We'll start with the National League to find out if this is interesting. Don't want to calculate the entire MLB if it's a boring question.
Since I used today's starting lineups, I added a couple of parentheticals if the regular starters would have made a significant difference.
Team Ht(In) ---- ------ Braves 73.38 (73.88 with Johnson) Marlins 73.50 Rockies 73.50 Brewers 73.38 Cardinals 73.25 (1 of 3 teams with two < 5'10" starters) Cubs 73.25 Reds 73.13 (73.75 with Votto and Bako) D-Backs 72.75 (73.25 with Hudson) Mets 72.75 Dodgers 72.63 Phillies 72.50 Astros 72.25 (71.875 with Wiggington) Giants 72.12 (2nd of 3 teams with 2 < 5'10" starters) Pirates 72.00 Padres 70.63 (71.12 with Bard) Nationals 70.63 (3rd of 3 teams with 2 < 5'10" starters)
Well I was wrong about the Cards. Glaus and Ludwick saved them, and Adam Kennedy and Brendan Ryan are not as short as they appear. David Eckstein, where are you?
The tallest lineup today was the Marlins, but if Kelly Johnson had played 2b instead of Omar Infante, the Braves would have the tallest lineup. If Votto and Bako had played for the Reds, instead of Andy Phillips and Hanigan, the Reds would have been second.
The Padres and Nationals tied for the lowest average height, but the Padres started Carlin instead of Bard at catcher. If Bard had played, the Nationals (which started a normal lineup), would have been the shortest.
Adam Dunn and Corey Hart are the tallest (6'6"). Ronnie Belliard is the shortest (5'8").
The presence of the Padres and Nationals at the bottom made me wonder if there is a correlation with the number of wins. Here they are sorted by starting lineup height (assuming a "normal" starting lineup), and the number of wins.
Team Wins ---- ------ Braves 55 Reds 52 Marlins 61 Rockies 53 Brewers 66 Cardinals 65 Cubs 70 D-Backs 59 Mets 62 Dodgers 58 Phillies 63 Giants 49 Pirates 53 Astros 57 Padres 45 Nationals 44
Visually height doesn't seem connected to wins, but the correlation is .59, which is a pretty strong positive correlation. The only thing that keeps it from being higher is the presence of the Braves and Reds at the top. If you take them out of the equation, the correlation jumps to .78. Of course, you can't do that.