Maybe margin of victory in a category has something to do with it, or should.

We should have a clear-cut objective way of knowing who won.

What if three different people each win one category?

Suppose we have 5 players. Who would you give the win to here? On a 5-4-3-2-1 basis, everyone has 9 points:
Code:
             AVG.   HR   RBI
Player A     .325    5    20
Player B     .350    3    21
Player C     .275    4    23  
Player D     .300    7    19 
Player E     .250    6    22
Same here:
Code:
             AVG.   HR   RBI
Player A     .250    7    16
Player B     .325    6    14
Player C     .350    4    15 
Player D     .300    3    19
Player E     .275    5    17
And here:
Code:
             AVG.   HR   RBI
Player A     .300    6    14
Player B     .250    7    15
Player C     .350    5    13  
Player D     .275    4    17
Player E     .325    3    16

"Difficult....not impossible"