On Hot Hands and Shooting Streaks: Does “momentum” in basketball really exist?

sports data statistics dataviz research journal

Basketball fans and players alike will attest to the ‘hot hand’ phenomenon, where the chances or a player making the shot are much higher following a series of successful shots than the chances following a miss. In this article, we feature a journal article that debunks this phenomenon as merely a figment of fans’ imaginations.

TJ Palanca https://www.twitter.com/tjpalanca
The Hot Hand Hypothesis. Many basketball fans believe that there are periods during a game when a player has 'hot hands', but does it hold up under statistical rigor? (Photo:<a href='http://www.flickr.com/photos/ryan_fung/2239687100/sizes/o/in/photolist-4pUYWQ-6egVNf-6pC6ZM-6qU5pB-6reH4r-6RuDLM-7bK7K2-7hR4Xy-fNL5iv-fNL5pT-9AoK2z-974pij-btuyo9-bLS29P-8St5Gc-aeXB9f-835JJe-dQQANP-bf6sNT-9io9am-9e3eeJ-9e3fhs-9dZ9kk-9e3dBL-9e3fEC-9dZamr-9e3fVq-9e3eEd-99MsjF-9j7HGC-bwdcKe-bwdAnn-bwdB5R-bweiu6-bwdbng-bwdRKF-bweGyp-bweMaK-bweUgi-bwdqgT-bwen7k-bweQz4-bwdejF-bwdu8M-bwdCmc-bweA82-bweo5V-bwdiR4-bwdngk-bwek9K-bwd5Tk/' rel='nofollow' target='_blank'> ryan_fung/Flickr</a>, <a href='http://creativecommons.org/licenses/by-sa/2.0/deed.en' rel='nofollow' target='_blank'>CC BY-SA 2.0</a>)

Figure 1: The Hot Hand Hypothesis. Many basketball fans believe that there are periods during a game when a player has ‘hot hands’, but does it hold up under statistical rigor? (Photo: ryan_fung/Flickr, CC BY-SA 2.0)

UPDATE (2018-04-15): We recently discovered more evidence in support of the hot hand and also assailing the 1985 paper featured in this article due to lack of statistical power. See here for a digestible piece of analysis.

We feature a journal article published in the Journal of Cognitive Psychology by Cornell and Stanford researchers Gilovich, Tversky, and Vallone entitled “The Hot Hand in Basketball: On the Misinterpretation of Random Sequences.” They proved, statistically, that there was no such thing as a ‘hot hand’, busting the myth that players have an inherent ‘momentum’. Instead, they found that these streaks were simply a result of our brains trying to detect patterns where none actually exist.

Debunking the ‘Hot Hand’ Hypothesis

The study tested the hypothesis in three ways: (a) they looked at player shooting data of the Philadelphia 76ers to determine any positive correlation between the outcomes of successive shots, (b) to cancel our defensive presure, they analyzed free-throw data for the Boston Celtics for the same correlation, and (c) to isolate any exogenous forces, they ran a controlled experiment with the members of the Cornell basketball varsity.

If ‘hot hands’ or shooting streaks were true, then the probability that one makes a shot after one, two, or three hits must be higher than if one makes a shot after one, two, or three misses. This is what they tested by comparing conditional shot probabilities computed from shot data on the Philadelphia 76ers in 1985.

They also performed a runs test and tests of serial correlation. A runs test is done by counting the sequences of consecutive hits or misses in the record. For example, HHMMMHM contains four runs. If evidence of the hot hand is to be gathered, there must be fewer runs that those expected by chance alone. Also, there must exist significant and positive serial correlation in the runs.

The following are their results for their analysis of shooting data for the Philadelphia 76ers:

HOT HAND? - The data seems to show that successful shots are more likely to follow misses rather than hits.

Figure 2: HOT HAND? - The data seems to show that successful shots are more likely to follow misses rather than hits.

If there is to be evidence of shooting streaks, there must be an upward line for each player and for the weighted mean. These results run counter to the ‘hot hand’ hypothesis; there seems to be, on average, a higher probability of successful shots following misses rather than hits.

Additional tests of serial correlation and runs test show that there the probability of making a shot does not significantly depend on whether the player made or missed his previous goal.

Others may argue that running hot or cold isn’t universal to all players; there are certain players who might be more psychologically prone to momentum. However, Andrew Toney (marked in blue), a player that many basketball fans at the time regarded as a streak player, did not fit the profile of the ‘hot hand’ either.

What if the defending team reacts?

What if, you say, there are other factors that influence the probability? After making successive shots, the player may have become confident and attempted more difficult shots, or the defending team might have reacted by doubling up the defense on that certain player, forcing him to take less advantageous shooting positions.

This is the reason why the researchers also analyzed free-throws, which are taken in the same place and without defensive pressure. They determined the conditional probability of making the second free-throw depending on the outcome of the first, this time for the Boston Celtics, and they found the following: