The March madness has already arrived, and basketball fans are making predictions: who will become Cinderella at the school tournament? Which teams will make it to the Final Four? And, of course, which of the players will become “hot” and lead their team to the championship?
To say that a player is “hot” or has “hot hands” means that the player is making a lot of consecutive throws. The question that has haunted researchers, coaches and fans for years is whether the players who participated in these series can defy a random coincidence, or hot hands are just an illusion and fit into the statistical norms.
We are two researchers who study information sciences, operations and decision-making technologies. In our recent study, we examined whether players can actually get excited in real game situations. Our analysis has shown that some players do consistently “fire up” during a game and shoot more shots than expected after two shots in a row. However, when we looked at all the players together, we found that usually when a player makes more shots than usual after successive shots, they are more likely to return to average shots by missing the next one. Hot hands exist, but rarely.
Science go to the lane
Fans have always believed in the ability of players to achieve successful results, which was reflected in video games such as NBA Jam, where a virtual ball would light up if the player made several shots in a row. But scientists have been skeptical of the idea ever since a 1985 study concluded that what people perceive as hot hands is nothing more than the human brain’s tendency to misunderstand randomness and averages.
That changed in 2017, when a seminal paper showed that the original study—and later ones based on it—suffered from a small but significant selection bias that skewed the statistical calculations. Basically, how the team chose which frames to look at when looking for streaks or hot hands was confusing to the math itself. When the researchers explained this bias, it turned out that the hot hand was real.
The vast majority of studies on successful streaks in basketball have focused on either free throws, three-point competitions, or controlled field experiments. We wanted to test the theory in real competitive games and used data from the 2013-14 and 2014-15 NBA seasons. But in real game situations, the shots are not identical. To control this, we developed a model that predicts how often a toss will be made based on a number of different factors. These include who shot, distance to the basket, type of shot, distance to the nearest defender, who was the closest defender, whether the shot was assisted, and other considerations. It is only thanks to the modern era of data-driven sports that we have been able to carry out such an analysis.
Using this model, we were able to simulate any toss by tossing a figurative coin that represents the probability that a particular toss would hit the target. We could then quantify the effect of the hot hand by comparing the player’s actual shooting percentage after he was on the field. a bar with the expected percentage obtained by simulating the same shots in our model.
For example, imagine that in the real world a player made 55% of their shots after they had made two shots before. But our model predicted that he would only hit 46% of shots after the previous two shots. If this difference between the model prediction and the real world is statistically significant over time, then this is good evidence that a player can get hot and continue to play streaks.
Who has a hot hand?
Our analysis included 153 players who made at least 1,000 shots in the 2013-14 and 2014-15 NBA seasons. Frames taken after two, three and four consecutive shots were considered.
By examining the shots of all qualified players, we found that if a person made two shots before that, their chance of making the next shot was 1.9% lower than the model predicted – their shot rate regressed to the average.
However, when we looked at the players individually, a significant group of players showed a hot hand. In particular, there were 30 players who demonstrated a statistically significantly higher field goal percentage after two shots compared to their expected field goal percentage. For players who demonstrated the ability to go into a hot streak, the average hot hand effect resulted in a 2.71% increase in the chance of making a third shot in a row.
For a series of three and four consecutive shots, the effect of a hot hand was even higher – an average of 4.42% and an average of 5.81%, respectively.
Why do some people get hot?
It is important to note that having a hot hand does not mean that any player can suddenly hit the ball from anywhere on the court. For example, Tim Duncan, Roy Hibbert, and Marcin Gortat have demonstrated the ability to hit streaks, but they are all centers who usually don’t shoot far from the basket. Their hot hands increased the percentage of hits at close range. This led us to hypothesize that part of the “hot hand” effect may be due to the so-called “explore and use” approach, which refers to a short period of exploring different approaches to solving a problem, followed by a period of using the best approach found. For basketball, it would look like a player discovering an inconsistency during a game – possibly a shorter player defending them than usual – and exploiting that by throwing more shots of a certain type. Research has also shown that the “explore and use” approach is associated with a string of success in creative and scientific careers.
While this hypothesis is plausible, it may not be the only factor that explains successful sales streaks. Could short-term neuroplasticity, the ability of the player’s brain to quickly adapt to the conditions of the game, be the cause? What about concentration and mental preparation? Whatever the reason, our study provides compelling evidence for the existence of hot hands. For coaches and players in the NBA or the March NCAA frenzy this year, it might be a good strategy to follow the old cliché: “Go with a hot hand.”
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