Author: Andrew Dados
Date: 12:02:34 02/02/01
Go up one level in this thread
On February 02, 2001 at 13:29:01, Uri Blass wrote: >On February 02, 2001 at 10:47:38, Andrew Dados wrote: > >>On February 02, 2001 at 06:59:06, Uri Blass wrote: >> >>>On February 02, 2001 at 02:55:44, Andrew Dados wrote: >>> >>>>On February 01, 2001 at 10:21:43, Uri Blass wrote: >>>> >>>>>On February 01, 2001 at 07:39:11, Leen Ammeraal wrote: >>>>> >>>>>>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 >>>>>> >>>>>>According to the little Windows app Whoisbetter by Steve Maugham, >>>>>>the certainty of being better for the winner is >>>>>>97% with the score 60 - 40, and >>>>>>99% with the score 7 - 0 >>>>> >>>>>It is clearly wrong. >>>>>The probablities that you talk about are not the probability that the winner is >>>>>better. >>>>> >>>>>We cannot know the probability that the winner is better unless we have more >>>>>knowledge. >>>> >>>>We can calculate this and if we disregard draws the chance that winner of 60-40 >>>>is better is indeed 97.4%. >>> >>> >>>Even without draws we cannot calculate it because we need information about the >>>apriori distribution of the probability of the better player to win. >>> >>>If we assume that it is 0.51 then we get 0.51^20/(0.51^20+0.49^20) >>> >>>If we assume that it is 0.6 we get 0.6^20/(0.6^20+0.4^20) >>> >>>If we assume that the probability of the better player to win has 50% >>>probability to be 51% and 50% probability to be 60% then we get something else. >>> >>>Uri >> >>Hell(o) Uri, >> >>With all respect I think you're wrong. >> >>You can enumerate through all possible rating differences and scores. >>(like, for score 60-40 chance of it for rating_diff 0 is d0, for rating_diff 1 >>is d1 etc...) > >I agree that we can calculate it but it is not the probability that I mean to. > >I am interested to know p(A is better than B after knowing that A won 60-40) > >You calculate p(the result is 60-40 when you know that A is d0 points better >than B). > >practically the data that I have is the 60-40 and I do not have the data which >program is better. > >I need to do some guess about the distribution of the probability of A to win B >that I call p or in other words the distribution of d that is the rating >difference between the players. >This guess is called the aprior distibution of p and you can translate is to an >aprior distribution of d. Thanks Arpad ELO system is based on _normal distribution_ of players... so we can calculate ELO differences. > >You can get 97.4% for some d0 but if you change d0 the 97.4% will be changed. > >>You get the function P(score,rating_diff). Factoring that through all >>rating_diff in some range gives you answer what is the chance that rating_diff >>lies in that range (you need to normalize P first). > >I agree that you can use the aprior disribution of rating diff to calculate the >probability that the difference in rating is at some range when you get the >result when a private case is the case when you calculate the probability that >the winner is better but you need an aprior distribution of d. > >I did not read your assumption about the aprior distribution of d when you >claimed that the probability that the winner is better given the result 60-40 is >0.974. > >Practically your assumptions may be different in different cases. > >if you do a small change in a chess program(changing the value of pawn by 1%) >your aprior distribution will be that d is small and you can be sure that it is >not more than 10 elo. > >If you do a big change and add evaluation code or add search rules you can have >assumtions that d can be big when it is possible that the new program is weaker >by 200 elo because of some logical bug. > >The distribution will not be symmetric in this case and it also mean that 60-40 >for A does not give the same confidence as 60-40 for B. > >Uri
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