Modeling Basketball Games as Alternating Renewal-Reward Processes and Predicting Match Outcomes

Abstract

We fit an Alternating Renewal-Reward Process model to basketball games and use the models to predict the outcomes of 1209 games in the 2012-2013 National Basketball Association (NBA) season. Using data collected from NBC play-by-play pages we fit various models for each team's renewal process (time of possession) and reward process (points per possession). Using these estimated distributions we simulate the outcome of each of the 1209 games. We introduce four seperate models to predict these games. To evaulate our models we compared their predictions with that of other commonly used methods such as team record, Pythagorean Win Percentage, and Bookmaker odds. The research suggests that an Alternating Renewal-Reward Process is an appropriate fit to a basketball game.