用机器学习量化职业盒式长曲棍球射门价值与进攻贡献，提升数据洞察力。
A Statistical and Machine Learning Framework for Quantifying Offensive Impact in Professional Box Lacrosse
- 构建基于多种模型的预期进球（xG）框架，融合射门上下文特征。
- 随机森林模型表现最佳，相比基线提升1.22%的对数损失和1.50%的布里尔分数。
- 提出预期挡拆价值（xPV）概念，但结果仅具探索性参考意义。
职业盒式长曲棍球统计数据虽记录结果，却难以反映射门质量或得分机会背后的参与角色。本研究基于13场2025-2026年国家长曲棍球联盟比赛中的1,006次手动标注射门尝试（含151粒进球），开发了一套可追溯的框架，用于估计预期进球（xG）并归因进攻参与度。通过留一场比赛外交叉验证，评估了逻辑回归、随机森林与极端随机树在三组嵌套特征集上的表现，其中上下文基准随机森林在合并日志损失（0.4189）与布里尔分数（0.1260）上最优，分别优于基线1.22%和1.50%；九种设定中仅五种超越基线。加入二人配合与挡拆类型特征未提升主要指标。核心进攻影响力属性通过射手xG及最终传球手的预期助攻来记录参与度。预期挡拆价值（xPV）对比有无挡拆状态下的实际概率，其幅度与模型噪声无异，方向性模式虽在200次行置换重复中显著，但尾部分辨率有限且未能保持比赛级挡拆构成，因此诊断为描述性而非推断性。故仅将xPV作为探索性增强成分报告。鉴于样本为单一球队、13场比赛，结果为初步案例研究，非联赛普适或因果推断。
原文摘要 · Abstract (English)
Professional box-lacrosse statistics summarize outcomes but provide limited information about shot quality or the roles behind scoring opportunities. This study develops a documented framework for estimating expected goals (xG) and attributing recorded offensive involvement using 1,006 manually annotated Rochester Knighthawks shot attempts, including 151 goals, from 13 consecutive 2025-2026 National Lacrosse League games. Logistic regression, random forest, and extremely randomized trees were evaluated across three nested feature sets using Leave-One-Game-Out cross-validation and a training-fold base-rate benchmark. The contextual baseline random forest had the lowest observed pooled log loss (0.4189) and Brier score (0.1260), improving on the benchmark by 1.22% and 1.50%; five of nine specifications did not beat the benchmark. Adding two-man-action and pick-type fields did not improve the primary metrics. Core Offensive Impact attributes recorded involvement through shooter xG and shot-based expected assists for final passers. Expected Pick Value (xPV) compares a qualifying pick's observed-state probability with a no-pick counterfactual. Its magnitude was indistinguishable from model noise. Its directional pattern exceeded 200 row-permutation replicates, but limited tail resolution and failure to preserve game-level pick composition make the diagnostic descriptive rather than inferential. Accordingly, xPV is reported only as an exploratory augmented component. Given the single-team, 13-game sample, the results are an initial case study rather than league-wide or causal estimates.
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