Beauty chart ?

The concept of beauty might be exposed by contrasting positional advantage to material advantage. Something like delta eval over delta material minus 1.

The problem here, as always, is that eval is calculated on the next moves while material is not. Let's say one sacrifices the queen for a pawn. The material then is first +1, for taking the pawn, while it gets to -8 on the opponent move. Moreover, next move you might take their queen, getting the material back to +1. Nothing special, just getting a pawn. Contrast this with a position where:

• the material is significantly lower than the eval, indicating a strong positional advantage
• the material will not significantly change for the next few moves
• one can backtrace the position to one of your moves from which opponent moves are very forced

However, this implies access to computer engine information that the simple eval value does not provide. To be investigated.

No files, tests, or entry points are named. First investigate whether lichessTools can access the engine information needed beyond the simple evaluation value, then define the proposed beauty metric and its data requirements. Done means a feasible, scoped implementation plan or a clear finding that the required engine data is unavailable.