The “hot hand belief,” that a basketball player would experience elevated performance for a certain period of time, during which consecutive shots are made in streaks, has been suggested to be a “cognitive illusion,” because, from the basketball-shooting data, no significant evidence has been found to reject the simple binomial model. The present study raises concerns about the statistical methods used to support this claim. It is argued that nonstationarity may manifest as a residual effect when the changes in shooting accuracy are interrupted by activities such as shot selection and defense effort. Reanalyses of the field goal data from the earlier study showed that the serial correlation varied substantially between positive (“hot hand shooting”) and negative (“over-alternation shooting”). In addition, a nested model comparison revealed that when a player's shooting accuracy fluctuated substantially in a short period of time, it was unlikely to be detected by the binomial model. Our results suggest that paying special attention to streak patterns in the hot hand belief may be an adaptive strategy in detecting changes in the environment.