Author: James T. Walker
Date: 21:40:32 10/30/04
Go up one level in this thread
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. 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. 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. 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 ! > >>The >>formula assumes you are 400 points below the average opponents and that is true >>in both cases cited above. Nobody says it's perfect. It's only an attempt to >>give a provisional score untill some concrete data is available. The 400 >points below your opponents average is as good a guess as any and easy to >calculate. > >The provisional score is actually a different story. You might be thinking of >the Glicko system where a provisional score is used to accelerate the process. > >The 400 is more like a rule of thumb, it's not accurate and it's certainly not >independent of the number of games. > >>Also how did you come up with a win expectancy of 1/4 point? Simply because >>that's the next possible score closest to zero? > >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. > >-S. >>Jim
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