Author: Uri Blass
Date: 13:51:59 12/21/02
Go up one level in this thread
On December 21, 2002 at 16:39:01, Peter Fendrich wrote: >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? difference in rating does not give probabilities for a draw. > >>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? Yes >Third: "no doubt" doesn't mean anything meassurable. There is always a doubt, >even if it's small. Yes I meant to say that practically the doubt is very small when you seee 1000-0 with 999999000 draws so practically you can be sure. > >>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? Yes Uri
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