TO THE NAKED EYE, IT MAY APPEAR THAT: Syracuse University's sophomore guard Michael Carter-Williams was on a hot streak Thursday night in Washington, D.C., posting a career-high 24 points and helping to upset the top-seeded Indiana Hoosiers 61-50 in the Sweet Sixteen round of the NCAA Men's Basketball Tournament.
BUT ACCORDING TO SOME PEOPLE WHO THOUGHT REALLY HARD ABOUT THIS: Perhaps no such hot streak ever happened, because there may not be such thing as a hot streak at all.
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In 1991, psychologist Thomas D. Gilovich and his colleagues Amos Tversky and Bob Vallone conducted the classic investigation of the phenomenon of the "hot hand"—that is, when a player gathers shooting momentum or gets "in the zone" to the extent that he or she seemingly can't miss a shot—and published their findings in The Wilson Quarterly. They discovered it didn't exist anywhere outside of players' and fans' imaginations; rather, the research team found, the "hot hand" happens when an optimistic interpretation and some funky psychology are applied to a statistically average outcome of shots missed and shots made.
To test this notion, Gilovich and his team created an experiment to test the hypothesis that if a player is subject to random periods of "hot" and "cold" shooting, he or she should be more likely to make a shot after making his previous one—or previous several—than after missing. So they gathered the shooting records from the 1980-1981 season of the Philadelphia 76ers (then the only team that kept records of the order of a player's hits and misses), and what they found was that
Contrary to the hot hand hypothesis, players were not more likely to make a basket after making their last shot. In fact, there was a slight tendency for players to shoot better after missing their last shot. They made 51 percent of their shots after making their previous shot, compared to 54 percent after missing it. They also had a better chance of making a basket if they missed their previous two or three shots.
But when they interviewed that year's team members, including the famous Julius "Dr. J" Erving, they were firmly convinced otherwise—as were... well, most people, according to Gilovich. They suggested that a "hot" player cools off because opposing players start to guard him more aggressively, or because he gets over-confident and starts taking tougher shots. So Gilovich, now a professor of psychology at Cornell, also studied the players' free-throw records. He found that, on average, they made 75 percent of their second free throws after making their first, and 75 percent after missing their first. In other words, the "streak" leading up to each free throw made no difference whatsoever on the outcome of the shot.
So why does the idea persist? According to Gilovich, it's all in the interpretation.
Research psychologists have discovered that people have faulty intuitions about what chance sequences look like. People expect sequences of coin flips, for example, to alternate between heads and tails more than they actually do. Because chance produces less alternation than our intuition leads us to expect, truly random sequences look too ordered. Streaks of four or five heads in a row clash with our expectations, even though in a series of 20 tosses there is a 50 percent chance of getting four heads in a row, and a 25 percent chance of a streak of five. The law of averages (in fact, statisticians call it the "law of large numbers") ensures the expected even split only after a large number of tosses. It is not uncommon for a player to make 50 percent of his shots and to take nearly 20 shots per game, so he stands a decent chance of making four or five shots in a row,and thus looking like he has a hot hand.
When the research team showed basketball fans a randomly generated sequence of X's and O's—OXXXOXXXOXXOOOXOOXXOO—and told the fans that the letters represented shots made and shots missed, 62 percent of subjects thought it constituted streak shooting even though the "hits" and "misses" had no effect whatsoever on one another.
It's easy to see, Gilovich wrote, why they thought this. "The sequence ... does look like streak shooting. Six of the first eight shots were hits, as were eight of the first 11! Basketball players do shoot in streaks, but the streaks do not exceed the laws of chance."
AND... ANYTHING ELSE? Yup. The greats of college basketball are vastly unimpressed with this theory. According to Gilovich,
Red Auerbach,the brains behind what is arguably the most successful franchise in American sports history, the Boston Celtics, had this to say upon hearing about our results: "Who is this guy? So he makes a study. I couldn't care less." Another prominent coach, Bobby Knight of the 1987 NCAA champion Indiana Hoosiers, responded by saying "there are so many variables involved in shooting the basketball that a paper like this really doesn't mean anything."
Other studies have come up inconclusive over the years—but when a team of scientists from Humboldt University conducted a study of just free-throw shooting in 2011, they found evidence that supported the theory of the hot hand. They found that, contrary to Gilovich's findings, "probability of success following a success is higher than the probability of success following a failure."
So, you know. Grain of salt.
AND THUS, WE CAN CONCLUDE THAT: Though Michael Carter-Williams scored a lot of points on Thursday night, he did not have a hot hand—not by Gilovich's logic, anyway. But if you were fooled, or remain unconvinced, you're in good company.