Does Size Matter (Part 6)

Wow, has it really been over a month? The last time we looked at the effect of player size, we discovered that short and fat pitchers tend to be better, and fat pitchers especially have an inherent advantage over other pitchers—not only playing better, but for longer. Today, we will finally, after three months of adventure and discovery, complete this series and conclude, does size matter?

Let me remind you of the parameters of the study. I looked at all consecutive pitcher seasons with at least 200 batters faced between 1946 and 2005, almost 10,000 such pairs in all. I calculated for each pitcher his run average, strikeout rate, walk rate, home run rate, and batting average on balls in play in each season, and adjusted for the league average. I also included his height, and the number of pounds above or below expectation (based on his height) he was, also adjusted for league average (as today’s pitchers are taller).

For each variable, I ran two separate regressions, first using height and that variable in the first year to try to predict that variable in the second year, and then using pounds overweight and that variable in the first year to try to predict that variable in the second year. The question was, would either of these measures of size have a significant predictive effect? The results follow.

Runs

So maybe I should put this last because it does seem to be the most important category, but I’ll start off with runs instead. What is the impact of size on runs allowed, if any?

Let’s look at height first. Every extra inch of height adds about .02 runs to a pitcher’s run average; if two pitchers performed equally, but one was 6’6” and the other 5’10”, our projection would prefer the latter pitcher by .15 runs per game—nothing to scoff at, but fairly insignificant given that the vast majority of pitchers fall somewhere within that range, and a lot of small skills that are generally left unaccounted for can have an effect that great or greater.

Why might shorter pitchers do better? Well, in part five we found that short pitchers are better overall; those familiar with a statistical concept known as regression to the mean know that a player should be regressed to his own mean—in laymen’s terms, we should expect a short pitcher to be better than a tall pitcher even if they performed equally well in the previous year just because shorter pitchers are better as a group.

My guess in Part 5 as to why short pitchers have lower run averages was selection bias: Short pitchers don’t look as good as tall pitchers, so to be called up to the major leagues, and given a good amount of playing time, means they have to be actually be pretty good, probably a bit better than a tall pitcher would have to be.

The results for overweight pitchers seem to confirm that hypothesis. What we find is that being overweight tends to improve a pitcher’s projection for the next season, by a little over .02 runs for every ten pounds. If we look at the same spread as for height, that is the range that encompasses 95% of all pitchers, we find that the difference between a thin and fat pitcher’s projection will be a little over .11 runs per nine, given that they performed equally in the previous season.

Fat pitchers also don’t “look good,” so we would expect that for a fat pitcher to be called up the majors, he would have to be a little better than an average pitcher. This, of course, is an unnecessary bias, but because it exists, fat pitchers tend to do a little bit better if they actually do make it.

Strikeouts

Now what about strikeouts? Does a pitcher’s size have any effect on the number of Ks he records? In part five, we found that tall pitchers strike out more batters than short ones, and fat pitchers get more punch outs than do thin hurlers. Do these results bear out?

In short, yes, they do. We find that both height and weight have an impact on a pitcher’s strikeout projection, though that impact is very, very small. A four standard deviation in difference in height (that’s the same thing as a spread that includes 95% of all pitchers) is equivalent to a difference of just .08 Ks per game (or less than two per season), with tall pitchers getting slightly more strikeouts than short ones.

Fat pitchers also get a few more strikeouts: Four standard deviations are equivalent to about .11 strikeouts per game, or a little more than two per season. The effect is small, but statistically significant.

In Part 5, I hypothesized that tall pitchers strikeout more batters because they throw from a higher angle, giving their pitches more movement, velocity, and making them harder to pick up. I also wrote that thin pitchers may simply have a harder time generating the power necessary to consistently strike batters out. I think both those theories hold.

Walks

Neither measure of size had any significant effect on walks. This makes a lot of sense, as walks are dependent solely on control, something which would not in any obvious way be effected by a player’s size (except for the case of selection bias making it harder for short or fat pitchers to make it to the major leagues).

Home Runs

I expected that player height would have at least some effect on home runs. This is not the case. My theory was that taller players throw with more of a downward slope, and so they should generate more ground balls—and thus fewer home runs. I was wrong; even if the ball does drop more for taller pitchers, it also has more room to drop. I should have realized this when I looked into the 2005 data in part five and found zero correlation between height and ground ball rate, but you live and you learn, I guess.

Weight showed no effect on home run rate as well.

Hits on Balls in Play

This might be the most interesting category of all, even more interesting than runs in a way, because we still know so little about what affects a pitcher’s batting average on balls in play (BABIP), despite the impressive array of knowledge acquired in the sabermetrics community since Voros McCracken published his article on DIPS. If we were to find that a pitcher’s size impact his batting average on balls in play, well, that would be interesting to say the least. And, what’s more, we do.

Weight has no effect whatsoever on a pitcher’s BABIP, but height is a whole other story. Each inch adds about .01 hits per game (or about half-a-hit a year) to a pitcher’s totals. If we translate that to runs, the impact of height on balls in play separates 95% of all pitchers by no more than .06 runs per game, which is a very small number, but nonetheless highly significant. Moreover, if we control for strikeouts (which also showed an effect batting average on balls in play in the next season, unlike walks and home runs), we find that the impact of height is even a little bit greater, though not much.

What could it be about height that would affect BABIP? In part five, I suggested that this has to do with tall pitchers having ground ball tendencies (ground balls result in hits more often than do fly balls), but this is almost certainly wrong. I have no alternative explanation: A test on 2006 data showed some (weak) correlations between height and line drives and height and infield flies, but both in the wrong direction.

Though the relationship is small, I would suggest further inquiry into why it might exist. Perhaps it will lend just a little bit more understanding as to what kind of pitchers allow less hits on balls in play, and why.

Concluding Thoughts

Size does matter, both for pitchers and for hitters. For hitters, the effect is roughly twice as great, maybe seven runs at the extremes, instead of three to three-and-a-half. Size is one of those little things serious analysts tend to ignore, which matters nonetheless, and which mainstream analysts often make too big a deal out of (“look at what a towering hulk that ballplayer is!”).

We shouldn’t ignore size, but it’s down on the list of things we should worry about when it comes to evaluating players. Size has some effect on future performance, and I believe that in this series, I have quantified exactly what that effect is.

Tall pitchers, we find, are slightly worse-off than short pitchers, and overweight pitchers tend to perform better than their skinny brethren. Given that overweight pitchers also survive for much longer time periods in the major leagues, all else being equal, invest in fat guys. But generally, all else is not equal, in which the case the answer should be obvious: Go for the better ballplayer, always.

References & Resources
I couldn’t have done any of this without the always-fabulous Lahman Database. However, the database does not quite contain full height and weight information, so the players for whom a height or weight was not listed were removed.

Here are links to each part of this series, for easy use:
Part 1
Part 2
Part 3
Part 4
Part 5

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