Predictive Bayesian selection of multistep Markov chains, applied to the detection of the hot hand and other statistical dependencies in free throws

When extended to data from the 2016--2017 NBA season specifically for LeBron James, a model depending on the previous shot (single-step Markovian) does not clearly beat a model with independent outcomes. An error-correcting variable length model of two parameters, where James shoots a higher percentage after a missed free throw than otherwise, is more predictive than either model.