Dirty baseball

Steroid use can double home run production, physicist finds

Steroid use by a Major League Baseball slugger may produce only modest increases in muscle mass and bat and ball speed but still boost home run production by 50 percent or more, according to a study by Tufts physicist Roger Tobin.

Babe Ruth, whose record of 60 home runs in a single season stood for 34 years, demonstrates his classic swing before a game in Yankee Stadium in 1921. © GETTY IMAGES

Babe Ruth’s record of 60 home runs in a single season stood for 34 years until Roger Maris hit 61 homers in 1961. For the next 35 years, no player hit more than 52 home runs in one season. But between 1998 and 2006, players hit more than 60 home runs in a season six times, according to Tobin. Barry Bonds hit 73 home runs in 2001—exceeding Maris’ mark by an astonishing 20 percent.

The explosion in home runs coincides with the “steroid era” in sports in the mid-1990s, Tobin said. However, that surge quickly subsided in 2003, when Major League Baseball instituted testing for performance-enhancing drugs.

Tobin’s findings will be published in a paper, “On the Potential of a Chemical Bonds: Possible Effects of Steroids on Home Run Production in Baseball,” in an upcoming issue of the American Journal of Physics.

Tobin’s research found that home-run hitting is particularly enhanced by banned substances. “A change of only a few percent in the average speed of the batted ball, which can reasonably be expected from steroid use, is enough to increase home run production by at least 50 percent,” he said. This disproportionate effect arises because home runs are relatively rare events that occur on the “tail of the range distribution” of batted balls.

“In most any statistical distribution—of people’s heights, SAT scores or how far baseballs are hit—there’s a large bump where most of the values fall, with the graph falling rapidly as you move away from that region in either direction toward the rarer values,” Tobin said. “It’s a well known statistical property of such distributions that a relatively small shift in the center point of the distribution can produce a much larger proportional change in the number of values well above or below the center. Because the distribution’s ‘tail’ is particularly sensitive to small changes in the peak and/or width, home run records can be more strongly affected by steroid use than other athletic accomplishments.”

For his research, Tobin reviewed previous studies of the effects of steroid use and concluded that muscle mass, the force exerted by those muscles and the kinetic energy of the bat could each be increased by about 10 percent through the use of steroids. According to his calculations, the speed of the bat as it strikes a pitched ball is about 5 percent higher than without the use of steroids, and the speed of the ball as it leaves the bat is about 4 percent higher.

To determine the effect on home run production, Tobin analyzed a variety of models for the trajectory of a baseball, accounting for gravity, air resistance and lift force due to the ball’s spin. While there was considerable variation among the models, “the salient point,” he said, “is that a 4 percent increase in ball speed, which can reasonably be expected from steroid use, can increase home run production by anywhere from 50 percent to 100 percent.”

Tobin is quick to acknowledge that athletes in many sports today achieve at a higher level than athletes of the past, and that, in itself, is not evidence of cheating. “Physics cannot tell us whether a particular home run was steroid-assisted, or even whether an extraordinary individual performance indicates the use of illicit means,” he said.

But the physics behind hitting a baseball yields telling results. “These results certainly do not prove that recent performances are tainted, but they suggest that some suspicion is reasonable,” Tobin said.

This story ran in the November 2007 issue of the Tufts Journal.