Calculating the LOS (likelihood of superiority) from results

[Isaac]

I would like to mention that the formula given in the wiki page (http://chessprogramming.wikispaces.com/Match+Statistics , which can be written as los=(1+erf ((wins-losses)/ (2*(wins+losses))**0.5) )/2. into a Fortran program) is not equivalent to the LOS given by Rémi Coulom in the first link he gives in this thread, namely http://www.talkchess.com/forum/viewtopi ... 82&t=30624.

For example if you tell the program that there is 1 win and 0 loss, the Rémi's program gives the value 0.75 while the formula on wiki programming gives 0.84.

The erf formula is an approximation that works well with large numbers of games. Using it with 1 win and 0 losses is not a good idea. But we are trying to answer questions about whether 10,000 games or 30,000 games is enough to get statistical significance, and that's done perfectly well by the erf formula.

I see thank you. I knew they were asymptotically equivalent but I didn't realize that it was not suitable for a low number of games.