Author: James T. Walker
Date: 04:42:24 11/02/04
Go up one level in this thread
On November 01, 2004 at 14:42:26, Uri Blass wrote: >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 Just plot a graph with 999 data points all with a value of zero. Then plot another graph of 1000 data points all with a value of zero. Then compare the difference. Jim
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