hi
I'd like to make some assumption and I need some good knowledge of statistics that I don't have.
Those are my assumptions, please correct me where I'm wrong.
cutechess cli reports elo and a uncertainity window.
Score of Vajolet dev vs Vajolet base: 2425  2290  5586 [0.507] 10301
Elo difference: 4.55 +/ 4.53
here the uncertainity is +/ 4.53, is this a confidence interval of 95% in sense of gaussian variable?
in this case sigma is 4,53 /2 = 2,265 and variance is 2,265^2 = 5,130225
assuming that I do 2 tournaments and assuming the result statistically indipendent ( problably this is not true at all....) and that Elo results is a gaussian probablity variable we have:
Elo_gain = elo1 + elo2
sigma_tot^2 = sigma1^2 + sigma2^2
so I have combined result of elo1+elo2 +/ 2*sqrt(sigma_tot^2)
ok.. magician please let me know if I have made some orrible errors with variance, signa, statistical independence and so on.... thank you all
statistic magicians help required
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Re: statistic magicians help required
First of all, I think they report 1.96 standard deviations, not 2. But that's small potatoes.
You haven't been precise enough in describing the twotournaments scenario. If you do two tournaments between the same two engines and you obtain Elo estimates with means Elo1, Elo2 and corresponding standard deviations sigma1, sigma2, I think the combined distribution is something like
mean = (sigma2^2 * Elo1 + sigma1^1 * Elo2) / (sigma1^2 + sigma2^2)
standard deviation = sqrt((sigma1^2 * sigma2^2) / (sigma1^2 + sigma2^2))
If you have a tournament AvsB and a tournament BvsC, then you can deduce the performance of AvsC with essentially the formulas you have
Elo(AvsC) = Elo(AvsB)+Elo(BvsC)
sigma(AvsC) = sqrt(sigma(AvsB)^2 + sigma(BvsC)^2)
You haven't been precise enough in describing the twotournaments scenario. If you do two tournaments between the same two engines and you obtain Elo estimates with means Elo1, Elo2 and corresponding standard deviations sigma1, sigma2, I think the combined distribution is something like
mean = (sigma2^2 * Elo1 + sigma1^1 * Elo2) / (sigma1^2 + sigma2^2)
standard deviation = sqrt((sigma1^2 * sigma2^2) / (sigma1^2 + sigma2^2))
If you have a tournament AvsB and a tournament BvsC, then you can deduce the performance of AvsC with essentially the formulas you have
Elo(AvsC) = Elo(AvsB)+Elo(BvsC)
sigma(AvsC) = sqrt(sigma(AvsB)^2 + sigma(BvsC)^2)
Re: statistic magicians help required
thank you for your reply.
The scenario is the latter, A vs B and then B vs C
The scenario is the latter, A vs B and then B vs C