Title: Evaluating the hot hand phenomenon using predictive memory selection for multistep Markov Chains: LeBron James' error correcting free throws,
Abstract: Consider the problem of modeling memory for discrete-state random walks using
higher-order Markov chains. This Letter introduces a general Bayesian framework
under the principle of minimizing prediction error to select, from data, the
number of prior states of recent history upon which a trajectory is
statistically dependent. In this framework, I provide closed-form expressions
for several alternative model selection criteria that approximate model
prediction error for future data. Using simulations, I evaluate the statistical
power of these criteria. These methods, when applied to data from the
2016--2017 NBA season, demonstrate evidence of statistical dependencies in
LeBron James' free throw shooting. In particular, a model depending on the
previous shot (single-step Markovian) is approximately as predictive as a model
with independent outcomes. A hybrid jagged model of two parameters, where James
shoots a higher percentage after a missed free throw than otherwise, is more
predictive than either model.