Success does not always breed success, at least in basketball

BASKETBALL FANS missing the squeak of sneakers on hardwood have lapped up “The Last Dance”, a documentary about the Chicago Bulls’ National Basketball Association (NBA) championship run in 1998. ESPN, the sports cable network that produced it, says the show is its most-watched documentary ever. The show owes its success to its protagonist, Michael Jordan, who is widely regarded as the greatest player of all time. His remarkable accomplishments were, at times, a mystery to the player himself. In the first game of the 1992 NBA Finals, Mr Jordan made six three-pointers in the first half alone. After hitting his sixth, he glanced at his friend, Magic Johnson, on the sidelines and shrugged. As Mr Johnson recalled in the documentary: “He was so hot that night.”

But is the “hot hand” a myth? The notion that a player becomes more likely to score with every successful attempt has been debated for decades. The idea that success begets success, irrespective of other factors, persists in other fields, too, such as investing and gambling. A well-known study published in 1985 threw cold water on the hot hand in basketball. But another published in 2015 found flaws in the earlier research, rekindling the debate. Unable to let it lie, economists have returned to the court once more. In a recent working paper, researchers at Ball State University in Muncie, Indiana, analysed over 500,000 free throws and 2m field goals attempted in NBA matches in 2004-16.

The researchers found that a slight hot-hand effect does exist, but that it is not strong enough for fans or players to detect. The effect is most noticeable from the foul line, where players enjoy a more controlled environment. A player who successfully makes a free throw is about two percentage points more likely to do so on his next attempt. This effect gets stronger with successive baskets (although after the fourth consecutive shot it starts to weaken). A player who hits four free throws in a row is 4.5 percentage points more likely to make his fifth as well. The authors speculate that this could be explained in part by the “muscle memory” that comes from repeated movements. In open play, where shooting is more frantic and unpredictable, the effect disappears. When a player makes three field goals in a row, his chance of scoring on the next attempt actually falls by 0.5 percentage points (see chart).

This may not be enough to convince some players. Indeed, the researchers found that, in both defence and offence, players tend to behave as if a “hot hand” exists. After scoring, they are more likely to take their team’s next shot. Subsequent attempts are taken faster and from a longer distance, on average, suggesting that the shooter is more confident of scoring. Defending teams, meanwhile, are more likely to make a substitution or call a time-out following a made shot, to halt the perceived momentum of their opponent.

Even if players and fans are wrong to expect a high-scoring streak to continue, they probably will not stop doing so. One of the few players who can match Michael Jordan’s reputation is LeBron James of the Los Angeles Lakers, who overtook Mr Jordan’s career points tally last year. After scoring five times in three minutes during a game in February, he was asked whether he still believed in the hot-hand effect, despite evidence to the contrary. Ever defiant, Mr James said that those number-crunchers who doubt the phenomenon “have never ever been in the zone in their lives”.