[salamo]

You'll also have some fun pinning down the difference between an "inaccuracy", a "mistake", and a "blunder". These are meaningful delineations for humans but not for a chess algorithm. Objectively, any amount of centipawn loss either changes the best possible outcome for the player or it does not.

So in practice, a drop in win probability greater than 14% is considered a blunder on Lichess.

For reference, lichess uses the following function to map centipawn advantage to the probability bar, derived from observed outcomes: https://github.com/lichess-org/lila/pull/11148

From an ML perspective, this is basically logistic regression with a single feature. However, once we leave the realm of theoretical centipawn value and begin to optimize predictive power, we could imagine adding in other things like the players' ELOs or time remaining per player, etc.

I think there are some interesting theoretical differences between predicted win probability derived from Stockfish CP and actual outcomes. As in, you could even imagine predicting positions where certain players struggle and steering them towards those positions. [0]

[0] https://www.youtube.com/watch?v=KgOC1D8wkyE