Does "The Zone" Exist? - Free Throws

We've all seen games like it - no matter what the defense does, a player on the opposing team just can't be stopped. He makes every shot, every catch, or strikes out every batter. Sports, with a history full of superstition, often chalks up "hot streaks" like this to a player being "in the zone". But does that zone really exist? Can we measure it using science?

Since we most frequently come across "the zone" hypothesis in professional sports journalism/commentary, the second analysis in this study is most interesting to me. 

The researchers looked at every field goal members of the Philadelphia 76ers took in the 1980-81 season, and separated the shots into six categories ones taken after 1/2/3 previous "hit" streaks, and 1/2/3 "miss" streaks. If the "hot hand" hypothesis held true, we would expect to seeing the chance of hitting the next streak to increase with a hit streak. In other words, the chance of making a shot would be greater after a hit than a miss on the previous shot. The probability of a hit after making two in a row would be greater than the probability of hitting after only making one in a row, and so on.

The statistics told a very different story. The weighted means for each category suggest that going on a hot streak actually makes it slightly less likely that you will make the next shot. (This seems to support basic statistics - the players were "due for" a miss to balance the hot streak and take them back to their baseline average). For eight of the nine players studied, there was not a statistically significant correlation between the outcome of previous shots and the outcome of the present shot (to put it in terms of Science 200, the p value > .05. There is a chance greater than 5% that the results were due purely to chance). 

The correlation was only statistically significant for one player, Daryl Dawkins. He experienced a correlation of -.142 that was significant at the p<.01 level, meaning that there is less than 1% chance that the result was due to chance. The statistics seem to indicate that he actually gets worse at shooting free throws as he goes on a hot streak. (Perhaps he starts to overthink what is making his shots go, throwing him off his game).

In order to control for the variable nature of athletics (a "hot" player might start getting double-teamed by the defense, lowering his probability of success on the next shot) and make sure that the 76ers weren't just a statistical outlier, they replicated this study with the Boston Celtics in the most standardized area in the game - the free throw line. The results held. There was no statistically significant relationship between the probability of success on a free throw and the result of the shot prior to it. According to the study, any "streaks" we see are solely due to chance. has a funny anecdote and about how the 76ers responded to this finding about their "hot hands":

"The 76ers were shocked by the evidence. Andrew Toney, the shooting guard, was particularly hard to convince: he was sure that he was a streaky shooter, and went through distinct "hot" and "cold" periods. (Toney is still regarded as a great clutch player. Charles Barkley has called him "one of the best kept secrets in the history of the NBA.") But the statistics told a different story. During the regular season, Tooney made 46 percent of all of his shots. After hitting three shots in a row-a sure sign that he was now "in the zone"-Tooney's field goal percentage dropped to 34 percent. When Tooney thought he was "hot," he was actually freezing cold. And when he thought he was cold, he was just getting warmed up: after missing three shots in a row, Tooney made 52 percent of his shots, which was significantly higher than his normal average."
This is a good look at the battle science has against the firmly-held beliefs of populations. As an athlete, it is easily to convince yourself that you are on a hot streak and just can't be stopped, or alternatively, blame your failures on a cold run. I believe that sports fans are also guilty of confirmation bias in assigning labels like "clutch shooter" to players - they see every last second shot made as evidence supporting the label and ignore evidence to the contrary. Here's what perhaps the greatest basketball player ever had to say about that:

"I've missed more than 9000 shots in my career. I've lost almost 300 games. 26 times, I've been trusted to take the game winning shot and missed. I've failed over and over and over again in my life. And that is why I succeed." - Michael Jordan

Of course, this study is merely correlational and doesn't necessarily establish any kind of causal link or mechanism. It would be interesting to see whether any physiological changes occur in an athlete's body during a hot streak in competition that give him an advantage. But that kind of study is difficult to imagine, and could very well change the outcome of the event studied (imagine Lebron James dribbling down the court with sensors attached all over his body, tracking the amount of adrenaline coursing through his body at any given time. With that in mind, It is extremely easy to be superstitious and irrational when dealing with a passionate area such as athletics, which makes the scientific study of it that much more interesting. In my next post, I'll take a look at how the concept of random chance could make one of the most unbelievable sports records in history just a little less impressive...

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