Author: Peter Fendrich
Date: 17:07:40 02/01/01
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On January 31, 2001 at 20:17:17, Bruce Moreland wrote: >I expressed very forcefully that a 10-0 result was more valid than a 60-40 >result. > >I've done some experimental tests and it appears that I'm wrong. > >I have no idea why. > >bruce Well, what is meant by valid? A 100 game match is always giving more (statistical) information than a 10 game match, regardless of the results. It's just as simple as that... The information, however, is maybe not the one you asked for. The standard formula to use here for small samples is the binomial distribution, probably given by someone else here but I couldn't find that. The scoring probability P = (N! / W!L!) p**W q**L (** means powered by) where p is the prob. of a win and q the prob. of a loss. W and L are No.of Wins and Losses respectivly. So p+q=1 and W+L=N. Considering that 0! = 1 and that q**0 = 1 in the 10-0 case we will get the simpler formula: P=p**10 It's no big deal to line up some histograms for different values of p. Do the same for the 60-40 case with different W and L values, and compare. This standard formula is easily transformed into a trinomial distribution, that is the correct one to use here with 3 different outcomes Win, Loss and Draw, but it will not give us much more insights. Only greater number of combined scores. When we reach say 50 games or so all these P values will be close to the normal distribution which is much more handy to use and by that we reaches the ELO system. //Peter
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