# Does Size Matter? (Part 2)

In the THT Dartboard last week, I criticized Jose Reyes. Well, I didn’t so much criticize him as say that Reyes is getting a little over-hyped, but based on the angry responses I got from Mets fans, we might as well say that I criticized Reyes. My specific argument was that Reyes will not turn out to be as good a player as Carl Crawford, who gets nowhere close to as much hype. Now there was plenty I said that people could (and did) get angry over, but for the focus of this column, let’s zero-in on one specific statement: “Crawford’s big (6’2”, 219 pound) frame suggests that he will continue to add power (as documented by yesterday’s article on the relationship between size and performance), while Reyes’ suggests that he will struggle to hit any substantial number of home runs.”

So is this actually true? In last week’s column, I looked at the variation of player performance based on size. My conclusion was, unsurprisingly, that big players tend to hit better. But that’s not really a discovery. What would be more pertinent would if big guys tended to continue to hit better. In question form, that is: If a large and small player are equally valuable hitters, should we expect the big guy to be more valuable at the plate than the little guy in the future?

For the purposes of this part, we will focus only on home runs. I’ll tackle other statistical categories in the future. Also, this installment will only look at players between the ages of 20-30. In our next installment, we’ll cover the older guys.

So here’s the setup. 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, his height, and his weight.

If size does not matter, then the only variable that would be significant would be a player’s home run rate in the previous season. As the following chart demonstrates, this is obviously not the case.

```Age	Height	Weight
20-21	-0.604	0.1265
21-22	0.166	0.1185
22-23	-0.016	0.1311
23-24	-0.115	0.1101
24-25	-0.008	0.1131
25-26	0.111	0.1081
26-27	0.034	0.1031
27-28	0.130	0.0921
28-29	-0.064	0.1181
29-30	0.130	0.0761

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

What we’re looking at here is the estimated effect of one pound of weight or one inch of height on the number of home runs a player will hit in the next season. In other words, for each extra 10 pounds, a 22 year-old is expected to hit an additional 1.18 home runs.

However, height happened to be insignificant in every regression that I ran. This is partially because height and weight are highly correlated. In fact, this detail can cause some problems in the weighting of the variables (statistically, this is known as “collinearity”). So let’s remove height from the equation, and do the math all over again.

```Age	Weight
20-21	0.1035
21-22	0.1271
22-23	0.1301
23-24	0.1021
24-25	0.1131
25-26	0.1161
26-27	0.1051
27-28	0.1011
28-29	0.1131
29-30	0.0861

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

First of all, the effect of weight on the number of home runs we expect a player to hit is surprisingly consistent, with an extra ten pounds adding a little over one home run to our forecast. Secondly, the effect is extremely significant.

Let’s take two 20-year-olds, both of whom hit 20 home runs. However, one ways 220 pounds and the other weighs just 160. The big guy is expected to hit six more home runs the next year, and 20 more at 26!

Even if the difference is much smaller—say, 20 pounds—our projection for the bigger player will be two home runs higher the next year and almost seven home runs better by 26 (the difference levels off at that age). Small differences in weight make for big differences in projections.

Let’s look at a real world example with Crawford and Reyes. Here is how each projects over the next five years in home runs, given this season’s numbers:

```Year	Crawford         Reyes
2006	19	        16
2007	21	        13
2008	23	        11
2009	23	        9
2010	24	        8
2011	24	        8
```

So while Crawford is just three home runs better than Reyes this season (per 150 games), we expect him to be 66 home runs better the next five years, or more than 13 home runs a year! What is now a small difference in power—equivalent to four or five runs in a season—becomes a huge difference, equivalent to almost 20 runs a year! You can see why I made the argument that I made.

For hitters, at least those younger than 30, size does matter and it has a large impact on their projected future performance. Being a big guy can lead to big results, when it comes to hitting for power.

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.

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