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.

翻译：美国职业篮球联赛（NBA）对球员薪资设有工资帽，因此开发衡量球员场上表现与其薪资实际回报率的工具具有重要意义。然而，目前相关研究极少。为此，我们提出首个已知的NBA球员合同投资回报率（ROI）估算框架。该框架包含五个步骤：（1）确定测量时间跨度（如标准82场常规赛）；（2）计算我们提出的新型"单场贡献率"（GCP）指标——这一单场比赛综合统计量在每支参赛队内求和为1，由传统数据、打法类型、拼搏数据、卡位数据、防守数据、追踪数据及篮板数据等NBA单场统计组成；（3）通过标准货币换算公式估算每场常规赛的"单场价值"（SGV）；（4）将SGV与实际GCP向量相乘，得到每位球员在单赛季中的实际现金流序列；（5）以球员薪资为初始投资额进行传统ROI计算。我们通过构建2022-2023赛季NBA常规赛的全新共享数据集（包含每场GCP统计与薪资数据）验证该框架，并以散点图展示所有球员薪资与ROI的关系（含前50名及后50名表现者）。值得注意的是，由于GCP是单场指标，缺阵场次将被视为违约事件。这使我们可以计算高绩效但频繁缺阵球员与低缺阵率平均表现球员之间的盈亏平衡点——通过比较安东尼·戴维斯与布鲁克·洛佩兹在2023年常规赛的数据进行实证。最后，我们提出框架的应用场景，探讨其通过定制化实现的灵活扩展性，并展望未来改进方向。