Re: [Bug-gnubg] Some idle musings re. ratings

[Joern Thyssen]

On Thu, Sep 11, 2003 at 01:38:01AM +0200, Jim Segrave wrote
> 
> This is not a realistic model in that no-one ever plays with a
> consistent MWC, but I was wondering if we could use the luck adjusted
> result as an indicator of MWC to model FIBS ratings and to compare them
> to the current function  which Kees van Doel generated.

I think that is exactly what what Kees did.

He calculated relative rating estimates of gnubg 0-ply versus gnubg
0-ply with noise and found a relationship between error rates and the
relative rating estimates.

Rethinking, I would have prefered to relate the error rates and MWCs,
and then apply the FIBS rating formulae afterwards. 

One of the issues raised by Douglas is if the experiment of 0-ply versus
0-ply noise really represents a good model of human play. 

Also, what relationship do we expect between error rates and lost MWC?
My guess would be linear for some fixed match length, but it depends on
if you make the errors in the beginning or towards the end of a match.

Using 0-ply with noise will roughly give constant error rates throughout
the match, so I'd expect to see a linear relationship between error
rates and lost MWC for a fixed match length. I'm not sure if this holds
for human play -- I guess you would need to investigate a large number
of human matches.

The FIBs rating formula is:

D = -2000/sqrt(n) * log10( 1/p - 1 )

For values of p around 0.5 the rating difference D is close to linear in
p, so we would get a linear relationship between D and error rates --
exactly that Kees found.

Kees uses a a/N+b extrapolation formulae for the match length.  I would
guess from the FIBS rating formulae that a/sqrt(N)+b would be better. 


Jørn

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