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.

Illustration by Mark Alan Stamaty

On May 24, the New England Journal of Medicine published an article making an astonishing claim—that the power of the placebo, a core belief of medical researchers for almost 50 years, might be a statistical phantom. A few hours later, San Francisco Giants left fielder Barry Bonds came to bat against the Colorado Rockies' John Thomson and deposited a baseball into San Francisco Bay. It was Bonds' 25th home run of 2001, putting him on pace for a preternatural total of 86 for the full season. Bonds cooled after that. He went into the All-Star break with 39 home runs in his team's first 88 games, still on pace to hit 72 home runs this year and break Mark McGwire's 3-year-old record of 70 home runs in a season.

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But Barry Bonds isn't going to hit 72 home runs for the same reason that there might be no such thing as the placebo effect. It's also the reason—according to the founder of eugenics—that humanity is doomed.

Baseball, like medicine, has more chance in it than its practitioners like to admit. There must be many reasons Barry Bonds has hit more home runs before the All-Star break than he, or anyone, ever has before. Maybe he tinkered with his stance; maybe he changed his weight-lifting regimen or took up yoga.

But one thing is almost certain: Bonds has been lucky. Is it more likely that 1) Bonds' true level of performance would have given him 30 home runs by midseason, but he caught some good breaks; or 2) that he was really hitting well enough to homer 45 times, but bad luck caused him to hit only 39? Since no one else has ever hit more than 37 home runs in a half season, the former option is the way to bet. That means we shouldn't expect Bonds to maintain his current pace; doing so would mean we were expecting Bonds to continue his run of good luck. And luck, by definition, can't be expected to persist.

Likewise, patients who are sick enough to join a clinical trial—where placebo studies are conducted—are more likely than not to be victims of bad luck. A person who's running a temperature of 104 degrees one day is relatively likely to be having a particularly bad day with respect to the fluctuations of his or her illness. On average, such people tend to have a lower fever the next day. That's true whether they take a sugar pill or not. According to the authors of the New England Journal paper, there's no strong evidence that the placebo effect amounts to any more than this. They argue that in trials where some patients are given a placebo and some are left untreated, the untreated patients don't fare measurably differently from those given the placebo. If that's so, then the placebo effect must be no more than a combination of the natural wax and wane of disease, reporting bias, and pure luck.

(That said, most researchers are not ready to chuck the placebo effect based on one article's analysis. John C. Bailar III, an editor at and former statistical consultant for the New England Journal, wrote an editorial that accompanies the placebo article in which he discusses the statistical limitations of the article's analysis, then goes on to remark, rather bravely, that with respect to the placebo effect "there is that pesky, utterly unscientific feeling that some things just ought to be true.")

What happens to the untreated patients in clinical trials, and what's going to happen to Barry Bonds, is a phenomenon called "regression to the mean," and it's been a basic principle of observational statistics ever since Francis Galton noticed in 1877 that the offspring of sweet peas tended to be closer to average size than their parents were. Galton, a first cousin of Charles Darwin and a pioneer of biostatistics, writes in his memoirs:

The following question had been much in my mind. How is it possible for a population to remain alike in its features, as a whole, during many successive generations, if the average produce of each couple resemble their parents? Their children are not alike, but vary: therefore some would be taller, some shorter than their average height; so among the issue of a gigantic couple there would be usually some children more gigantic still. Conversely as to very small couples. But from what I could thus far find, parents had issue less exceptional than themselves. (Memories of My Life, Chapter 20)

Galton's experiment with sweet peas proved that, indeed, children were on average less exceptional than their parents, for the same reason that the second half of Bonds' 2001 season is likely to be less exceptional than the first. Large parents are large partly because of their genes, partly because of luck. In the next generation, the genes are passed on, but the luck runs out.

Galton's real interest was in people, not peas. What "regression" meant to him was that the human race, if allowed to breed freely, was doomed by mathematical law to concentrate itself in the unimpressive center of the bell curve. That's why Galton is famous today not for his contributions to the science of heredity but as the creator of eugenics and the inspiration for a centurylong wrong turn in anthropology and social policy.

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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