The Physics of Steroids in Baseball

Robert K. Adair’s The Physics of Baseball covers everything in baseball from the trajectory of a curveball to batter reaction time to fundamental bat vibrations.

Adair provides an equation relating bat speed to player weight:

V = k sqrt(M/(m+M/81))

Note: V is the velocity of the bat in miles per hour, m is the bat weight in pounds, M is the player’s weight in pounds, sqrt means square root and k is a constant, 10, in mph.

In an article on by Patrick Huber, entitled 616*(*No Asterisk Required), he relates Adair’s formula to Bonds.

According to Adair’s formula — and don’t worry, we asked him to double-check the calculations, since our last math class came in high school — the 206-pound Bonds generates a bat speed of 67.34 mph, while the 228-pound Bonds swings the same 32-ounce bat at 68.81 mph, an increase of 1.48 mph.

Hruby goes on to make the reasonable claim that while Bonds bat speed was increasing in his late thirties, it should have been decreasing. Page 2 charted every Bonds home run from 1999 to May 2006 and subtracted the 83 home runs that would have landed on the warning track.

Hruby failed to compensate for the fact that Bonds surely would not have been able to play 147 games in the outfield at age 39, and would surely have spent some time on the disabled list. Removing whole sections of games and adding nagging injuries that would surely affect a 37 or 38 year old with bad knees would have accounted for a lot of home runs. Bonds’ career could very easily have been over before the 2004 season at age 39, just due to his body naturally breaking down. He’s hit 64 home runs since then. Adding the confidence factor to the physical ones, subtracting 150 home runs seems like a very fair and cautious estimate.

Without steroids, Bonds is a Hall of Famer, with over 500 home runs, MVPs, Gold Gloves, and Silver Sluggers. With them he has over 700 home runs, more MVPs, no respect, and no Hall of Fame.

Dr. Steroids

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