Optimal shot selection strategies for the NBA

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Abstract
In this paper we conduct an equilibrium analysis of the 2015–2016 NBA record breaking season culminating in the dramatic final series upset produced by the Cleveland Cavaliers (CLE) over the Golden State Warriors (GSW). A Stackelberg equilibrium (Conitzer and Sandholm 2006) is constructed for each pair of NBA teams, as a pair of mixed offensive strategies defined over 2- and 3-point shot court locations. The first component corresponds to Team A’s offensive strategy playing against team B’s defense, and the second component is team B’s offensive strategy playing against team A’s defense. The results support the following insights. First, the results suggest that future NBA 3-point averages are headed higher to 37.9%, in contrast with current regular and playoff season averages for the 2015–2016 of 28.6% and 30.9%, respectively. Second, the results provide a means for evaluating the influence of an opposing team’s defense upon offensive strategy. Third, the results provide a strategic interpretation of the final NBA 2015–2016 playoff series where CLE upset GSW. GSW started close to their predicted strategy and then almost monotonically shifted further away whereas CLE moved closer to their predicted strategy. Realized outcomes correlate with these strategic trends.