Baseball season is about to start (Go Phillies! and Go Mudcats!), and when I took a look at the Phils' roster, I noticed that they have three pitchers who are listed at under six feet tall: Antonio Bastardo, Mauricio Robles, and Raul Valdes. Curiously, all three are left-handed. We're defining handedness as the hand with which one throws. Does anyone really care that Antonio Bastardo bats righty? I'm sure that's not on Charlie Manuel's mind when he calls Bastardo in from the bullpen.
This got me thinking: two easily recognized physical traits that are valued in pitchers are (1) height, and (2) left-handedness. Well, what's their relative value? Is left-handedness valued over height, or are they more-or-less the same?
If being left-handed is more valuable than being tall, then if I were to look at the shortest pitchers in MLB, I'd expect to find more lefties than a random sample. So, I made a spreadsheet of all the pitchers on the 2013 40-man rosters (thank you, ESPN.) There are 663 pitchers, and of them, 203 are left-handed. That's an incidence rate of 30.62%. Next, I had to decide on a definition of "short." For our purposes, I decided that our group of short pitchers would be those listed under 6'0". Of these 663 pitchers, 51 are listed at 5'11" or shorter, so I'm looking at the shortest 7.7% of pitchers.
Among these 51 pitchers, there are 17 left-handers. That's an incidence rate of 33.3% slightly larger than the incidence of left-handedness among all the pitchers, so maybe we're on to something with this idea, but we need a little bit more information to make that call. Let's suppose I took 663 slips of paper, wrote "Left" on 203 of them, "Right" on the other 460, put them in a hat, and pulled out 51 of them (without putting the pulled out slip back into the hat, which is important.) If I did this experiment many times over and wrote down how many Lefts I got each time, the average would be about 15.6, but the deviation -- that is, how much I can reasonably expect my number of Lefts selected to vary from one experiment to the next purely due to chance, is about 3.2 Lefts. Our 17 short lefties are well within what we'd expect from choosing pitchers completely at random.
It appears that being left-handed is not valued over being tall for Major League pitchers. There goes my chance of ever being a professional baseball player, unless in the next few years I can figure out how to throw an unhittable knuckle ball.