Does Size Matter? (Part 3)

It’s been four weeks since we last looked at this issue, but let’s get back to looking at the impact of player size on performance. Last time, we found that player size, specifically weight, has a large impact on the number of home runs we expect a player to hit between the ages of 21 and 30. That is, even if they hit the same number of home runs in one year, we expect a large player to hit more home runs the next. The exact effect we found last time indicated that 10 pounds are worth a little more than one home run in a player’s projection.

But that was for young guys. What about the older players? My hypothesis was that the effect would not be as large for older players because there is less room for them to grow. Young players see an increase in home runs that is attributable to size because size means strength, and when you can harness that strength, it translates to power. But by the time you cross 30, that strength has either translated or it hasn’t. Well, at least those were my thoughts.

Indeed, last time we found that the effect of weight on a player’s home run projection was much smaller going from 29 to 30 than at any other age. Does this observation continue? Let’s take a look, finally.

Before we do, let me just remind of you of what exactly I did. I looked at all post-World War 2 seasons in which a player had more than 200 plate appearances in consecutive years. I calculated their home run rate, defined as HR/(AB-K)*475 (which corresponds to about a normal season, or 150 games), in each of those years. Then I tried to predict how many home runs a player would hit in one year based on his home run rate the previous season and his weight (which is highly correlated with height, but turns out to be an ever-so-slightly better predictor).

Here are the results:

Age	Weight
30-31	0.1161
31-32	0.0891
32-33	0.1341
33-34	0.0821
34-35	0.0771
35-36	0.1201
36-37	0.0885
37-38	0.1145
38-39	-0.020
39-40	0.097

1 = Statistically Significant at the 1% level
5 = Statistically Significant at the 5% level

There’s a lot of information in the above table, so let’s go through it slowly. First, though the effect of weight on home runs in this sample is less stable than it was for players 30 and younger, the average effect through age 38 is pretty similar (.103 home runs per pound versus .110). So it doesn’t seem like there is less of an effect as players age (and if there is, the change is minimal).

Some might find the coefficient for players going from age 38 to 39 interesting, but I think it’s just an effect of small sample size (just 66 players). This is supported by the quite average effect we find with players going from 39 to 40, which is close to being significant, and probably is not only because of another small sample (only 42 players).

In fact, it seems that the effect of player size is quite stable, with 10 pounds adding about one home run to our projected totals. In that case, my original hypothesis—that player size is significant in our power projections because it corresponds to a player “filling out” or learning to use his strength—is likely incorrect. Older players certainly are done with both, yet the effect is just as pronounced for them. So what could it be?

Perhaps instead size simply indicates what a player should be doing. That is, if a small guy hits a dozen home runs, it’s more than likely that this is all anyone expected from him. If a big guy hits a dozen home runs, he’s probably had a bad season. So maybe size doesn’t have an actual impact on how many home runs a player will hit, but rather, it’s just a variable that indicates our expectations for him.

This idea was actually suggested to me by a reader, who asked not be named, but to whom I’ll give credit anyway. He suggested that size may just be acting as a stand-in for a player’s position; that is, controlling for size in our regression would be the same thing as controlling for position.

One way to test his hypothesis would be to re-run the tests with an extra variable for position. However, because position is highly correlated with size, as I showed in part one, a nasty problem known as collinearity may muck up the results.

Luckily, there’s another way: We can re-run my regression results within a position. That is, we can repeat the test separately for each position, and see if the coefficient for size is still significant. If it is, that’s a good indicator that in fact size has an effect on a player’s projection independent of his position or expectation. If not, that doesn’t render this whole series useless, but rather it tells us why size is important. Which is a good thing as well.

So here’s the setup. I looked at all players from age 25 to 26. Each player was assigned a position based on the position he played most at 25. Then I re-ran the same test that we used earlier in this article, but for each position separately. Because the coefficient for weight is stable from year-to-year, there should be no problem in using just this age group.

Position   Weight
C	   0.0861
1B	   0.1061
2B	   0.0505
3B	   0.0661
SS	   0.1551
OF	   0.1121

1 = Statistically Significant at the 1% level
5 = Statistically Significant at the 5% level

Weight is still significant at every position! In fact, the average coefficient across these positions is .096, only marginally smaller than the coefficient derived for the whole age group (.116). What that means is that controlling for position does little to alter our results. While we can’t say anything we total certainty, it seems that size does indeed matter in a player’s development. Big guys will hit more home runs, and they’ll do so because they’re big. There does not seem to be a better explanation.

Next week, we’ll look at the impact of size on other statistical categories, and draw some conclusions about just what size means for hitters.

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.

A Hardball Times Update
Goodbye for now.

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