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Statistical distribution of centipawn losses

Hi, I appreciate your project! I am wondering what mathematical function describes best the statistical distribution of centipawn losses for players at given rating. (I do not mean the average centipawn loss for a completed game, but losses of single moves.) And I do not mean the average CPL but its statistical distribution.
I guess, with your program it should be possible to generate such sets of data: distributions of CPL (in form of a histogram or so) for a given rating (or say, a small range [R1,R2]) and compare it for various rating values.
I wrote a question on Chess StackExchange on it: https://chess.stackexchange.com/questions/45085/statistical-distribution-of-centipawn-losses with more details.
I would be happy to cooperate on that!

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