Author: James T. Walker
Date: 14:15:20 10/27/04
Go up one level in this thread
On October 27, 2004 at 08:35:55, Uri Blass wrote: >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 In the case of 0/12 it can also be 1500. So what? In the case of 0/4 it can also be 1500. So what? The assumption that 0/4 is stronger than 0/12 is not logical. It simply means that the 0/4 player has not played enough games to give a reliable rating. It means that his rating probably is less reliable than the 0/12 player. It does not mean that his rating is higher.
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