Author: Andrew Dados
Date: 01:35:45 02/03/01
Go up one level in this thread
On February 02, 2001 at 15:33:11, Uri Blass wrote:
>On February 02, 2001 at 15:02:34, Andrew Dados wrote:
><snipped>
>>Thanks Arpad ELO system is based on _normal distribution_ of players... so we
>>can calculate ELO differences.
>
>We can calculate an estimate for the elo difference based on the result.
>We cannot know the exact elo difference.
>
>The estimate does not tell us the distribution of the elo difference.
>
>You can assume that the elo difference is distributed normally but you need to
>know the standard deviation of it
The base of ELO system is 'we need to assign some numbers to players that will
obey Normal Distribution'. So you calculate ratings in that way.
You can take it as definition of ELO system. If you need some numbers which obey
different distribution, then you can devise your own rating system, but ELO
definitely obeys normal distribution of ratings (as it defines ratings in that
way).
Practically for fide and uscf standard deviation (sigma) is about 280. That's
what simplified formula of 1/(1+10^(-k/400.0)) used to calculate ratings
implies.
If you ever used Mathematica this is the 'real thing':
(sig is Sigma)
Dist[X_]=1/(sig*(2*Pi)^0.5)*Exp[-X*X/(2*sig*sig)];
P[D_]=Integrate[Dist[X],{X,0,D}]+0.5; (* Integration from 0 to D *)
You definitely have your point about 'not enough data to anchor sigma' thing,
but for starters and for most real life match scores you can even simplify that
'normal distribution' model and say: all rating differences are distributed
equally. Within the range of +-200 ELO difference and around most programs
strength (being way above avg of 1740 rating) it will be valid enough to draw
conclusions....
>and the average of it that is 0 if you have no
>idea which player is better before you start the games.
>
>Only after getting this information it is possible to calculate the probability
>that the winner is the better player after you know the result.
>
>Uri
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