A player sinks his fourth shot in a row and the crowd goes wild, while commentators say what the crowd is thinking the magic phrase "he is on fire!" But is he? There is a significant body of literature related to the hot hand in sports. Some of the papers claim that they have found the effect, while the others try to disprove it.
Recently we have also added our own insights into this problem  by replying to another paper in which the existence of hot streaks in NBA team winning records was shown by using DFA technique . We have shown that the authors have slightly over estimated Hurst exponents, which could indicate presence of hot/cold streaks. We have also shown that the corrected Hurst exponents, although indicating the presence of streaks, are still quite consistent with purely random models. Similar approach can be used for individual performance as well.
The main idea in disproving hot hand is to shuffle the studied series. Obviously shuffling should destroy any presence of streaks. If the shuffled time series still have the same statistical properties as original time series, then those statistical properties can't be used as evidence for the hot hand (hot streak) phenomenon. See the detailed explanation of such approach in the Numberphile video below.
- A. Kononovicius. Illusion of persistence in NBA 1995-2018 regular season data. Physica A 520: 1075-1083 (2019). doi: 10.1016/j.physa.2019.01.039. arXiv: 1810.03383 [physics.soc-ph].
- P. Ferreira. What detrended fluctuation analysis can tell us about NBA. Physica A 500: 92-96 (2018). doi: 10.1016/j.physa.2018.02.050.