According to researchers, hot hand shooting in basketball is real and they have mathematical proof.

Fans, players and coaches in basketball have long sworn about hot hand shooting, the idea that a player can enter a winning streak after successfully making shots in a row. But researchers were more skeptical of hot hand shooting, especially after repeatedly disproving the existence of the phenomena, calling it no more than a cognitive illusion. Two economists, however, are proving the skeptics wrong, publishing a paper in the Social Science Research Network. According to them, prior research was flawed and hot hand shooting might be real, after all.

For their study, Joshua Miller and Adam Sanjurjo used a basic example of an experiment involving flipping a coin four times. According to Sanjurjo, the results of every throw were recorded and they immediately calculated the percentage of heads tossed after another head result in all of the possible sequences.

"The results were unexpected: the proportion is not 50 percent, as we intuitively believe, but actually around 40 percent," he said, adding that this result suggests the presence of a bias.

When taken within the context of basketball and hot hand shooting, the results mean that when the overall field goal percentage for a player is 50 percent, the average goal percentage for the shots carried out after a series of three shots will also be 50 percent. While this is counter-intuitive, it statistically validates the existence of hot hand shooting.

In particular, the results of Miller and Sanjurjo's work show that average difference in goal percentages while on a streak is +13 percentage points. This becomes specifically significant given that the difference between a median shooter and the best three-pointer for the 2013-2014 NBA league was +10 percentage points.

After this study, both Miller and Sanjurjo have also gone on to publish articles exploring winning streaks over multiple shot databases further. Under various circumstances, they said that they were able to discover strong evidence in basketball players, ranging from semi-professionals to university students, that hot hand shooting does exist.

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