The Value of Energy: Quantifying the Relationship Between Energy Expenditure and Player Performance in the National Basketball Association

Abstract

This paper uses player tracking data from a subset of games from the 2015-16 NBA season to estimate the relationship between energy expenditure and player performance. Using locational tracking data, several measures of energy expenditure are calculated, along with one baseline measure. To account for each individual player's skill level, a ridge regression is performed and the residuals are used as the dependent variable in a second regression. Binning is used to estimate the relationship between measures of energy expenditure and player performance, and the coefficients from binning are subsequently used to estimate parametric transformations of energy expenditure that are included in the final model. Finally, generalized additive models (GAMs) are used to estimate the relationship between energy expenditure and performance for individual players. I find three notable results. First, energy expenditure is a significant predictor of a player's deviation from their average skill level. Second, player tracking data can be used to generate measures of energy expenditure that allow for significantly more accurate predictions of player performance than measures not derived from player tracking data. Third, there is strong evidence that players require a period of time when they first enter the game to warm up, during which they perform at a lower level than normal.