虚拟RAPM：代表正则化调整正负值中的低出场时间球员
Dummy RAPM: Representing Low-Minute Players in Regularized Adjusted Plus-Minus
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中文总结 AI 辅助
该研究提出虚拟RAPM方法，通过新增指标恢复低出场时间球员的阵容信息，在16个NBA赛季的验证中提升了得分差预测精度，且效果稳定。
中文摘要 AI 辅助
正则化调整正负值（RAPM）使用上场时段级别的阵容指标来估算球员对得分差的贡献。当移除低出场时间球员的列时，他们的上场时段仍保留在数据中，但设计矩阵不再代表完整阵容。虚拟RAPM通过五个指标来恢复此信息，这些指标用于表示每方阵容中被排除球员的数量。在16个NBA赛季中，时间序列验证选择了每出场10分钟的阈值和虚拟变量对球员的惩罚比率为2.2。在留出的3月至4月比赛中，虚拟RAPM将赛季比赛得分差的均方根误差（RMSE）从12.897降低至12.856，且在16个赛季中有13个赛季的RMSE更低，平均降低0.042分，即0.30%。尽管比赛级预测精度的提升幅度较小，但具有一致性：RAPM在记录每方被排除球员数量时表现更优。
英文摘要
Regularized Adjusted Plus-Minus (RAPM) uses stint-level lineup indicators to estimate player contributions to scoring margin. When low-minute player columns are removed, their stints remain in the data, but the design matrix no longer represents the complete lineup. Dummy RAPM restores this information using five indicators for the number of excluded players on each lineup side. Across 16 NBA seasons, chronological validation selects a 10-minute-per-appearance threshold and a dummy-to-player penalty ratio of 2.2. On held-out March-April games, Dummy RAPM reduces mean season game-margin RMSE from 12.897 to 12.856 and achieves lower RMSE in 13 of 16 seasons. The average reduction is 0.042 points, or 0.30%. Although the improvement in game-level predictive accuracy is small, it is consistent: RAPM performs better when it records how many excluded players are on each side.
