A Statistical and Machine Learning Framework for Quantifying Offensive Impact in Professional Box Lacrosse

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.