The 'hot hand' in basketball: Does it exist?

By thrashing Michigan State in the 2009 NCAA championship game, North Carolina's basketball team lifted a huge monkey off its back.

Sure, there was a lot of pressure to live up to many fans' preseason prediction that the team would win the national title. But there had to be pressure to avenge the team's embarrassing loss to Kansas in the 2008 Final Four.

On April 5, 2008 -- a date that will live in infamy for Carolina fans -- the Kansas Jayhawks pummeled the Tar Heels and advanced to the national championship game. The 84-66 final score hardly tells the story.

In the first half, the Jayhawks went on a 25-2 run, including an 18-0 stretch. Over those agonizing 9 minutes and 7 seconds, UNC did not make a single field goal (0-for-13, including five missed layups), while Kansas made 6 of 12 field-goal tries and 3 of 4 3-point attempts.

It seemed like UNC would never make another shot -- and Kansas would never miss.

Even when UNC went on a 14-0 run in the second half to close the gap to four points, Kansas responded with a 13-0 run and put the game away.

While the game was excruciating for UNC fans, it provided great fodder for statisticians. After all, the game saw two of the best teams in the country go on three amazing runs.

Were the teams "in the zone" during those stretches? Or are we placing too much emphasis on the inevitable scoring runs that occur in most basketball games?

The 'hot hand'

Another way of phrasing the question is this: By going on that 25-2 stretch (or the 13-0 stretch), did the Kansas players really have a "hot hand?"

The "hot hand" is a concept used to describe a player who seems to be playing way beyond his natural level. Every shot seems to go in, often while the opponent can't make a basket.

In statistics parlance, the "hot hand" is really asking: Does the outcome of one trial (like a basketball shot, or a throw of the dice) influence the success of the next trial? If a player makes his first free throw, is he more likely to make the second one? If a team has made 10 of its last 16 shots, is it more likely to keep making shots?

Most statisticians say that the evidence provides a clear answer: no.

In the early 1980s, Thomas Gilovich, Robert Vallone, and psychologist Amos Tversky studied the field-goal shooting of the Philadelphia 76ers and the free-throw shooting of the Boston Celtics.

The results? There was no evidence that the 76ers were more likely to make a shot after they had previously made one. In fact, several players exhibited a negative effect -- tending to miss their next shot more often after a made shot. The Celtics' free throws turned up the same results: The odds of making their second free throw didn't increase just because they made the first one.

The authors of the paper argued that "hot hands" are really just a human misperception -- we tend to see patterns where they don't really exist because we give too much weight to small samples. Over the course of a few shots, or even an entire game, players will naturally tend to go on some hot streaks -- and some cold streaks.

Proponents of the hot hand idea argue that shooting baskets is not like flipping coins, whose outcomes can be neatly predicted using statistical models.

Additionally, everyone who has played a sport can recall instances where non- quantifiable effects -- such as muscle memory, confidence, and fatigue -- seemed to have produced stretches where we really "in the zone" (and, of course, days where we couldn't make a single basket).

In the future

The authors of the 76ers paper concluded that humans make too many inferences from small samples of data, yet that conclusion itself was derived from only half a season of 76ers games and two seasons of Celtics free throws. Not a very big sample.

Of course, they didn't have anything else available in the early 1980s. However, with the recent growth of record-keeping in sports, perhaps we now have enough information to redo the basketball study in-depth by looking at decades' worth of players and games. It would be a huge project but certainly worth the effort.

Maybe the results will only confirm that basketball players really don't go on excessive stretches of hot or cold shooting and that the "hot hand" is just the result of our selective memory.

Or maybe it will reveal what North Carolina fans have known all along: 18 months ago, Kansas won not because it was the better team -- but because the Jayhawks happened to have the hot hand and were just in one of those zones where they couldn't be stopped.

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