So how about a player who is fighting on behalf of a:
Pawn must lose 1 game to lose the set
Knight or Bishop must lose 2 games
Rook must lose 3 games
Queen must lose 4 games

Any fight involving the King is a best of 3.

So if a white knight attacks a black rook, the white player must win 3 games to capture but the black player must only win 2 to hold the knight off.