A condensed matter physicist says that a small increase in muscle mass induced by anabolic steroid use, can pay off in a dramatic increase in home runs. Roger Tobin, a physicist from Tufts University in Boston, puts it this way in Science Daily:
"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 says. This disproportionate effect arises because home runs are relatively rare events that occur on the "tail of the range distribution" of batted balls.
Steroid use increases muscle mass (lean body mass), which leads to increased strength, power, acceleration, and explosiveness (some of this is logic by induction). The increase in power increases bat speed and therefore imports more force to the batted baseball. That results in more distance for the hit ball.
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.
It is astonishing that some would argue that increased muscle mass would not result in more kinetic energy applied to the batted ball (longer hits). One argument held that steroids do not improve hand-eye coordination, and thus do not import an advantage in the hitter. That argument appears simplistically naive. Obviously anabolic drugs will not benefit an nonathletic player and thus that argument is irrelevant to elite athletes. The effects of the drugs on the accomplished athlete should be the issue.
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."
Pitchers gain an advantage by increasing their muscle mass too. That effect is less dramatic than the benefit of steroids for hitters, according to Tobin's calculations. And also remember that the velocity of the pitched ball will increase the rebound on the batted ball; in other words an enhanced fastball will rebound off the bat harder.
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 increase the speed of a thrown ball by about 5 percent, or four to five miles per hours 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," says Tobin. "The unusual sensitivity of home run production to bat speed results in much more dramatic effects, and focuses attention disproportionately on the hitters."
Anabolic drugs alone cannot produce increases in power or acceleration. A strength training, and conditioning, program would be key to development. Thus it might be difficult to separate out the effects of anabolic drugs from the effects of a solid weight-training program. Nonetheless, the use of anabolic drugs constitutes cheating, and should be treated as such.