I have a general impression that ha 25-30 move scramble (3x3x3) is not quite enough to separate all pieces from each other. When I scramble randomly myself with 40-50 moves, I find it more difficult to find a good start.

As a result, I started thinking whether it is possible to find some kind of metric that calculates how well a cube is scrambled.

A possible metric would be to calculate the entropy of the cube. Entropy is a well defined metric within mathematics and chemistry and should be suitable way to calculate how well a cube is scrambled. A solved cube has entropy 0, and grows the more unordered the cube is.

Has anyone looked into this?