I think that player rating shows rating what is in the end of the game...so if player with low stamina have 10 minutes, then he play them good, but if he have 40 minutes, then he play first 10 good and all other time he just get more tired and he cant show all of his skills..
if player 1 is much better skills like player 2, but player 2 have much bigger stamina, then i think in start of game player 1 will own player 2 but later they will get equal. something like that in my opinion. :)