Empirical Demo of Lineup Points Lost (LPL)
This repository contains shot and lineup data from the NBA stats api (gathered via nbastatR in conjunction with the lineup construction code from https://github.com/jwmortensen/pbp2lineup) and code to perform an empirical analysis of the allocative efficiency methods introduced in our full paper Measuring Spatial Allocative Efficiency in Basketball.
The demo can be carried out by running empirical_lpl_demo.R, which calculates and produces plots for a specified lineup's ranks, rank correspondence, LPL, and PLC surfaces empirically using the court regions defined in dicrete_court_regions.R.
Description of Plots/Metrics
While we recommend that users read our paper to understand the full details for each metric shown in this demo, we've provided a list of high-level definitions for reference:
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Rank Plots: Ranks of FG% (Field Goal %) and FGA (Field Goal Attempts) for each region of the court for all 5 players of a given lineup code. FG% is calculated as the percentage of shots that player X made. FGA rate is the number of shot attempts per 36 minutes by player X
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Rank Correspondence: Rank Correspondence is defined as
(Rank of FGA) - (Rank of FG%)
This measures how strongly each player's FG% rank matches their FGA rank. A Rank Correspondence bigger than 0 is labeled asunder-usebecause player X is taking fewer shots than his FG% warrants. On the other hand, a Rank Correspondence smaller than 0 is labelled asover-usebecause player X is taking more shots than his FG% warrants. -
Lineup Points Lost (LPL): LPL is defined as the difference in expected points (EP) between the actual distribution of shot attempts from a given lineup and the expected points had those same shots been taken according to the optimal redistribution. Specifically, for court region i
where j indexes the 5 players in the lineup. In theory, higher LPL values correspond to greater inefficiencies while lower LPL entail higher efficiency. The demo shows LPL per 36 minutes and LPL per shot.
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Player LPL Contribution (PLC): PLC is defined as each player's individual contribution to LPL, while maintaining the directionality of their contribution (i.e. whether their contribution is due to over-use or under-use). These plots in this section show PLC per 36 minutes and PLC per shot for the 5 players in a given lineup.
