"How are the scores decided in Chess?" - Correct? Recent question:


  How are the scores decided in Chess?


It has been argued that PV scores for Stockfish (the engine being used by chess.com) can be interpreted as something like:


  +1.0 is a pawn advantage for White. -0.5 is a half-pawn advantage for Black. 


Is that correct? The weights and parameters in Stockfish are either manually calibrated or tuned by something like the SPSA optimiser. We only care if the optimization can give the engine gradients to a local optimum solution.

The objective function is to maximise the playing strength. Maximising playing strength has nothing to do with making sure "+1.0 is a pawn advantage for White". In fact, we should be able to scale all all the PV scores by a constant. As long as the engine makes the same move, the magnitude of the scores shouldn't matter.

This is consistent to the minimax algorithm, where both players only care how to minimize/maximise the evaluation. Again, there are no efforts to make the PV scores human-interpretable.

To me, the PV scores are only important relatively, not absolutely. For instance, we should be able to say "+2.0 is about two-times advantage for White than a position with +1.0 for White.", but that shouldn't have anything to do with pawns. Similarly, if I modify the source code and scale the outputs by a factor of 10. I can still say: "+20.0 is about two-times advantage for White than a position with +10.0 for White". We shouldn't be able to connect the scores to pawns, knights, bishops etc.

I haven't seen anybody in the Stockfish development team spent any efforts to make the outputs interpretable. To me, the scores have no direct interpretation to chess.

Should I call all answers in the question technically incorrect?

EDIT

This is in response to @D_M. How would you scale the outputs to make it human interpretable? What's the algorithm? How would you define the loss function? How to test for the changes? I don't see it's a trivial problem.
In fact, we should be able to scale all all the PV scores by a constant. As long as the engine makes the same move, the magnitude of the scores shouldn't matter.


True. We can even add a constant to all scores (e.g. an equal position would have a score of +1) without any effect on the engine's decisions.

However, it's useful to keep the well-known score definitions:


  +1.0 is a pawn advantage for White


for 'backwards compatibility', just like we still have a 'meter bar' in Paris while the meter is currently defined with Krypton 86, so the 'meter bar' is technically slightly longer or shorter than a meter.