Although I can't find it at the moment, I remember reading an analysis a while back about why ground balls are often hit to a hitter's pull-side and fly balls are often hit the other way. The idea was essentially that the bat is not level as it is swung--it extends at a downward angle from the batters shoulders--and so if the batter misses such that the ball hits the top half of the bat, it will tend to drift upward and away from the batter, while if the batter misses such that the ball hits the bottom half of the bat, it will tend to move downward and to his pull-side.
This batted ball distribution would likely be advantageous for a pitcher for at least two reasons. Most importantly, home runs (and to a lesser degree, doubles and triples) are overwhelming hit to a batter's pull side. If a pitcher could decrease the ratio of fly balls that are pulled, he would likely significantly decrease his opponents' slugging percentage. Secondly, if a pitcher achieves a high ratio, it is likely because hitters are not squaring up the ball well on the bat, and may be hitting the ball with less velocity. This could limit hits on both flies and grounders.
What I'd like to do if I had the time/data would be to determine if the pull/push split on ground balls and fly balls is a repeatable skill for pitchers, and how it correlates with opponent slugging percentage and pitching BABIP. A second study could be conducted for hitters. Thoughts? Advice?