Author: Ralf Elvsén
Date: 07:43:13 02/04/01
Go up one level in this thread
On February 03, 2001 at 04:35:45, Andrew Dados wrote:
>
>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.
What are you saying here? That if we apply this rating system (based
on the formula below) the resulting numbers in the rating pool
will be normally distributed?
Or that we assume that the "true" ratings are normally distributed
and we therefore apply this system? Or something completely different?
Ralf
>
>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....
>
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