The Merits of the Pitcher Hitting 8th

As the Brewers wrap up a series against the Cardinals and Tony LaRussa's peculiar lineup strategy, I thought it might be worth thinking about what would make certain lineups advantageous.  LaRussa has been hitting the pitcher in the 8th spot, with a position player hitting behind him in the 9th slot, for several years now.  Why?

Well, the aim is to have more men on base for the likes of Pujols as the game progresses.  This seems like a worthy goal, but I think what I'd like to see is a small study done on the benefits of simply getting Pujols (or any elite hitter) more plate appearances rather than trying to put runners on in front of him.  For instance, let's assume that over the course of a season, each slot in the lineup has 20 more plate appearances than the slot below it.  (That is, slot 1 has 20 more PA than slot 2, and slot 2 has 20 more PA than slot 3, etc.)   Then one way to gain more offense is simply to hit Pujols leadoff: he'll have 40 more PA than he does from the 3-hole.  He currently has about 360 PA and 31 HR, so he homers about every 12 PA.  If we round down, we're talking about adding 3 HR to his season simply by giving him more plate appearances.

Importantly, the extra 3 HR will not necessarily occur to leadoff a game (though they might), so there's a chance that there could be men on base from the bottom of the lineup when he hits them.  So this is at least 3 extra runs, and potentially as many as 12 (if all 3 HR were grand slams) gained from moving him to leadoff.  Furthermore, he'll hit doubles (every 17 PA) and singles (every 3.7 PA) too, so he'll be on base plenty to lead off the game--or after driving some guys in later in the game when he normally would still be 2 hitters away at that point.

What do you lose?  You lose the certainty of 2 guys hitting in fromt of him during the first inning of every game.  So the tradeoff involves calculating how many runs he drives in during the first inning of games.  After that, the two strategies are equivalent, because the game will dictate when he gets up and how many men are on base in front of him.  You could even hit your current 1 and 2 guys in the 8 and 9 slots so that once the first inning is over, the lineup looks like it would in the middle of any other game.  But Pujols will bat 40 more times during the season.  This would be the logical limit of the strategy La Russa is currently employing.  Anyone know how many runs Pujols drives in during the first innings of games this season?