A basketball paradox: exploring NBA team defensive efficiency in a positionless game

In the last decade, the offensive and defensive philosophies employed by teams in the National Basketball Association (NBA) have changed substantially. As a result, most players can no longer be classified into only one of the five traditional positions (PG, SG, SF, PF, C) and instead spend a percentage of their playing time at multiple positions, making positional data compositional. Further, given the desirability for versatile players, an argument can be made that traditional positions themselves are archaic. Using data from the 2016–17, 2017–18, and 2018–19 seasons, I explore how Bayesian hierarchical models can be used to estimate team defensive strength in three ways. First, only considering players classified by their majority traditional position. Second, by using compositional traditional positional data. Third, using compositional data from modern positions (archetypes) defined by fuzzy k-means clustering. I find that the fuzzy k-means approach leads to a modest improvement in both the root mean squared error and median 95 % posterior predictive interval width for the test data, and, more importantly, identifies 11 modern archetypes that, when combined, are correlated with team win total and adjusted team defensive rating. The modern archetype compositions can be used by stakeholders to better understand team defensive strength.