Author: Uri Blass
Date: 11:42:26 11/01/04
Go up one level in this thread
On October 31, 2004 at 11:32:11, James T. Walker wrote: >On October 31, 2004 at 07:11:04, Sune Fischer wrote: > >>On October 31, 2004 at 00:40:32, James T. Walker wrote: >> >>>On October 30, 2004 at 23:45:49, Sune Fischer wrote: >>> >>>>On October 30, 2004 at 21:59:36, James T. Walker wrote: >>>>> >>>>>As long as you realize you are making a "best guess" and not giving a real >>>>>rating that's fine. >>>> >>>>It was of course a back of the envelope, I have not derived it rigorously. >>>> >>>>I think a more accurate guess can be made if you solve for the case where the >>>>binomial distribution should give 50% or more for the X straight wins. >>>> >>>>> The problem is that in real life untill you actually score >>>>>some real points you cannot get a score which is anything but a guess. >>>> >>>>It will always be a guess as long as all you have is a finite sample. >>> >>>Well I'm talking about reality not theory. >> >>I don't understand why you make that distinction. The "real" rating is build >>upon the theorical model which we are discussing, so in essence there is no >>"real" rating there is only what the theory pridicts. >> >>I'm not sure model is good out in the tails, but that's a different story. >> >>>If you play 4 games and score 0 >>>points vs players averaging 1400 your provisional rating will be 1000. At that >>>point it's not a guess it's your actual rating which you take into your next >>>tournament. NOBODY claims it's an exact rating which follows you through all >>>the days of your life. This same formula is used to provide a "Performance >>>rating" in a match/tournament. >> >>The 400 is just a lazy mans approximation, for practical reasons people don't >>run around with calculators and use the exact formula, they often lookup the >>result on a small printed table. >>If you lose too much you end up outside the range of this table and they just >>subtract the 400. >> >>> It's again not just a guess it's how you >>>performed in that particular match/tournament. Again this is not your actual >>>rating that you carry with you but simply an attempt to measure how you did in >>>one particular match/tournament. But after you have played in some pre-defined >>>number of games you get an "established" rating. Of course you know all this >>>but you want to quote some mathmatical theory that says that 0/4 is stronger >>>than 0/12. >> >>Losing 12 times in a row is worse than losing only 4 times, isn't this logical? >> >>If I play 4 grandmasters I will lose 4 times, does this mean I'm rated 2100? >>It only means that I'm probably rated below 2100, we cannot say much more than >>that. >>If I play 12 times against them and loses them all, then we can say that I'm >>probably 1800 or below. >> >>So you get more and more information with each game, one can say that the >>measurable range slowly extends out from the 2500 and it will eventually reach >>you. >> >>>I am saying you can't prove it untill some more data is acquired >>>which will separate the 0/4 player from the 0/12 player. I'ts like saying >>>0/999 is stronger than 0/1000. Prove it ! >> >>I guess one can say that it is "proven" that the 0/1000 guy is weaker than X, >>where for the 0/999 it is only "proven" that he is weaker than X+epsilon. >> >>The estimated score must be slightly higher for the 0/999 guy, as it has not >>been proven he is bad enough to lose all 1000. > >That is an invalid assumption on which you base your entire argument. When in >fact if you have lost 999 games in a row the odds are that you will lose the >next game also. Yes,but you still cannot be sure about it so getting the information is relevant. You may be sure only with 94.99% that he is weaker than X after 999 games when you are sure in 95% that he is weaker than X after 1000 games. If you want to build some interval for his rating when you can be sure with 9 5% confidence that his rating is inside the interval then the interval may be (0,X) with 1000 games and something like (0,X+0.0001) with 999 games. Uri
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