Author: Uri Blass
Date: 05:35:55 10/27/04
Go up one level in this thread
On October 27, 2004 at 07:29:26, James T. Walker wrote: >On October 26, 2004 at 03:08:09, Uri Blass wrote: > >>On October 25, 2004 at 18:21:23, James T. Walker wrote: >> >>>On October 24, 2004 at 17:02:44, Uri Blass wrote: >>> >>>>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 >>> >>>Uri it is impossible to come up with a practical score for anyone who is winless >>>or undefeated in his/her first few games. It does not matter who they play or >>>what the opponents rating is. The performance formula is used only to establish >>>a "performance" rating in a short match/tournament. If its the first rated >>>games you have ever played then you are only given a "provisional" rating untill >>>a more accurate rating can be established in later tournaments/matches. Someone >>>rated 400 points above you has about a 91% chance of beating you and you have >>>only a 9% chance of winning. If you think you can give an accurate rating to >>>someone who has never won a game in his life and has only played 4 games then >>>you are dreaming. >> >>I did not claim that you can give an accurate rating. >>rating is not accurate. >>I only claimed that you can give a better estimate. >> >>rating is always an estimate and even if you know only the results you can use >>them to calculate some estimate. >> >> >> Computer programs calculate the performance rating and nobody >>>actually looks at the games to see how strong/weak the player may actually be >>>(In their estimate). In fact by the time they play their next 4 games they may >>>have improved by 400 points. I know several people who have done this because >>>they waited 2 years before playing again. >> >> >>It only suggest that the dates of playing should be also used to calculate >>performance and old games should get smaller weight. >> >> In the case of the one win scenario >>>you mention the link you gave gives two "ratings". The one you quote is a >>>"performance" rating and the second is the actual "new" rating. In the problem >>>you quote there is no reason for these two ratings to differ. They should both >>>show 1067. Therefore the link has improperly applied the formula which >>>calculated the score below 1000. IMHO. >>>Jim >> >> >>The estimate for 0 out of 12 against 1400 players should be smaller than the >>estimate for 0.5 out of 12 against 1400 players. >> >>The estimate for 0 out of 12 against 1400 players should be smaller than the >>estimate for 0 out of 4 against 1400 players. >> >>If these rules are not kept then my opinion is that the estimate can be >>improved. >> >>Uri > >I still don't follow your logic. Your assumption that 0/12 is worse than 0/4 is >not logical. In both cases the actual rating of the person playing may be >something like 500. In fact it could be the same person that played 4 games one >day and then a week later played another 8 games. As you say it is only an >estimate untill enough data can be obtained to make a more accurate assesment. >Jim In both cases it can be something like 500 but in the case of 0/4 it also can be something like 1300 in significant part of the cases so the average rating of players who do 0/4 against 1400 players is higher than the average rating of players who do 0/12 against 1400 The best estimate is simply the average rating of players who get practically that result and the average rating of players who get 0/12 is simply smaller. Uri
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