“Hot Hand” on Strike: Bowling Data Indicates Correlation to Recent Past Results, Not Causality
On the upper left we show how for binary sequence (a game) we calculate (see figure 1) which are averaged to obtain . On the upper right we show how for each binary sequence we make a random permutations of it (R) and then calculate the corresponding . For each realization (R) we calculate , save this value and repeat these steps many times (100,000). On the bottom plot we show a typical distribution of (in this case it is for player number 11534, Walter Ray Williams Jr who happen to show negative correlation to previous roll); since this distribution is very close to a normal distribution we can take advantage of it and measure the deviation of the observed value () from the expected one () in units of the standard deviation (). If the observed value falls into the right of the mean (red area), it means the player has a “Hot hand” tendency while if the observed value falls in to the left of the mean (blue area), it mean the player has “Cold hand” (“anti hot hand”). The resulting reflects the statistical significance of this observation.