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  • Writer's picturehenryfarleyjohnson

Height, Handedness, and Simpson's Paradox

Here’s a hypothetical for you: suppose two MLB players approach you in the dark. You can’t see them, and you can’t identify them, but you’ve been asked to guess which one is taller. The only information you’ve been given is that one throws with his left hand, while the other throws with his right hand.

Who do you think will be taller: the lefty or the righty?

OK, now let’s alter the situation slightly. Suppose you’re presented with the same challenge— with no physical evidence, guess which player is taller. Only now, there’s an extra nugget of information: one player throws with his left hand, one player throws with his right hand, and they play the same position.

Does your guess change?? Why would it?

All right, enough riddles. The other day, while watching the MLB playoffs, I got to thinking about how lefties don’t play catcher. There are different reasons for this, but no lefty has caught an MLB game for decades and decades.

And it’s not just catching that lefties are steered away from. In fact, lefties are limited to a fairly small set of defensive positions: pitcher, first base, and outfield.

One thing that stands out about these positions? The people who play them tend to be taller. Tall first basemen can stretch for balls, tall pitchers can use their length to throw harder, and many outfielders are power hitters (which correlates with having a bigger frame).

This all sets up a nice little syllogism: if those positions attract taller players, and lefties are slotted into those positions, is the average lefty in the major leagues taller than the average righty?

It turns out that the answer is yes! Over the past 50 years, the average left-handed MLB player has been 73.62 inches tall, while the average righty has been 73.53 inches tall. It’s a minor difference, but lefties are, in fact, taller!

But here’s where things get interesting.

Lefties are a hot commodity in baseball. They have matchup advantages as hitters and pitchers and they have defensive advantages at first base.

For these reasons, scouts may be willing to overlook a smaller frame if a player is a lefty. In fact, in one of the great abuses of the word easy, you might say it’s easier to make it to the big leagues as a lefty.

This leads us to our next syllogism: if lefties have an advantage in making it to the pros, are the lefties at any given position shorter than the righties at the same position?

Here again, the answer is yes! If we define a player’s position as the spot he played most games at in his debut season (a flawed measure but a solid blunt instrument), we can see that the average righty is taller than the average lefty at every single position!

This is kind of surprising, no? Righty pitchers are taller than lefties, righty outfielders are taller than lefties, etc. and yet it’s LEFTIES who are taller overall! So should those MLB players approach you in the dark, the fact that they play the same position is a HUGE piece of information!

This phenomenon— that lefties are shorter at every position but taller overall— is an instance of Simpson’s Paradox, a first-rate hall of fame concept from first-year stats. Simpson’s Paradox occurs when some trend in a population fizzles out or even reverses when you break the population down into smaller groups.

It’s been used to elucidate truths about everything from political beliefs to medical treatments, but in keeping with the baseball theme, we’ll use the example of batting averages that Wikipedia has so kindly provided:

Even though David Justice had a higher batting average than Derek Jeter in 1995 and 1996, when you combine the two years, it's Jeter who had a higher batting average overall!

This is because more of Jeter's at-bats came in 1996, just as more of the lefty heights in our sample came from tall positions!

Is this interesting?? Maybe like 5/10? In the spirit of biased samples, I'd say this is more interesting than most things on this blog but less interesting than most things in life.


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