The main reason for this is that players are not equidistant: you can have at most 3 equidistant points on a plane. It much more likely for a player to be influenced by a neighbouring opponent than by the one diagonally opposed.
So what I’m proposing is that every 4P game is played 3 times (same seed, different positions), with players A,B,C,D placed:
AB AD AB CD CB DC
Only in this way we would be able to determine a meaningful ranking on the particular map.