on this and wrote a little program for computing: "given a result in win/loss/draws, what is the probability that the winner is the better player". All based on the trinomial distribution. I'm sure it can be adjusted to be used in a t-test manner or to apply confidence intervals instead of the used fixed interval [0.5, 1.0]. The post: http://ccc.it.ro/search/ccc.php?art_id=155024 The program: ftp://cap.connx.com/pub/tournament_software/ Download theory0_8.zip Dann Corbit made some small changes to it but I don't remember the name of the new file and couldn't log in to his site, but it's there. If you have the same problem to connect to his site, please let me know and I'll send the program to you. Peter > >Kerry
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