Let's examine some random players.
Hoak-3rd baseman-.282/.366/.445 (120 OPS+) with 16 HR, 79 RBI, 97 Runs, 5.4 WAR, 2nd place
Groat-shortstop-.325 (league-leading)/.371/.394 (110 OPS+) with 2 HR, 50 RBI, 85 Runs, 6.2 WAR, 1st place.
It's interesting that even though the WAR stat didn't exist, the one with higher WAR still won. I wonder if it was an argument of intangibles during that time? Shortstops have won a lot of MVP awards.