Is this division reliable when considering the player’s (counterfactual) productivity “out of sample”? Consider a teammate all of whose lineup teammates improve in ability (i.e., in every lineup in which the player plays). Due to the asymptotic property of consistency, that is, APM is capable of dividing credit at the player level based on the lineups and performances in which the player actually played. APM measures can divide each such pie into constituent slices that represent consistently estimated player contributions. From this, however, can we interpret the measure as providing teammate-independent player contribution values? Let us think of the value that a player creates-along with his lineup teammates-as a pie whose size represents (score margin) performance.
2007 NBA PLAY BY PLAY DATA PLUS
It is the case that regularized adjusted plus minus measures feature (asymptotically) consistent estimators of player value toward an understanding of marginal player contributions from the season that occurred. In a related paper, Brian McDonald points out that APM values seek to disentangle player marginal effects from one another by using lineup variation across a season of play and are thus commonly interpreted as teammate independent. APM measures were created to disentangle setting-of-play spillovers and render player value measures that are adjusted for teammate and opponent quality and thus (purportedly) unrelated to teammate quality. In an ESPN article introducing the real (adjusted) plus minus measure, Steve Ilardi highlights the serious flaw in the much familiar unadjusted +/- statistics: each player’s rating is heavily influenced by the play of his on-court teammates. We extend the analysis by using ESPN’s estimated values as explanatory variables in a set of fixed effects and the two-stage least square (2-SLS) regressions that seek to explain player-season APM variation. The measure utilizes ridge regression in an effort to isolate individual contributions to average team score margin differentials per 100 possessions. It has become a leading measure for comprehensive player analysis. In basketball, a player’s APM value represents his marginal effect on the score margin per 100 possessions as compared to a league average player.
As such, RPM is not suited for out-of-sample prediction.Īdjusted plus minus (APM) measures have redefined our understanding of player value in basketball and hockey, where both are team games featuring player productivity spillovers. Despite adjusting for teammate and opponent quality, RPM does not control for complementarity effects. We find strong evidence that RPM is related to on-court teammate quality. Both empirical approaches address potential endogeneity in the relationship of interest. We also employ a two-stage least square (2-SLS) method for robustness check. We run sets of linear fixed effect regression models to explain variation in RPM across player-seasons. Herein, we use data from NBA player-season Real Plus Minus (RPM)-a leading APM measure-for all recorded player-seasons from 2013–19 and player lineup data to test whether RPM is related to teammate quality.
However, they do not account for the possibility that better players can increase the overall size of the pie and thus increase the size of the slice (overall APM value) for teammates. If a team's overall score margin success is figuratively represented by a pie, APM measures are well-designed to slice the pie and attribute individual contributions accordingly. APM measures use seasonal play-by-play data to estimate individual player contributions.
Adjusted plus minus (APM) measures have redefined our understanding of player value in basketball and hockey, where both are team games featuring player productivity spillovers.
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