There are a “standard” set of values for chess pieces: pawn = 1, bishop = 3, knight = 3, rook = 5, queen = 9. How well do these check out? Given a chess position one can find the difference in the number of each type of piece between the two players and see who wins. It turns out (according to this analysis) that the standard analysis gets the relative value of the pieces (i. e. non-pawns) right but undervalues pawns; this may be because the games in the dataset used are between very strong players, and pawns may be more valuable in their games.
I’ve thought of doing this analysis myself, but just haven’t gotten around to it. The obvious extension would be to take into account context – are pawns further up the board worth more because they have a likelihood of being promoted? Do values change based on the stage of game?