Centipawn Loss Distribution

@Benny-Frandsen said in #16:
> I'm pretty sure this distribution can be directly converted into ELO estimate. All you need to do is to calculate it for a bunch of players with established ratings from their games and find out how distribution parameters correlate with ELO. And yes, probably better to look at winning percentage drop than at centipawns loss.

I'm not sure if this is quite so easy since CPL also depends on the style of the players. Famously Tal played less accurately than other world champions, but since his games were so complicated, his opponent's made more mistakes as well.
In general, things like CPL and accuracy depend a lot on the play of the opponent. It's much easier to play good moves when your opponent isn't challenging you.

@somethingpretentious said in #20:
> It might be easier to read your CPL graphs with some sort of smoothing / density. You say that 30-130 is roughly constant but to my eye it seems there are more around 50 than 130 for sure. Smoothing will help assess this by eye.
>
> Cool work regardless!

There might be too much smoothing, and not enough dispersion signal sharing I would say we need both. Spreading the region of information might be another way to do both, visually. But in the realm of per position evaluations statistics over many games, I think in chess data analysis habits we should keep transmitting the dispersion. There may not be enough data yet to agree on a model from which error bars (that assume often some smooth and simple population distribution, e.g. normal distribution of dispersion).

A superposed interpolation might do the job, though, without sweeping the "accidents" under the rug, like some conversion curves I might have seen. I enjoy point clouds to be honest. At least one per smooth curve.

Cool direction of work, I agree.