Author: James T. Walker
Date: 08:32:11 10/31/04
Go up one level in this thread
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. > >>>Imagine that you have an infinitely large bag and that this bag contains >>>infinitely many chips. >>> >>>You pull out 4 chips, all of them red. >>>How certain can you be that all of the chips in the bag are red? >> >>How certain can you be if you pull 10000 chips out and they are all red? It >>only takes one of a different color in an infinite series. You can't be certain >>in either case. > >Well 1/infinity is 0, so you don't have to worry about that :) > >-S.
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