American paleontologist Stephen Jay Gould was one of the most popular and highly regarded science writers of the late 20th century. All 300 of the monthly columns that he wrote for Natural History magazine were collected in books, and his numerous awards include the National Book Award (1981), the Distinguished Scientist Award (1997), Humanist of the Year (2001), and the Darwin-Wallace Medal (2008).
Gould was also a devoted baseball fan. In his essay "The Streak of Streaks" (first published in The New York Review of Books in 1988), he explored the significance of Joe Dimaggio's 56-game hitting streak in 1941, generally considered to be "the greatest accomplishment in the history of baseball, if not all modern sport." In the follow excerpt from that essay, Gould relies on examples and statistics to explain--and debunk--the popular belief known as "hot hands," a version of the gambler's fallacy.
From "The Streak of Streaks"* by Stephen Jay Gould
Start with a phenomenon that nearly everyone both accepts and considers well understood--"hot hands" in basketball. Now and then, someone just gets hot, and can't be stopped. Basket after basket falls in--or out as with "cold hands," when a man can't buy a bucket for love or money (choose your cliché). The reason for this phenomenon is clear enough; it lies embodied in the maxim: "When you're hot, you're hot; and when you're not, you're not." You get that touch, build confidence; all nervousness fades, you find your rhythm; swish, swish, swish. Or you miss a few, get rattled, endure the booing, experience despair; hands start shaking and you realize that you shoulda stood in bed.
Everybody knows about hot hands. The only problem is that no such phenomenon exists. The Stanford psychologist Amos Tversky studied every basket made by the Philadelphia 76ers for more than a season. He found, first of all, that probabilities of making a second basket did not rise following a successful shot. Moreover, the number of "runs," or baskets in succession, was no greater than what a standard random, or coin-tossing, model would predict. (If the chance of making each basket is 0.5, for example, a reasonable value for good shooters, five hits in a row will occur, on average, once in thirty-two sequences--just as you can expect to toss five successive heads about once in thirty-two times, or 0.5.)
Of course Larry Bird, the great forward of the Boston Celtics, will have more sequences of five than Joe Airball--but not because he has greater will or gets in that magic rhythm more often. Larry has longer runs because his average success rate is so much higher, and random models predict more frequent and longer sequences. If Larry shoots field goals at 0.6 probability of success, he will get five in a row about once every thirteen sequences (0.65). If Joe, by contrast, shoots only 0.3, he will get his five straight only about once in 412 times. In other words, we need no special explanation for the apparent pattern of long runs. There is no ineffable "causality of circumstance" (if I may call it that), no definite reason born of the particulars that make for heroic myths--courage in the clinch, strength in adversity, etc. You only have to know a person's ordinary play in order to predict his sequences. (I rather suspect that we are convinced of the contrary not only because we need myths so badly, but also because we remember the successes and simply allow the failures to fade from memory.)
Selected Works of Nonfiction by Stephen Jay Gould
- Ever Since Darwin: Reflections in Natural History, 1977
- The Panda's Thumb: More Reflections in Natural History, 1980
- Hen's Teeth and Horse's Toes, 1983
- The Flamingo's Smile: Reflections in Natural History, 1987
- Time's Arrow, Time's Cycle, 1987
- An Urchin in the Storm: Essays About Books and Ideas, 1988
- Wonderful Life: The Burgess Shale and the Nature of History, 1990
- Bully for Brontosaurus: Reflections in Natural History, 1991
- Full House: The Spread of Excellence from Plato to Darwin, 1997
- Rocks of Ages, 1999
- I Have Landed: The End of a Beginning in Natural History, 2002
- The Hedgehog, the Fox, and the Magister's Pox: Mending the Gap Between Science and the Humanities, 2003
*Stephen Jay Gould's "The Streak of Streaks" (a review of Streak: Joe DiMaggio and the Summer of '41 by Michael Seidel) first appeared in The New York Review of Books, Aug. 18, 1988. The essay was reprinted in Gould's collection Bully for Brontosaurus: Reflections In Natural History (Norton, 1991).