Drunkard's Walk - Leonard Mlodinow [92]
For his accomplishments, Miller was heralded “the Greatest Money Manager of the 1990s” by Money magazine, “Fund Manager of the Decade” by Morningstar, and one of the top thirty most influential people in investing in 2001, 2003, 2004, 2005, and 2006 by SmartMoney.22 In the fourteenth year of Miller’s streak, one analyst was quoted on the CNNMoney Web site as putting the odds of a fourteen-year streak by chance alone at 372,529 to 1 (more on that later).23
Academics call the mistaken impression that a random streak is due to extraordinary performance the hot-hand fallacy. Much of the work on the hot-hand fallacy has been done in the context of sports because in sports, performance is easy to define and measure. Also, the rules of the game are clear and definite, data are plentiful and public, and situations of interest are replicated repeatedly. Not to mention that the subject gives academics a way to attend games and pretend they are working.
Interest in the hot-hand fallacy began around 1985, in particular with a paper by Tversky and his co-workers that was published in the journal Cognitive Psychology.24 In that paper, “The Hot Hand in Basketball: On the Misperception of Random Sequences,” Tversky and his colleagues investigated reams of basketball statistics. The players’ talent varied, of course. Some made half their shots, some more, some less. Each player also had occasional hot and cold streaks. The paper’s authors asked the question, how do the number and length of the streaks compare with what you would observe if the result of each shot were determined by a random process? That is, how would things have turned out if rather than shooting baskets, the players had tossed coins weighted to reflect their observed shooting percentages? The researchers found that despite the streaks, the floor shots of the Philadelphia 76ers, the free throws of the Boston Celtics, and the experimentally controlled floor shots of the Cornell University men’s and women’s varsity basketball teams exhibited no evidence of nonrandom behavior.
In particular, one direct indicator of “streakiness” is the conditional probability of success (that is, making a basket) if on the prior attempt the player had achieved success. For a streaky player, the chance of a success on the heels of a prior success should be higher than his or her overall chance of success. But the authors found that for each player a success following a success was just as likely as a success following a failure (that is, a missed basket).
A few years after Tversky’s paper appeared, the Nobel Prize–winning physicist E. M. Purcell decided to investigate the nature of streaks in the sport of baseball.25 As I mentioned in chapter 1, he found, in the words of his Harvard colleague Stephen Jay Gould, that except for Joe DiMaggio’s fifty-six-game hitting streak, “nothing ever happened in baseball above and beyond the frequency predicted by coin-tossing models.” Not even the twenty-one-game losing streak experienced at the start of the 1988 season by Major League Baseball’s Baltimore Orioles. Bad players and teams have longer and more frequent streaks of failure than great players and great teams, and great players and great teams have longer and more frequent streaks of success than lesser players and lesser teams. But that is because their average failure or success rate is higher, and the higher the average rate, the longer and more frequent are the streaks that randomness will produce. To understand these events, you need only to understand the tossing of coins.
What about Bill Miller’s streak? That a streak like Miller’s could result from a random process may seem less shocking in light of a few other statistics. For instance, in 2004 Miller’s fund gained just under 12 percent while the average stock in the S&P gained more than 15 percent.26 It might sound like