François-André Danican Philidor (1726–1795) on the Power of the Pieces

Of the Powers of the Pieces, calculated on the probability being equal of their occupying any given square in the course of the game.

Pawn   . . . .  2
Knight . . . .  9 1/4
Bishop . . . .  9 3/4
Rook   . . . . 15
Queen  . . . . 23 3/4

The nature of the game puts the king's value above comparision. The pawn's chance of promotion increases his value to about 3 3/4.

In making this estimate, the part of the board within the sphere of each respective piece is supposed to be unoccupied.

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The values are dated, but I found the method of calculation interesting. Something to have in the back of the mind when estimating the relative value of the pieces during a game.

Comparing Philidor's estimates to the modern evaluations is another interesting exercise.

Pawn   . . . .  3
Knight . . . .  9
Bishop . . . .  9
Rook   . . . . 15
Queen  . . . . 27