April 27, 2005

Lies, Damned Lies

Does Size Matter?

by Nate Silver

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

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