Author: Andrew Dados
Date: 09:34:33 02/04/01
Go up one level in this thread
On February 04, 2001 at 10:43:13, Ralf Elvsén wrote:
>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
I'm saying here that rating numbers are not 'given' just like e.g. sizes of
leaves. When building rating system we have to define it. So it is defined in
the way that rating numbers agree with normal distribution; we also define
standard deviation (which scales our system) and average rating. So your second
sentence is correct.
-Andrew-
>
>>
>>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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