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April 27, 2005

Lies, Damned Lies

Does Size Matter?

by Nate Silver

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Size matters. At least that's what PECOTA thinks. One of the biggest surprises when I first began to fiddle with the forecasting system three summers ago was that height and weight have a significant predictive impact on a hitter's forecast line, even after all other statistics are accounted for. If you take two players who had identical statistical lines, each of whom hit 30 home runs last year, and one of whom is bigger and taller than the other, the larger player is more likely to sustain that home run production. To take a working example, let's see what PECOTA would do if we took Adam Dunn (listed at 6'5", 240 pounds in our system), and shrunk him down to David Eckstein's size--5'8", 168.


2005 PECOTA Forecast                 BA    OBP    SLG    HR   VORP
Adam Dunn, Adam Dunn Size          .270   .395   .562    35   42.4
Adam Dunn, David Eckstein Size     .265   .387   .542    32   36.1

This might not seem like a huge difference, but keep in mind that height and weight are the only variables that we have changed. By being compared to folks like Dick Kokos and Art Shamsky instead of Fred McGriff and Jim Thome, Dunn loses about 25 points of OPS, or six runs off his VORP forecast. The differences become even more profound if we look out further into the future, as bigger, and presumably stronger players are more likely to have sustained peaks, and long major-league careers. Here is Dunn's five-year WARP forecast, before and after:

Five-Year PEOCTA WARPs              2005  2006  2007  2008  2009  TOTAL
Adam Dunn, Adam Dunn Size           6.5   6.5   5.9   6.6   5.5   31.0
Adam Dunn, David Eckstein Size      5.9   5.7   5.4   4.1   3.4   24.5

PECOTA thinks that Big Dunn is worth around 25 percent more than Mini Dunn over the course of the next five seasons. Maybe all of this shouldn't be surprising; the correlation between a batter's official listed weight and his home run rate, normalized to his park and league, is around .43. But it surprised me. I didn't expect a player's body type--which seems like the scoutiest of all scouty things--to play a prominent role in my forecasting system.

Fast forward to two weeks ago, when Will Carroll sent me an e-mail asking if baseball players have grown larger over the years. I suspect that Will knew the answer--they most certainly have. Here are the average position player heights and weights since 1946, weighted based on plate appearances.

In 1946, the average position player was 71.7 inches, 182 pounds. In 2004, he was 72.7 inches, 192 pounds. All of these numbers, by the way, are underestimates. The heights and weights listed here are taken from baseball-reference.com, which generally has the practice of taking a player's listed height and weight when he comes into the league, and not updating it as he fills out and bulks up later in his career. If we use the heights and weights provided by our PECOTA data contractor, who makes at least some effort to update the information, we wind up with an average-sized hitter in 2004 of 73.0 inches, 197 pounds. If we used information from team media guides, we'd wind up with even bigger hitters still. Of course, all it takes is one afternoon spent watching a replay of the 1985 World Series on ESPN Classic to know this intuitively.

How much of the leaguewide increase in home run rates can be attributed to bigger size alone? If you run a regression of height and weight on home run rates (HR per 650 PA) over the years 1995-2004 (hitter size has been relatively constant over this period), you come up with the following:

HR/650 = .492 * Ht (in) + .216 * Wt (lbs) - 59.17

We can plug in heights and weights from different eras into our model and see what impact they might have:


Year                       HT     WT     HR/650 (Predicted)
1946                       71.7   182     15.42
1965                       72.4   187     16.84
1984                       72.7   189     17.42
1994                       72.6   192     18.02
2004 (low estimate)        72.7   192     18.07
2004 (higher estimate)     73.0   197     19.30

For example, if we go from 1984 to the higher estimate for 2004 heights and weights, the model predicts around an 11 percent increase in home run rates. Or, if we were told way back in 1946 what baseball players would be shaped like some sixty years later, we'd have predicted about a 25 percent increase in home run rates. This doesn't explain all of the increase in offensive levels, but it explains some of it.

You're probably wondering why I haven't mentioned pitchers; they've grown bigger too:

The average pitcher in 1946 was 72.9 inches, 187 pounds. In 2004, he was 74.5 inches, 198 pounds. So pitchers have grown at least as much as batters have. The catch is that--scouts take note--pitching performance isn't nearly as strongly related to body size as offensive performance is. The correlation between pitcher height and strikeout rate, for example, is in the neighborhood of .05. That passes the threshold of statistical significance given the large sample sizes we have the luxury of working with, but only barely so. If everybody is getting bigger, it's the offense that is going to benefit.

The unresolved question, of course, is why baseball players are getting bigger. And, no, the answer I'm looking for is not steroids: it's clear that being bigger and stronger helps a player to hit for more power, and if steroids help a player to get bigger and stronger, they're probably going to benefit his game. But that is a tangential issue here.

The first thing to notice is that Americans who aren't playing professional sports are getting bigger as well. I don't just mean that Americans are getting fatter: the average American male grew about an inch-and-a-half between 1960 and 2002, as a result of improved nutrition and health care, and possibly longer-term genetic effects. (A diet of Big Macs and burritos makes you heavier, but it doesn't make you taller--or stronger). Even though professional athletes are far from typical Americans, and are selected out for their superior physical health, it is likely that there is at least some carryover effect, and that scouts today are selecting from bigger, stronger 17-year-olds than they were thirty years ago.

This chart tells an interesting story. These are the Body Mass Indexes (BMIs) for pitchers and hitters since 1968. Body Mass Index is a measure of weight relative to height--what we might call "body type."

Between around 1984 and 1993, there was a sharp increase in BMI for both pitchers and position players. My guess is that this was the result of the underlying genetic trends described in the CDC study I linked to above--American teenagers were getting bigger and stronger--delayed and regulated by selection biases. Baseball was thought of as a speed-and-defense game throughout most of the sixties and seventies, and being bulkier doesn't help you to play defense or steal bases. The Oakland and Cincinnati dynasties of the 70s, for example, routinely placed near the top of the league in stolen bases. Starting around 1977, though, there were a run of successful clubs that were built around a more contemporary, power-based model. The Yankees, Dodger and Oriole mini-dynasties of the era were veteran teams that followed Earl Weaver's credo of waiting for the three-run homer. The 1980 Phillies, 1982 Brewers, and 1984 Tigers also fit this typology; the only obvious exceptions are early iterations of the Royals and Cardinals clubs. Baseball organizations parrot success, and the result of these bulkier, slower, uglier teams winning so many games was an increasing disposition in scouting and development circles toward bulkier, slower, and uglier players. The Greg Luzinski clones were getting their chance, and the floodgates were opened for the big, well-nourished suburban boys that had been sitting around in farm systems for so long.

The bulkier hitters stuck--position player BMI peaked in 1994, and has held about steady since. But the bulkier pitchers didn't. While pitcher BMIs also rose markedly throughout the 1984-1993 period, they began dropping again as of about 1998, creating a "body type" gap between pitchers and position players that hadn't existed before. Pitchers are still getting taller, but they're no longer getting bulkier--we're getting more Mark Priors but fewer Jeff Judens.

This appears to me to be the result of a sort of natural selection process. Bulkier hitters proved to be real assets, because being bulkier helps you to hit for more power, and before long, the body type of the entire league had changed. The 6'3", 200-pound shortstop, if you will, was one of the more successful technological innovations in baseball history. But bulkier pitchers didn't stick, because being bulky doesn't provide any meaningful advantage to a pitcher.

What's more, attitudes toward body type and were changing not just in player development circles, but also with regard to established major league players. The weight room became a focal point for position player training in a way that it hadn't been before, and hitters were not only coming into the league bulkier, but getting bulkier still as they aged. And where the muscles went, the home runs followed.

Nate Silver is an author of Baseball Prospectus. 
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