Author: Stephen A. Boak
Date: 22:51:05 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 Why do you compare players that scored 0/4 against 1400 players with players that scored 0/12 against 1400 players? [I understand the relative rating scale.] If a player has scored 0/4 against 1400 players, which is more likely: 1. The player is 400 points lower than his 1400 opponents? 2. The player is 100 points above his 1400 opponents? In both cases, without any draws or wins, we have absolutely *zero* idea how much, if any, chess skill does the particular player have (other than being able to move the pieces). The question then is, how low is the player most likely to be (in practice). 2000 points lower than the 1400 opponents seems highly unlikely. Not sure if negative 600 is permitted on the Elo scale (I believe it is not permitted). 1000 points lower is possible, but may be very unlikely unless the player is a very young beginner. (Beginners, very young pre-school or grade school players, may obtain initial ratings of 400 Elo. Usually teenagers will score much higher when they first play in tournaments. But any first time tournament player, no matter what age, may easily lose his first 4 games to 1400 players. In practice in the United States, very young pre-school or grade school players will not be playing 1400 level opponents in their initial rated tournament. Few of their opponents will be likely to be rated that high--especially if they lose round after round in a 4-round Swiss tournament.) 400 points lower is certainly is not guaranteed, but *may* be (not guaranteed) the approximate mean or average delta rating for all 0/4 scorers against 1400 opposition. Due to my probability scenario, set forth above, it is likely that there will be many more 1000 rated players who score 0/4 against 1400 players, than 1500 players who initially score 0/4 against 1400 players. Hence, the mean or average delta *may* likely be farther below 1400 than you suggest. I think Elo set the formula for Provisional Ratings very well (not perfect, whatever that is, but very well). Two standard deviations, when scoring 0/any is perhaps the best overall compromise. One standard deviation is too small. Three or four standard deviations is often way too much in practice. Don't forget, 1400 players do not always play at 1400 strength. Due to randomness in rating measurements (and randomness in results of human play), out of the 4 games, the 1400 player likely played 2 games at something less than 1400 strength (perhaps 100 to 200 points less strength when on the lower side of random performance). Or, similarly, the 1400 player may not really be 1400 in strength, but simply had a few random but better than average results to get (temporarily) to 1400 rating. If the player lost 4 games to 1400 players, he likely lost two games to 1400 players who were only playing 1200 or 1300 in two of the games. Or lost two games to two 1300 players who returned to their normal ratings (perhaps a bit lower) in those particular games. These considerations mean the 0/4 player is readily (perhaps) 400 points below the rated 1400 players in all likelihood. [not guaranteed, but perhaps on the average] --Steve
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