The relative wages of offense and defense in the NBA: a setting for win-maximization arbitrage?

Abstract

Abstract In basketball, a point scored on offense carries a nearly identical on-court (win) value as a point denied on defense (e.g. within the Pythagorean expected wins model). Both outcomes bear the same score margin implication. As such, a win-maximizing team is expected to value the two outcomes equally. We ask whether the salaries of NBA players reveal such an equality among NBA teams. If not, a win-maximizing team would enjoy a disequilibrium arbitrage opportunity, whereby the team could improve, in expectation, even while reducing roster payroll. We considered the 322 National Basketball Association (NBA) players during the 2016–2017 season who were on a full-season contract for which the salary was not stipulated under the NBA Collective Bargaining Agreement. We estimated the implied marginal wage of an additional point created on offense (denied on defense) per 100 possessions. Namely, we constructed a set of fixed effects, ordinary least squares regression models that specify a player’s pre-assigned 2016–2017 player salary as a function of primary team fixed effects, offensive adjusted plus minus, defensive adjusted plus minus, position-of-play, and control variables such as age. We conclude that a win-maximizing NBA team currently faces a substantial arbitrage opportunity. Namely, one unit of offense carries the same estimated implicit salary as approximately two and a half to four units of defense. We also find moderate between-team variation in adjusted plus minus return on payroll allocations.