There's a strong correlation between steroid use and the number of home runs a batter hits, according to a statistical analysis completed by a physicist.

Just moderate increases in muscle mass and a 4 percent increase in batted ball speed appear to increase the number of home runs hit by a batter dramatically, concluded Tufts University physicist Roger Tobin in his analysis.

Tobin, a specialist in condensed matter physics with a longtime interest in the physics of baseball, was to publish his 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 paper notes that 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. Barry Bonds hit 73 home runs in 2001 — topping Maris' mark by 20 percent.

Tobin said the explosion in home runs coincides with a mid-1990s "steroid era" in professional sports. Use dropped to historic levels in 2003 when Major League Baseball instituted steroid testing, the article offers as background.

"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," Tobin said in a news release.

This disproportionate effect arises because home runs are relatively rare events that occur on the "tail of the range distribution" of batted balls, Tobin explained.

Tobin applied a similar, though less extensive, mechanical analysis to pitching and found a smaller impact. He calculated that a 10 percent increase in muscle mass should increase the speed of a thrown ball by about 5 percent, or 4 to 5 miles per hour for a pitcher with a 90-mile-per-hour fastball. That translates to a reduction in earned run average of about 0.5 runs per game.

"That is enough to have a meaningful effect on the success of a pitcher, but it is not nearly as dramatic as the effects on home run production," Tobin said.

Tobin concluded that while steroid use by Major League Baseball players cannot be proven, it can be reasonably suspected based on his findings.