Author: Peter Fendrich
Date: 13:39:01 12/21/02
Go up one level in this thread
On December 20, 2002 at 20:01:17, Uri Blass wrote: >On December 20, 2002 at 19:56:58, Peter Fendrich wrote: > >>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 > >No Do you really mean that increased rating diff doesn't mean increased probability that A beats B and vice versa? >It is not the same suppose player A beat B 1000-0 with 999999000 draws > >you are going to have no doubt that A is better but if the result is >500000500-499999500 with no draw then it is clearly possible that the results >are random. First: Then you are saying that draws has something to with it. Second: That is not the full answer (A is better than B). A is probably better than B, we know that. The question is how confident we are saying that. That confidence is changing if the ratings are. I would say that it's more likely that a 2800 rated player will beat you than a 1800 rated player. Wouldn't you? Third: "no doubt" doesn't mean anything meassurable. There is always a doubt, even if it's small. >If you throw a fair coin 1000000000 times then in most of the cases the >difference between the number of heads and the number of tails is going to be >more than 1000. Yes? >Uri > >if you
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