Barry Bonds and the Placebo Effect

A mathematician's guide to the news.
July 12 2001 9:00 PM

Barry Bonds and the Placebo Effect

Why Bonds won't break the homer record and the placebo effect might be bunk.

(Continued from Page 1)

One question still needs to be answered: How many home runs will Barry Bonds hit this year? That is, how strong is regression to the mean? If our discussion above is correct, then hitters who lead the major leagues in home runs at the All-Star break should tend to decline in the second half of the season. Thanks to David Vincent of the Society for American Baseball Research, we have those numbers in hand for every non-strike season since 1933. (Click here for the list of home-run leaders.) Of the 74 hitters involved (there are more hitters than years because of ties) only 12 equaled their pre-break production in the second half. The average ratio between the hitters' home runs per game in the second half and their home runs per game in the first half was approximately two-thirds. So, a reasonable guess—a reasonable statistical guess, that is, taking into account no knowledge about the properties of baseball—would be that Barry Bonds, having hit 39 home runs after 88 games, will get 39/88 x 2/3 x 74, or about 22, more. Sixty-one home runs is a formidable total but no longer a record in the present Age of the Dinger. Galton would call it a regression to mediocrity. For fans of Bonds and the Giants, it's just another great year from a great hitter—aided, this time around, by a little great luck.

Jordan Ellenberg is a professor of mathematics at the University of Wisconsin and the author of How Not to Be Wrong. He blogs at Quomodocumque.

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