Dirk's Hot Hand?

From the day I decided to select sport psychology as a proposed career trajectory I have been forced to explain what it is that a sport psychologist does. I like to think that I had a prepackaged, oversimplified explanation ready for mass consumption. The truth of the matter is that I’m not sure people always bought it. So for those still seeking answers to this particular question, I offer the following. One thing the field of sport psychology does is to examine issues and phenomena within the athletic domain from an empirically-based perspective. More on that later.

Tonight I came across SportsCenter and discovered that Dirk Nowitzki had scored 50 points as the Mavs beat the Suns in Game 5 giving them a 3-2 advantage in the Western Conference Finals. That’s right I missed it. I was busy watching the 79th Scripps National Spelling Bee. No, actually I was outside enjoying the nice weather, a cold beer (or six) and good friends (who don't happen to be NBA fans). Anyway, during post game discussions I was inundated with a rash of superlatives describing Nowitzki’s performance. ESPN analysts argued that his teammates had encouraged Dirk to step up in Game 5 and to be more aggressive. Following the game Nowitzki himself said, "When we were down seven in the third quarter, I saw everything slipping away. I tried to make something happen." The pundits were also sure to contrast this performance with his Game 4 effort. In that game, Nowitzki was just 3-of-13 from the field and finished with 11 points as the Mavericks lost by 20.

Nowitzki’s Game 5 line looked like this: 14-26 from the field, 5-6 on three-pointers. 17-18 from the free-throw line and 12 rebounds. Truly a performance worthy of our admiration. And the obvious conclusion that the average NBA fan makes is that it was simply Dirk’s night and all the Mavs had to do was make certain that he got his shots in order to ensure a victory. In other words, Nowitzki had the “hot hand”.

Here’s where sport psychology steps in. In 1985 a group of researchers (Gilovich, Vallone & Tversky) decided to examine the notion of the “hot hand” in professional basketball. For their research they defined the “hot hand” as the belief that during a particular period a player's performance is significantly better than expected on the basis of a player’s overall record. They first spoke to a group of basketball fans and found that 91% of fans agreed that a player has “a better chance of making a shot after having just made his last two or three shots” and 68% said the same for free throws. Overall, 84% of fans believed that “it was important to pass the ball to someone who has just made several (two, three, or four) shots in a row.”

Gilovich et al. (1985) then analyzed a professional basketball team’s shooting over the course of a season in order to see if streaks occur more often than expected by chance. They found that for each individual player, the proportion of shots made was unrelated to how many previous shots in a row he had either hit or missed. Analysis also showed that the number of runs of hits or misses for each player was not significantly different from the expected number of runs calculated from a player’s overall shooting percentage and assuming that all shots were independent of each other.

In other words, the question that Gilovich et al. (1985) sought to answer was whether basketball players produce more streaks of hits or misses than expected by chance given their underlying shooting percentage. Their analysis showed that the answer to this question was "no", for an individual player. The reason why is that each successive shot in basketball is indeed independent from the last. This came to be known as the "hot hand fallacy". The independence between successive shots, however, does not mean that basketball is a game of chance rather than skill, nor should it render the game less exciting to play, watch, or analyze. Their findings merely reiterate that the probability of a made basket is largely independent of the outcome of previous shots, although it clearly depends on other parameters such as the skill of the shooter, distance from the basket, and defensive pressure (although keep in mind Dirk was playing the Suns).

In their conclusion Gilovich et al. (1985) stated the following concerning the "hot hand fallacy":

This situation is analogous to coin tossing where the outcomes of successive tosses are independent but the probability of heads depends on measurable factors such as the initial position of the coin, and its angular and vertical momentum. Neither coin tossing nor basketball are inherently random, once all the relevant parameters are specified. In the absence of this information, however, both processes may be adequately described by a simple binomial model. A major difference between the two processes is that it is harder to think of a credible mechanism that would create a correlation between successive coin tosses, but there are many factors (e.g., confidence, fatigue) that could produce positive dependence in basketball. The availability of plausible explanations may contribute to the erroneous belief that the probability of a hit is greater following a hit than following a miss.

It's research like this surrounding issues such as the "hot hand fallacy" that excites me about sport psychology. I mean it seems like a simple concept, but as a former junior high point guard I know that I was often guilty of feeding the apparent "hot hand". But regardless of this information, great game Dirk and congratulations to champion speller Katharine Close. Oh and Mr. Cuban if you’re by any chance reading this…I’m looking for a job,