Author: Peter Fendrich
Date: 16:56:58 12/20/02
Go up one level in this thread
On December 20, 2002 at 19:30:38, Uri Blass wrote: >On December 20, 2002 at 19:07:04, Peter Fendrich wrote: > >>On December 20, 2002 at 12:16:25, Uri Blass wrote: >> >>>On December 20, 2002 at 11:03:14, Peter Fendrich wrote: >>> >>>>On December 20, 2002 at 04:10:35, Rémi Coulom wrote: >>>> >>>>>On December 19, 2002 at 19:28:01, Peter Fendrich wrote: >>>>>> >>>>>>I did, some 15-20 years ago, in the Swedish "PLY" a couple of articles that >>>>>>later became the basics for the SSDF testing. >>>>>>A year or so ago you posted a question about how to interpret results with very >>>>>>few games. In a another thread I posted a new theory for this as an answer >>>>>>"Match results - a complete(!) theory (long)". >>>>>>I also made a program to use for this that can be found at Dann's ftp site. >>>>>>/Peter >>>>> >>>>>Hi Peter, >>>>> >>>>>If you had not noticed it, you can take a look at a similar program I have >>>>>implemented: >>>>>http://remi.coulom.free.fr/WhoIsBest.zip >>>>>Basically, I started with the same theory as you did, but I went a bit farther >>>>>in the calculations. In particular, I proved that the result does not depend on >>>>>the number of draws, which is intuitively obvious once you really think about >>>>>it. I also found a more efficient way to estimate the result. I checked the >>>>>results of my program against yours and found that they agree. >>>>> >>>>>Rémi >>>> >>>>Hi, >>>>For me it's not so obvious that you can through the draws out. >>>>I just took a short look at your paper and maybe I misunderstood some of it. >>>> >>>>Take this example: A wins to B by 10-0 >>>>Compared with: A wins to B by 10-0 and with additional 90 draws. >>>>Not counting the draws will get erronous results. >>>> >>>>The results between our programs shouldn't agree, I think, because I heavily >>>>relies on the trinomial distribution (win/draw/lose). One can use the binomial >>>>function (win/lose) and add 0.5 to both n1 and n0 for draws. That will probably >>>>give a fairly good approximate value but the only correct distribution is the >>>>trinomial. >>>> >>>>/Peter >>> >>>If the target is only to find which programs is better we can throw draws. >>> >>>You can imagine the following game chessa: >>> >>> >>>One game of chessa includes at least one game of chess. >>> >>>chessa is finished only when a chess game is finished in a win. >>>if a chess game that is played as part of chessa is finished in a draw then >>>chessa continues and the sides play chess with opposite colors. >>> >>>By these rules in both cases the winner won 10 games of chessa with no draws >>>(draw in chessa cannot happen). >>> >>>Uri >> >> >>In that case you don't need anything more than the result. >>What I'm doing is producing a statment like: >>A is better than B with the probability of x%. >>The 10-0 result will raise x very high but the 55-45 result will lower the >>probability even if A is still regarded as the best. >>/Peter > >if the 55-45 is result of 90 draws then 55-45 give the same probability that the >winner is better as 10-0. > >The draws are only relevant for estimate of the difference in rating but not for >deciding about the better player. That is essentially the same thing. Different estimates of rating gives different probabilities of A beating B. The both are closely related. If the ratings are changed the probabilties should be changed. /Peter
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