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"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," explains Tobin. "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."

Muscle Mass Boosts Bat and Ball Speed

Tobin reviewed previous studies of the effect 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 the pitched ball will be about 5 percent higher than without the use of steroids and the speed of the ball as it leaves the bat will be about 4 percent higher.

To determine the ultimate impact on home run production, Tobin then analyzed a variety of models for trajectory of the 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 says, "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."

What About the Pitchers?

Tobin applied a similar, though less extensive, mechanical analysis to pitching and found that smaller impacts were possible. He calculated that a 10 percent increase in muscle mass should
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