Paper: arXiv 2309.05783

Authors: Jackson P. Lautier

Abstract

The National Basketball Association (NBA) imposes a player salary cap. It is therefore useful to develop tools to measure the relative realized return of a player’s salary given their on court performance. Very few such studies exist, however. We thus present the first known framework to estimate a return on investment (ROI) for NBA player contracts. The framework operates in five parts: (1) decide on a measurement time horizon, such as the standard 82-game NBA regular season; (2) calculate the novel game contribution percentage (GCP) measure we propose, which is a single game summary statistic that sums to unity for each competing team and is comprised of traditional, playtype, hustle, box outs, defensive, tracking, and rebounding per game NBA statistics; (3) estimate the single game value (SGV) of each regular season NBA game using a standard currency conversion calculation; (4) multiply the SGV by the vector of realized GCPs to obtain a series of realized per-player single season cash flows; and (5) use the player salary as an initial investment to perform the traditional ROI calculation. We illustrate our framework by compiling a novel, sharable dataset of per game GCP statistics and salaries for the 2022-2023 NBA regular season. A scatter plot of ROI by salary for all players is presented, including the top and bottom 50 performers. Notably, missed games are treated as defaults because GCP is a per game metric. This allows for break-even calculations between high-performing players with frequent missed games and average performers with few missed games, which we demonstrate with a comparison of the 2023 NBA regular seasons of Anthony Davis and Brook Lopez. We conclude by suggesting uses of our framework, discussing its flexibility through customization, and outlining potential future improvements.

Complexity vs Empirical Score

  • Math Complexity: 2.5/10
  • Empirical Rigor: 5.5/10
  • Quadrant: Street Traders — practical and empirical, lighter on theory

Why this score: The paper introduces a practical financial framework (ROI) applied to sports analytics, leveraging straightforward arithmetic and cash flow conversion rather than advanced mathematics. Empirical rigor is modest, supported by a novel 2022-2023 NBA season dataset and clear application examples such as evaluating player availability vs. performance.

Research Flowchart

  flowchart TD
    A["Research Goal: Measure NBA Player ROI<br>Given Salary Cap & Performance"] --> B["Data Inputs: 2022-2023 NBA Per-Game Stats<br><i>(Box score, hustle, tracking)</i> & Salaries"]
    B --> C["1. Calculate Game Contribution % (GCP)<br><i>(Per-game summary stat summing to 1.0)</i>"]
    C --> D["2. Calculate Single Game Value (SGV)<br>& Multiply by GCP for Player Cash Flows"]
    D --> E["3. Traditional ROI Calculation<br><i>(Cash Flows vs. Salary as Initial Investment)</i><br>*Missed games treated as defaults*"]
    E --> F["Key Outcomes & Applications<br>• Mapped 2022-23 Season (Top/Bottom 50)<br>• Break-even Analysis (e.g., A. Davis vs. B. Lopez)<br>• Customizable Roster/Contract Tool"]