Hot and Cold Streaks in Basketball and
the Stock Market
Misinterpreting random sequences is common in
sports and investing. In both arenas, the statistical facts collide with commonsense
intuition.
Basketball Players' "Hot Hands"
Every basketball player and
every fan intuitively "knows" that
players have hot and cold streaks. Players who have "hot hands" can't
seem to miss. Those who have "cold" ones can't find the center of
the hoop. When Thomas Gilovich, Robert Vallone, and Amos Tversky (1985) interviewed
Philadelphia 76ers, the players estimated they were about 25 percent more likely
to make a shot after they had just made one than after a miss. In one survey,
9 in 10 basketball fans agreed that a player "has a better chance of making
a shot after having just made his last two or three shots than he does
after having just missed his last two or three shots." Believing
in shooting streaks, players will feed the ball to a teammate who has just
made two or three shots in a row. Many coaches will bench the player who has
just missed three in a row.
The only trouble is (believe it or not), it isn't true! When Gilovich and his collaborators studied detailed individual shooting records, they found that the 76ers—and the Boston Celtics, the New Jersey Nets, the New York Knicks, and Cornell University's men's and women's basketball players—were equally likely to score after a miss and after a basket. It is true during the National Basketball Association's 3-point shooting contest, despite announcers being amazed by players who seem to be "in a zone" or "on fire" (Koehler & Conley, 2003). A typical 50 percent shooter averages 50 percent after just missing three shots, and 50 percent after just making three shots. It is true with free throws, too. Celtics star Larry Bird made 88 percent of his free throws after making a free throw and 91 percent after missing.
Did this reduce Larry Bird to a mere puppet, manipulated by statistical laws? No, basketball shooting, unlike coin-tossing, involves skill, and Bird's skill was reflected in his 90 percent average. (Of course, streaks of made baskets occur more among players with Larry Bird-like shooting ability; so giving the ball to the one with the "hot hand" often means giving it to the team's best shooter [Burns, 2004].)
Why, then, do players and fans alike believe that players are more likely to score after scoring and to miss after missing? (The same phenomenon turns up in baseball, where the individual and team streaks and slumps that fascinate sportswriters are to be expected, given mere random variation [Myers, 2002].) It's because streaks do occur, more than people expect in random sequences. In any series of 20 shots by a 50 percent shooter (or any 20 flips of a coin), there is a 50‑50 chance of 4 baskets (or heads) in a row, and it is quite possible that one person out of five will have a streak of 5 or 6. Players and fans notice these random streaks and so form the errant conclusion that "when you're hot, you're hot" (Figure 1).
Mutual Funds: Does
Past Performance Predict Future Returns?
The same misinterpretation of
random sequences occurs when investors believe that a mutual fund that has
had a string of good years will likely outperform one that has had a string
of bad years. Based
on that assumption, investment magazines report the performance of various
mutual funds' collection of stocks. But, as economist Burton Malkiel (2004)
documents, past performances of mutual funds do not predict their future
performance. If on January 1 of each year since 1980 we had bought the previous
year's top-performing funds, our hot funds would not have beaten the next year's
market average. If we had put our money instead on the Forbes "Honor
Roll" of funds each year for the two decades following 1975, we would
have made a 13.5 percent annual return (compared with the market's overall
14.9 percent). Of the top 81 Canadian funds during 1994, 40 performed above
average and 41 below average during 1995 (Chalmers, 1995).
When funds have streaks of several good or bad years, we may nevertheless think that past success predicts future success. "Randomness is a difficult notion for people to accept," notes Malkiel. "When events come in clusters and streaks, people look for explanations and patterns. They refuse to believe that such patterns—which frequently occur in random data—could equally well be derived from tossing a coin. So it is in the stock market as well."
The point to remember: In various sports, in stock investing, and in other life arenas, streaks happen and command notice. "Hot hand" research asks whether such streaks are more pronounced than random streakiness, such as appears in coin tossing (Reifman, 2004). When watching basketball, choosing stocks, or flipping coins, remember that our intuition often misleads us. Random sequences frequently don't look random. Expect streaks.
Figure 1: Who is the chance shooter? Here are 21 consecutive shots, each scoring either a basket or a miss, by two players who each make 11. Within this sample of shots, which player's sequence looks more like what we would expect in a random sequence? (adapted from Barry Ross, Discover, 1987.)
REFERENCES:
Burns, B. D. (2004). Heuristics as beliefs and as behaviors: The adaptiveness
of the
"hot hand." Cognitive Psychology, 48, 295-331.
Chalmers, R. (1995, September 19). Sizing sizzle of mutuals.
Edmonton Journal, p. E1.
Gilovich, T., Vallone, R., & Tversky, A. (1985). The hot hand in basketball:
On the misperception of random sequences. Cognitive Psychology, 17,
295ˆ314.
Koehler, J. J., & Conley, C. A. (2003). The "hot hand" myth
in professional basketball. Journal of Sport and Exercise Psychology, 25,
253-259.
Malkiel, B. (2004). A random walk down Wall Street (8th ed.).
Myers, D. G. (2002). Intuition: Its powers and perils.
New Haven:
Yale
University Press.
Reifman, A. (2004). Hot hand in sports. A comprehensive website at http://www.hs.ttu.edu/hdfs3390/hothand.htm