How to Get a Ball During Batting Practice

I wrote about my full background in this post from the Angels' SB Nation page, but here's a short summary:

I am a game theorist by trade--I study how to optimally play games when the competition is trying to maximize their performance as well. Catching baseballs during batting practice is such a game. Everyone wants to get a ball, but the way I try to get a ball affects your ability to get a ball and vice versa. I used to struggle to get a ball until I realized batting practice was merely a spacial optimization game. So I sat down one day and tried to mathematically solve that game. Since then, I have managed to at least three balls per event.

I'm posting here because I am moving across country on my way to grad school, making stops at a bunch of baseball parks along the way. Phoenix was last night, and I caught three. Here's the basic idea of my strategy:

In the context of Chase Field, I think the "upper deck" is the right field bleachers. I started out in the left field bleachers, but there were waaaay too many people there. I know the right field bleachers aren't right up against the field like they are in left, but there is so much less competition--for a while, only three people were there actively trying to get a ball. Your odds are a LOT better in right, even if fewer balls go to right field on the whole. (Until everyone reads this and shifts to right field...at which point we might reach that equilibrium I talked about in the video.)

Other than that, can someone tell me why the Diamondbacks are so stingy with batting practice balls? I didn't see a Diamondbacks player throw a ball into the crowd a single time. Given that balls are cheap to produce, encourage fan loyalty for years to come, and incentive people arriving early (and thus buying more overpriced food), why don't they toss more into the stands? I think a grand total of three made it into the stands during the Diamondbacks' part of batting practice, which is extremely low.