Author: Peter Fendrich
Date: 15:18:43 12/21/02
Go up one level in this thread
On December 21, 2002 at 16:51:59, Uri Blass wrote: >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. Of course it does: Big difference, low probability of a draw. Low difference, more probability 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. I can't see how that proves your point. 1000-0 is a very big number and so is all those draws. You're right that 1000-0 with 999999000 draws is more in favour for A than the result 500000500-499999500 without draws but that doesn't tell me anything about removing the draws and look at only the result 1000-0 and that's what the question is about (removing all the draws). If you agree with me that a draw result will affect the rating than you are also saying that it affects the probability that A is better than B. The rating is all about what probability we have for A being better than B. /Peter >>>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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