I was reading the comments to this U.S.S. Mariner post, and one particular comment got me thinking:

This Utley-Howard thing reminds me of the Phillie-related debate James described in an earlier abstract, where he debunked Larry Bowa’s fielding prowess. People were saying things like “well, look at all the balls Mike Schmidt fields which Bowa might have gotten to” and James basically said “if there are two players who can get to the ball, then one of them ought to move over.”

This is, effectively, the flipside of it. Utley is getting balls that someone else ought to get but isn’t. So how do you properly credit him with them (after all, he really does field them)? More importantly, how do you rate him when he’s essentially playing a different position from all the other second basemen?

That comment was in response to this criticism of Dewan's system:

There’s also positioning issues in how Dewan ended up calculating his +/- ratings, as can be seen best in his Chase Utley numbers. Because Utley shifts towards the first base bag to make up for Ryan Howard’s ridiculous lack of range, he gets to far more balls in the 1B/2B hole than most second baseman. Dewan doesn’t adjust for this, and gives Utley credit for a +32 rating to his left (compared to +6 straight on and +8 to his right). Because of how Dewan is measuring plays saved (based on normal positioning for all players across the league), Utley would look worse defensively by his system if the Phillies just got a better defensive first baseman and Utley shaded back towards the 2B bag to play a more normal second base.

Here's the thing, though...

If Utley shifts farther over towards the middle, because there's a normal fielding first baseman, then doesn't his straight on and to the right numbers go up?

Because if you are going to ding him for positioning on plays to his left because he shades so far to his left, it seems you have to give him extra credit on plays to his right.  The fact that he's a +8 on plays to his right while shading over so dramatically to his left seems to emphasize how impressive his range really is.

So if Utley plays in a normal position for second base, his + rating going to his left maybe drops in half...but he presumably is also making more plays going to his right than he is currently making, and probably more plays on balls hit "straight on" (which, if he's shading left, is actually slightly to his right).

So if Utley makes 16 fewer plays on balls to his left if he plays normally, but makes, say, 5 more plays on balls straight on and 10 more plays on balls to his right, then he still ends up grading out with the same +/- as he does under Dewan's current system.

So what I don't understand is, how would the fact that Utley shades himself to the left more to cover Ryan Howard's lack of range something that makes his overall +/- lower than it otherwise would be?  If anything, I have to think that if he's got a normal first baseman and plays a more normal second base position, he'd end up making more plays on balls to his right than he loses on balls to his left by changing his position.

Can someone explain this?