“Hot Hand” on Strike: Bowling Data Indicates Correlation to Recent Past Results, Not Causality
The top four rows of the top table show a typical scoring box of a bowling game. The fifth row is our way of transforming this information into a binary sequence of success/failure (strike/non strike) for each frame. This series is broken into (ten in this case) ordered pairs of consecutive results, which in turn populate the bottom contingency table. From this table one can use the hypergeometric distribution to obtain an expectation (mean) and variance for the upper left cell . The final step is to calculate a value for this table based on the expectations and the observed value.