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Subject: Re: ELO & statistics question

Author: Ratko V Tomic

Date: 16:33:40 04/26/02

Go up one level in this thread


> for score 10/20
>
> error is +- 4.47
>
> 95% confidence interval is 1.06 - 18.94  / 20

No, that's not what I had in mind. Although 20 isn't
large enough for sqrt(N) error interval approximation,
for the sake of clarification, this is how you would
use sqrt(N) to get the rating error interval:

The E=sqrt(N)/2 applies to the absolute score,
i.e. you obtain max and min scores: N1=10+E, N2=10-E.
Then you normalize y1=N1/N and y2=N2/N and compute
ratings r1 and r2 for y1 and y2 using r=400*log(y/(1-y)).
The two ratings r1 and r2 give you the rating error interval.
Note that the rating error interval is neither symmetrical
nor linear (in E) around the average rating r(y).

The same path from E to rating error applies also
to the exact combinatorial value of E (as sketched
in the earlier messsage). For small N such as N=20,
you would probably want to use the exact combinatorial
E, or at least the approximation Uri suggested:
(absolute) E=sqrt(y*(1-y))*sqrt(N) (which is the same
as E I used: sqrt(N)/2 only for y=1/2, and smaller
than sqrt(N)/2 for y<>1/2).




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