Author: Uri Blass
Date: 14:02:44 10/24/04
Go up one level in this thread
On October 24, 2004 at 13:04:07, Stephen A. Boak wrote: >On October 24, 2004 at 02:12:51, Uri Blass wrote: > >>On October 24, 2004 at 01:47:54, Stephen A. Boak wrote: >> >>>On October 23, 2004 at 18:47:26, Vincent Lejeune wrote: >>> >>>>On October 23, 2004 at 16:37:37, Stephen A. Boak wrote: >>>> >>>>>On October 22, 2004 at 18:52:13, Uri Blass wrote: >>>>> >>>>>>On October 22, 2004 at 18:30:34, James T. Walker wrote: >>>>>> >>>>>>>On October 22, 2004 at 13:32:57, Uri Blass wrote: >>>>>>> >>>>>>>>go to the following link >>>>>>>> >>>>>>>>http://georgejohn.bcentralhost.com/TCA/perfrate.html >>>>>>>> >>>>>>>>enter 1400 for 12 opponents >>>>>>>>enter 0 for your total score >>>>>>>> >>>>>>>>Your performance is 1000 but if you enter 1 to your total score your performance >>>>>>>>is only 983. >>>>>>>> >>>>>>>>It seems that the program in that link assume that when the result is 100% or 0% >>>>>>>>your performance is 400 elo less that your weakest opponent but when your score >>>>>>>>is not 100% it has not that limit so they get illogical results. >>>>>>>> >>>>>>>>Uri >>>>>>> >>>>>>>My take on this is they are using a bad formula or have screwed up the program >>>>>>>to calculate the Rp. >>>>>>>The USCF uses Rp=Rc + 400(W-L)/N >>>>>> >>>>>>It seems that the USCF does not do it in that way >>>>>> >>>>>>They admit that the formula is not correct for players who won all their games >>>>>> >>>>>>Note: In the case of a perfect or zero score the performance rating is >>>>>>estimated as either 400 points higher or lower, respectively, than the rating of >>>>>>highest or lowest rated opponent. >>>>>> >>>>>>It is probably better to estimate the preformance based on comparison to the >>>>>>case that the player did almost perfect score. >>>>>> >>>>>>Uri >>>>> >>>>>Dear Uri, >>>>>What is the *correct* formula for a player who has won (or lost) all his games? >>>>>:) >>>>>Regards, >>>>>--Steve >>>> >>>> >>>>For such a player, the error margin = infinity >>>> >>>>the perf = average opp +400 to +infinity >>> >>>Thanks, Vincent. I know the formula well. :) >>> >>>I was poking fun at Uri (just teasing) for complaining about 'logic' when in >>>fact the formula for all wins or all losses is purely arbitrary. >>> >>>[I've read that Uri is a mathematician, so I like to occasionally jump in and >>>comment when he seems to overlook something basic. All in good fun--I >>>appreciate his postings and chess programming contributions.] >>> >>>I asked Uri what formula would he suggest as 'correct'. >> >>I think that it is possible to calculate the performance of a player that get >>1/2 point instead of 0 point and use the result as an upper bound for the >>performance of the player that got 0 points. >> >>It is not done. >> >>Another idea is to assume probability of win draw loss for every difference in >>rating and to calculate the maximal rating that the probability to get 0 points >>is 50% or more than it. > >Ok, Uri, I accept the challenge. > >Assume a player scores 0 points out of 10 total games. > >What Win, Draw, Loss probabilities should be used (arbitrary once again, for an >unknown player's strength, who has scored m=0 out of m games--right?), and for >what difference in rating? The opponents are players with known rating. We can calculate the probability of player with rating 1300 to get 0 points against the players because we have some assumption about probabilities based on the difference in rating. We can choose every different number than 1300 and calculate the probability for every x so we have a function p(x) and later solve the equation p(x)=0.5. > >What is the 'logic' for your choice of 'difference in rating'? That choice has >to be illogical (totally arbitrary), when the new player doesn't yet have a >rating, right? > >ELO does exactly that already--assumes the player is exactly 400 points less >(i.e. assumes a particular rating difference) than his opponents' average >rating, against which opponents he has scored m=0 points). > >What is a more logical rating estimate for the player than 400 points less than >the average rating of his opponents? What is the improved 'logic' for your >suggested rating approach? We want the best estimate for the rating of the player based on the results. 400 elo less than the average of the opponents is llogical because by that logic if a player lose against 10 players with rating 1400 and 10 players with rating 2400 the player get 1900-400=1500 and it is clear that the player is weaker than 1500. Even in the relevant link minimal rating minus 400 and not average rating minus 400 was used but it is still illogical. > >My thesis is that any suggested formula involves as much guessing, as much >arbitrary choice, as much 'illogical' thinking (because it is totally arbitrary) >... as the original +/- 400 points rule used in the ELO system. No You need to give an estimate for the rating. It is logical to give smaller estimate to player that score 1/2 point and not to player who scored 0 point. Every frmula that does not does not do it simply can be improved to a better estimate easily. If the estimate for players that score 1/2 point is correct the estimate for players who score 0 point need to be smaller(I do not know how much smaller but it need to be smaller) If you lose against many players the estimate need to be smaller relative to the case that you lost only against one of them. I do not know how much smaller but the formula should promise that it will be smaller. It is possible to test different methods in practise by investigating real cases of players who got 0 points and find their real level based on games against weaker opponent. The problem what is the best estimate is a practical problem and I did not investigate it(incestigation can try many possible methods and testing their errors in predicting future results when you choose the method that reduce the error to be minimal) but one clear rule is to give better performance for players who do better results. It was not done by the link that I gave. Uri
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