Re: [Bug-gnubg] Re: The importance of METs

[nis]

On Tue, 2 Sep 2003, Joseph Heled wrote:

> Here are the numbers.
> E1 (woolsey wins both) - 31747
> E2 (mec26 wins both)   - 32067
> E3                     - 186186
>
> The verdict is?

I believe I have to revisit my calculations, at least to understand them
myself, and avoid confusion. We now look at this as 250.000 samples of the
unbiased estimator for game winning chances given by (result1 + result2)/2

That is, E1 has value 0, E2 has value 1, E3 has value 1/2

The variance of this measure is

((p1 + p2) - (p2 - p1)^2)/4

and thus the 95% confidence interval size (CI)

1.96 * sqrt(p1 + p2 - (p1 - p2)^2)/2/sqrt(trials)

Inserting your values, I get

p1 = 0.128
p2 = 0.127

and CI

1.96 * sqrt (0.128 + 0.127 - (0.128-0.127)^2)/2/sqrt(250.000)

= +- 0.0010

This is a little better than the result I get by viewing this as 500.000
independent trials:

1.96 * sqrt(0.5012*0.4988)/sqrt(500.000) = 0.0014

Note that in the worst case scenario (app. p1=p2=0.25, that is "no
correlation") the two methods give similar reults. This was one of my
tests for reasonability.

I expected the correlation to be much higher - I am surprised that the MET
used influences the outcome of more than a quarter of matches (although
these MET's are much more different than Snowie and mec26)

Nis