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

Robert Jimerson Jr

arXiv:2609.06610v1cs.LG

TL;DR

Conventional box-score statistics provide limited information about shot quality and the different roles involved in creating scoring opportunities. The study develops a documented statistical and machine-learning framework for quantifying recorded offensive impact in professional box lacrosse. Among fixed specifications, observed out-of-fold log loss (0.4189) and Brier score (0.1260) improved on a constant base-rate predictor by 1.22% and 1.50%, respectively; five of nine evaluated specifications failed to beat that predictor.

  • Problem

    Conventional box-score statistics provide limited information about shot quality and the different roles involved in creating scoring opportunities.

    Source: §1.1 · p. 2, §11 · p. 31

  • Method

    The study develops a documented statistical and machine-learning framework for quantifying recorded offensive impact in professional box lacrosse.

    Source: §1.2 · p. 2, §11 · p. 31

  • Results

    Among fixed specifications, observed out-of-fold log loss (0.4189) and Brier score (0.1260) improved on a constant base-rate predictor by 1.22% and 1.50%, respectively; five of nine evaluated specifications failed to beat that predictor.

    Source: §11 · p. 31

  • Takeaways & Limitations

    The framework adds a way to quantify recorded offensive impact beyond conventional box-score summaries.

    Source: §11 · p. 31

    The dataset contains 1,006 attempts and 151 goals from thirteen Rochester Knighthawks games, so further validation is required before the model can be interpreted as a general estimate of NLL shot quality.

    Source: §10.2 · pp. 28–29

Abstract

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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.

1 Introduction

Box-score statistics provide limited information about shot quality and the roles behind scoring opportunities. The study proposes a documented framework for expected goals and offensive attribution, with probability-model performance only modestly better than a base-rate benchmark.

1.1 Motivation and Problem Context

  • Box-score goals, assists, and shots on goal omit shot quality and give little credit for pick-created separation; documented methods remain less developed in professional box lacrosse.The study frames this as a gap in distinguishing opportunity generation from conversion.Source: §1.1 · p. 2

1.2 Research Objective and Framework Overview

  • The study develops a documented statistical and machine-learning framework for quantifying recorded offensive impact in professional box lacrosse.Its transparency specifies event definitions, feature construction, estimator settings, random seed, and game-level validation for implementation on independently collected data.Source: §1.2 · p. 2
  • The empirical analysis uses a manually annotated dataset of 1,006 Rochester attempts from thirteen consecutive 2025–2026 games, including 151 goals.The framework evaluates logistic regression, random forest, and extremely randomized trees with Leave-One-Game-Out cross-validation.Source: §1.2 · pp. 2–3
  • Core Offensive Impact combines shooter xG and shot-based xA for identified final passers, while exploratory xPV compares pick-aware observed-state probabilities with no-pick counterfactuals.xPV is not treated as a validated goal-equivalent quantity, and finishing above expected remains separate from opportunity creation.Source: §1.2 · p. 3

1.3 Research Questions and Contributions

  • The contextual baseline random forest improved on the training-fold base-rate benchmark by 1.22% in log loss and 1.50% in Brier score; five of nine specifications did not.Adding two-man-action and pick-type variables did not improve the primary probability metrics.Source: §1.3 · pp. 3–4
  • With thirteen games from one team, the model is an initial empirical baseline rather than a definitive league-wide estimate.The paper also notes that the reported model comparison is descriptive because the same cross-validation predictions were used for comparison and selection.Source: §1.3 · p. 4

2 Related Work

Prior work establishes shot-quality modeling and broader player-value analysis, but the paper positions its contribution as integrating these ideas with NLL-specific data and player attribution. It emphasizes that models and features require validation in the sport being modeled.

2.1 Expected Goals and Shot-Quality Modeling

  • Expected-goals models assign shot-level scoring probabilities, distinguishing opportunity volume from estimated quality; distance and angle offer an interpretable spatial baseline whose added value must be tested in the modeled sport.Prior soccer and hockey work also uses contextual and preceding-event features.Source: §2.1 · pp. 4–5

2.2 Opportunity Creation and Player Evaluation

  • Shot-based xA credits the final passer with the resulting shot’s expected scoring value, while broader action-value and off-ball methods often rely on tracking or complete event sequences.Structured video annotation offers a more limited way to identify observable contributions associated with shots.Source: §2.2 · pp. 5–6

2.3 Lacrosse Analytics and Data Availability

  • Field-lacrosse work has modeled shot quality, while professional box-lacrosse research includes possession-level strategy analysis; research-ready NLL shot-level data were not publicly available in the form needed here.Field and box lacrosse differ in geometry, rules, personnel, and offensive structure, so models require validation before transfer.Source: §2.3 · p. 6

2.4 Research Gap and Positioning

  • The paper’s contribution is integrating NLL event collection, sport-specific probability modeling, game-level validation, and on- and off-ball attribution in one documented framework.Its attribution covers shot value for shooters, resulting-shot value for final passers, and counterfactual pick value for qualifying actions; xPV remains exploratory.Source: §2.4 · p. 7

3 Dataset

The dataset is a manually annotated, quality-checked collection of Rochester Knighthawks shot attempts from thirteen consecutive games. Its scope and video-based measurement constrain the reach of later analyses.

3.1 Data Source and Scope

  • Public NLL statistics summarize outcomes but lack the shot-level spatial and contextual information needed for expected-goals analysis, prompting manual video review for this Rochester case study.The frozen file covers thirteen consecutive games from January 3 through April 4, 2026, not the full eighteen-game season.Source: §3.1 · pp. 7–8

3.2 Data Collection

  • The author reviewed each game in full, retained goals, saves, misses, and blocks, left uncertain contextual categories unassigned, and conducted manual and automated quality checks.Checks included reconciling goal totals with official statistics, reviewing games again, and validating record counts, ranges, and categories.Source: §3.2 · p. 8

3.3 Dataset Summary

  • The frozen file contains 1,006 attempts: 151 goals, 587 saves, 203 misses, and 65 blocks; 225 qualifying shot-producing picks were identified.All observations come from one team over thirteen games, making this an initial team-level case study rather than a league-wide sample.Source: §3.3 · p. 9

3.4 Sentinels and Picker Validation

  • Picker annotation identified the non-shooting picker and classified qualifying directly shot-producing actions as on-ball or off-ball; picker identity was excluded from model inputs.Automated checks required picker number, pick type, and two-man-action state to agree.Source: §3.4 · p. 9

3.5 Coordinate Normalization

  • The analysis mirrored periods attacking the left goal so every attempt was expressed toward the right-side goal at (85, 0), then used normalized coordinates and derived spatial features.Raw coordinates and the inferred attacked-goal coordinate were retained for audit.Source: §3.5 · pp. 9–10

3.6 Dataset Limitations

  • A single-team, thirteen-game sample limits generalization across teams, playing styles, and seasons; manual annotation may also introduce measurement or classification error.Without continuous player tracking, the data cannot directly measure defensive positioning, spacing, or every off-ball contribution.Source: §3.6 · p. 10

4 Event Representation and Feature Engineering

The paper builds shot-level xG from spatial, temporal, situational, and offensive-context features, then evaluates fixed classifiers with game-level cross-validation. Among the evaluated specifications, the contextual baseline random forest had the lowest observed loss.

4.1 Event Representation

  • Each attempt used ten numeric and seven categorical baseline fields; nested extensions added two-man-action role and qualifying pick type.Shooter, passer, and picker identifiers were excluded from default inputs, and picker number was used only after prediction for xPV attribution.Source: §4.1 · p. 10, §5.3 · p. 13

4.2 Spatial Features

  • Spatial features used coordinates normalized toward the attacking goal at (85, 0), with distance in feet and angle in degrees.Raw coordinates and inferred goal location were retained for audit but excluded from the model; attempts behind the goal line were separately marked.Source: §4.2 · pp. 10–11

4.3 Temporal Features; 4.4 Situational Context Features

  • Temporal features captured period, time remaining, shot-clock time, and disabled-clock status; context fields captured strength, offense type, score differential, and pulled-goalie state.The disabled-clock indicator kept the −1 sentinel from being interpreted as possession time.Source: §4.3 · p. 11, §4.4 · p. 11

4.5 Offensive Context Features

  • Offensive-context fields described shot type, swing and off-pass status, and two-man-action role; qualifying pick type formed the xPV intervention, while picker number remained attribution-only.The recorded action roles were ball carrier, picker, or not two-man action; qualifying pick types were on ball, off ball, or no qualifying pick.Source: §4.5 · pp. 11–12

4.6 Outcome Variable; 5.1 Problem Formulation

  • The binary target marked goals as 1 and saved, missed, or blocked attempts as 0; the model estimated the probability of a goal, assigned as shot xG.That probability represents opportunity quality independently of the observed shot outcome.Source: §4.6 · p. 12, §5.1 · p. 12

5.2.1 Feature Engineering; 5.2.2 Feature Validation; 5.2.3 Feature Encoding

  • Automated feature engineering and validation checked coordinate geometry, categories, record counts, missingness, ranges, and sentinel combinations; all 1,006 raw records yielded validated observations.Fold-level imputation handled unassigned contexts, but visibility-related missingness may not be random and is a stated limitation.Source: §5.2.1 · p. 12, §5.2.2 · p. 12, §5.2.3 · p. 13

5.3 Machine Learning Models Evaluated; 5.4 Cross-Validation Strategy

  • Three fixed classifiers were tested with three nested feature sets using Leave-One-Game-Out validation, with preprocessing and fitting restricted to the other twelve games in each fold.The same aggregate out-of-fold predictions were used to compare specifications and select the lowest-loss model, so differences were descriptive rather than statistically established gaps.Source: §5.3 · p. 13, §5.4 · p. 14

5.7 Final Model Selection

  • The contextual baseline random forest was the lowest-loss general xG specification; adding two-man-action and pick-type fields did not improve the primary probability metrics.The reported comparison is descriptive because the same out-of-fold predictions were used for model comparison and selection.Source: §5.4 · p. 14, §5.7 · p. 15

6 Model Results

Across 13 held-out games, the contextual baseline random forest modestly outperformed a training-fold base-rate benchmark, while adding recorded pick fields did not improve its primary probability metrics. xPV’s magnitude was indistinguishable from model noise, so it remains exploratory; game-level results also varied substantially.

6.1 Base-Rate Benchmark

  • The benchmark assigned each held-out shot its training-fold goal rate using the same LOGO partition and no features; pooled log loss was 0.4241.Source: §6.1 · p. 16

6.2 Nine-Model Comparison

  • All three random-forest specifications ranked ahead of extremely randomized trees and logistic regression in these fixed configurations, but this does not establish universal random-forest dominance.Source: §6.2 · p. 16

6.3 Effect of Pick Features

  • Adding two-man-action role raised random-forest log loss from 0.4189 to 0.4195, while adding pick type raised it to 0.4197; neither extension improved the primary metrics.Source: §6.3 · p. 16

6.2 Nine-Model Comparison

  • The contextual baseline random forest had log loss 0.4189 and Brier score 0.1260, beating the training-fold base-rate benchmark by 1.22% and 1.50%, respectively; five of nine specifications did not beat it.Source: §6.2 · p. 16, §6.3 · p. 16, Table 4 · p. 17

6.4 Validation of Counterfactual xPV

  • xPV magnitude was indistinguishable from model noise: 74 of 200 permutations had smaller mean absolute contrasts, and no-pick placebo contrasts were comparable.Source: §6.4 · pp. 17–18
  • Positive xPV contrasts covered 82.2% of qualifying picks versus a 55.1% permutation mean, but across-row shuffling ignored game composition, making this diagnostic descriptive.None of 200 replicates reached the observed value; every held-out game had positive contrasts for more than half its qualifying picks.Source: §6.4 · pp. 17–18
  • Player xPV totals were close to rescaled pick counts (Spearman ρ = 0.98), while mean per-pick xPV varied little across credited pickers.Source: §6.4 · p. 18

6.5 Game-Level Variation

  • Baseline random-forest log loss ranged from 0.295 to 0.597 across held-out games, and it was lower than the full pick-aware model in eight of thirteen games.This game-level variation exceeded aggregate differences among the three random-forest specifications.Source: §6.5 · p. 19

7 Offensive Impact Framework

The framework attributes modeled shot value to shooters and final passers, while treating picker value as a separate exploratory counterfactual contrast. It keeps conversion distinct from opportunity involvement and cautions against reading shared attributions as unique marginal contributions.

7.1 Framework Overview

  • The framework uses shot-level xG to attribute recorded offensive involvement to shooters and final passers, with qualifying pickers represented separately through exploratory xPV.Source: §7.1 · p. 19

7.2 Expected-Goal Generation

  • Total xG combines shot volume and modeled opportunity quality; average xG per shot describes mean opportunity quality, so both should be reported with shot count.Source: §7.2 · pp. 19–20

7.3 Finishing Above Expected

  • Finishing Above Expected compares observed goals with modeled shot value, but should not be treated as persistent shooting ability without substantially more attempts.Source: §7.3 · p. 20

7.4 Expected Assists and Opportunity Creation

  • Expected assists sum modeled shot value for a player’s recorded final passes, whether the attempt becomes a goal, save, miss, or block; attempts without an identified passer receive no xA.Source: §7.4 · pp. 20–21

7.5 Per-Event Rates and Finishing

  • Totals, rates, and event counts should be considered together because high per-event values may rest on few involvements; unavailable possession and time-on-floor data prevent per-possession or per-minute adjustment.Source: §7.5 · p. 21

7.6 Definition of Offensive Impact

  • Core Offensive Impact combines shooter xG and passer xA, while FAE remains separate so short-term finishing does not obscure opportunity involvement.Source: §7.6 · pp. 21–22

7.6.1 Expected Pick Value

  • xPV contrasts a qualifying pick’s recorded-state probability with a no-pick counterfactual while holding other recorded shot context fixed; it is exploratory, not a causal treatment effect.Source: §7.6.1 · pp. 22–23

7.7 Aggregation and Interpretation

  • Core OI indicates expected value associated with recorded shooting and passing, not necessarily per-event quality or unique marginal contribution; player totals share attribution.Source: §7.7 · p. 23

8 Empirical Offensive Impact

The player results distinguish accumulated expected scoring value from average shot quality, while treating the exploratory augmented ranking and small-sample rates cautiously. Ryan Lanchbury led the augmented score through final-pass xA, whereas high-volume shooting drove Connor Fields’s total xG.

8.1 Player Offensive Impact

  • 45.27 xA put Ryan Lanchbury first on the exploratory augmented score, which is not a validated goal-equivalent player comparison.Table 6 covers nine players with at least five qualifying picks; ranks are calculated among all 25 players in the attribution dataset.Source: Table 6 · p. 24, §8.1 · p. 24
  • 233 attempts made Connor Fields the largest total-xG shooter, although his 0.140 xG per shot was lowest among the five high-volume shooters.Total xG measures accumulated opportunity value, while xG per shot measures average modeled opportunity quality.Source: §8.1 · pp. 24–25
  • McConvey ranked first among the five high-volume shooters at 0.161 xG per shot, followed by Smith at 0.160 and Williams at 0.156.A 0.010 xG-per-shot difference corresponds to approximately one additional expected goal per 100 attempts, holding shooting volume constant.Source: §8.1 · p. 25
  • Williams had 0.156 xG per shot but only 14.47 total xG across 93 attempts; his 18 goals exceeded that xG by approximately 3.53.His conversion result is separate from his modeled average opportunity quality.Source: §8.1 · p. 25
  • McCulley led the nine selected players at 0.166 xG per shot, but that rate came from only 15 attempts and should not be treated as established skill.Source: §8.1 · p. 25
  • xG per shot reflects modeled shot context rather than conversion and does not by itself establish shooting talent or finishing ability.The authors recommend presenting it alongside total xG, shot count, goals, and finishing relative to expectation.Source: §8.1 · p. 25

9 Practical Applications

The framework turns annotated games into player and game reports, passing and pick summaries, and automated outputs. Given the model’s roughly one-percent improvement over the base rate, these reports are intended to organize evidence for film review rather than replace it.

9 Practical Applications

  • The framework produces xG, xA, core OI, and exploratory xPV outputs, but its roughly one-percent improvement over the base rate supports film review rather than replacement of it.Source: §9 · p. 25
  • Player profiles pair volume, attributed expected value, and per-event rates; keeping components separate helps prevent a combined score from concealing role.FAE is kept separate because it describes conversion rather than opportunity involvement, and rates should appear with event counts.Source: §9 · p. 26
  • At game level, low goals with low xG indicate limited opportunity value, while low goals with substantial xG indicate finishing below expectation.The framework provides a fuller shooting account than shots-on-goal counts alone, but game xG totals track attempt volume closely.Source: §9 · p. 26
  • Passer–shooter tables credit the recorded final passer whether or not the attempt converts, while pick-pair xPV values identify combinations for review rather than effectiveness rankings.Individual and pairwise xPV magnitudes are not distinguishable from model noise; one shot may receive both xA and xPV attribution.Source: §9 · p. 26
  • Historical reports use out-of-fold probabilities, while newly collected games use a model fitted on the full development set; automated checks precede report generation.Video annotation remains outside automation and is the framework’s binding scaling constraint.Source: §9 · p. 26

10 Discussion

The discussion frames the analysis as an initial case study, noting modest predictive value beyond the base rate, no primary-metric gain from pick fields, and descriptive or exploratory player attribution, especially xPV. It calls for broader data, validation, and more reliable annotations while proposing extension of the transparent, game-level-validated probability framework beyond offensive shot creation.

10.1 Principal Findings and Implications

  • The contextual baseline random forest achieved 0.4189 out-of-fold log loss and 0.1260 Brier score, improving on the base-rate benchmark by 1.22% and 1.50%, respectively.Five of nine specifications performed worse than the benchmark; the model ranking is descriptive because the same Leave-One-Game-Out predictions selected the lowest-loss model, and ROC AUC was 0.604.Source: §10.1 · p. 27
  • Adding two-man-action role or qualifying pick type did not improve the primary probability metrics, with log loss rising to 0.4195 and 0.4197, respectively.The sparse action categories, including only fifteen observed off-ball picks, may lack predictive power at this sample size; held-out-game baseline log loss ranged from 0.295 to 0.597.Source: §10.1 · p. 27
  • For qualifying picks, positive xPV contrasts occurred in 82.2% versus a 55.1% null mean and exceeded all 200 permutation replicates, yet remained exploratory, indistinguishable from arbitrary partitioning, and not calibrated goal-equivalent values.This was a descriptive model-response pattern, not a formal significance test.Source: §10.1 · pp. 27–28

10.2 Limitations

  • The dataset contains 1,006 shot attempts and 151 goals from thirteen Rochester Knighthawks games; evaluation measures generalization to unseen games within the focal offensive team.In an illustrative coordinate-perturbation scenario, adding Gaussian noise of one foot to each recorded axis changed predicted xG by a mean absolute 0.0116; at three feet, the change was 0.0227.Source: §10.2 · pp. 28–29
  • The event-level probabilities omit defensive pressure and other shot-quality factors, while xA and xPV credit only immediate recorded shot-producing actions and are shared role attributions, not causal contributions.Fixed model settings, unavailable possession and playing-time data, unestimated player uncertainty intervals, and possible unmeasured confounding further limit player comparisons and league-wide interpretation.Source: §10.2 · pp. 29–30

10.3 Future Work

  • Future work prioritizes a league-wide dataset, annotation-reliability assessment, richer shot and sequence features, and tests of attribution stability with game-preserving xPV diagnostics.Possession, shift, and time-on-floor data could enable usage-adjusted measures; future xPV work should include more off-ball picks and permutation replicates that preserve game-level event composition.Source: §10.3 · p. 30
  • Delayed pick effects should remain separate from the directly shot-producing definition, consistent with preserving transparent event definitions.Source: §10.3 · p. 31
  • The framework could support goals saved above expected, defensive-impact measures, transition evaluation, and possession-value models while preserving transparent event definitions and game-level validation principles.These applications would broaden the representation of professional box-lacrosse performance.Source: §10.3 · p. 31

11 Conclusion

The contextual baseline random forest had the lowest observed out-of-fold log loss and Brier score, but five of nine specifications failed to beat the constant base-rate predictor. The study’s contribution is a documented attribution framework, with qualifying-picker value treated as exploratory and the findings bounded to a single-team, 13-game case study.

11 Conclusion

  • The framework addresses limits in conventional statistics by documenting event representation, validation, and attribution of recorded shot-producing value to shooters and final passers.Finishing and per-event rates remain visible as distinct dimensions.Source: §11 · p. 31
  • Among the fixed specifications, observed out-of-fold log loss was 0.4189 and Brier score was 0.1260; these improved on a constant base-rate predictor by 1.22% and 1.50%, respectively, while five of nine evaluated specifications failed to beat that benchmark.Source: §11 · p. 31
  • xPV magnitude was indistinguishable from model noise, while positive contrasts exceeded all 200 row-permutation replicates; limited tail resolution and game-composition handling make it descriptive, not inferential.The paper reports xPV only as an exploratory directional contrast, not a validated measure of causal pick impact or goal-equivalent player value.Source: §11 · pp. 31–32
  • The analysis used 1,006 shots and 151 goals from thirteen games involving one focal team, so it is an initial case study rather than a definitive league-wide estimate.The next phase is to collect more data and build a league-wide model for independent team- or season-level validation.Source: §11 · p. 32

Data Availability

The annotated event data are not publicly available, and the reported numerical analysis cannot be directly replicated from an open dataset. The paper documents the schema for implementation on independently collected data.

Data Availability

  • The manually annotated event data are not publicly available and are retained for potential proprietary research and practitioner applications.The annotations were derived from NLL broadcast video.Source: Data Availability · p. 32
  • Appendix A provides variable definitions, sentinel encodings, and a feature dictionary for implementing the schema on an independently collected dataset.Source: Data Availability · p. 32
  • The study contributes a documented methodology rather than an open dataset or directly replicable numerical analysis.Source: Data Availability · p. 32

Code Availability

The analysis code is not publicly released, though the paper documents procedures for independent methodological implementation. The study was conducted independently, without external funding or declared competing interests.

Code Availability

  • The analysis code is retained for potential proprietary use; Sections 5 and 6.4 and Appendix B document procedures for independent methodological implementation.Exact replication of the reported numerical results requires the unreleased event data and code.Source: Code Availability · p. 32

Research Independence, Funding, and Competing Interests

  • The author conducted the study independently; Rochester did not sponsor, fund, supply data for, participate in, or review the analysis, and no external funding or competing interests were declared.Rochester was selected because the research originated from a Rochester-specific coaching question and annotation was practically feasible.Source: Research Independence, Funding, and… · p. 32

A Current Feature Dictionary

The appendix documents the corrected dataset’s variables, feature specifications, validation settings, software environment, and complete attribution roster. It also records game-level variation and cautions against treating exploratory rankings as validated player value.

A Current Feature Dictionary

  • The corrected dataset retains raw event fields and derived variables; player identifiers support aggregation but are excluded unless an optional player-identity analysis is requested.Source: A Current Feature Dictionary · p. 35

A.1 Feature Specifications

  • The baseline used ten numeric and seven categorical source fields; the two-man specification added two-man action, and the pick-aware specification also added qualifying pick type.One-hot encoding determined the final matrix width within each training fold, so source-field counts are reported instead of one encoded-column total.Source: §A.1 · p. 36

B.1 Common Settings

  • All combinations used thirteen-fold Leave-One-Game-Out validation, with aggregate out-of-fold log loss primary and Brier score and ten-bin ECE as tie-breakers.Numeric fields were median-imputed and standardized within training folds; categorical fields were most-frequent imputed and one-hot encoded.Source: §B.1 · p. 36

B.2 Game-Level Variation

  • Baseline random-forest game log loss ranged from 0.294984 to 0.596580; pooled metrics governed ranking because games contained different numbers of shots.The full pick-aware random forest had lower game-level log loss in five of thirteen games.Source: §B.2 · p. 37

B.3 Software Environment

  • The corrected rerun documented its software versions and settings, but the package omits the processed dataset, code, out-of-fold predictions, and fitted models; exact replication requires unreleased data and code.Source: §B.3 · p. 37

C Complete Attribution Roster

  • The complete roster lists players with any xG, xA, or xPV; its exploratory augmented-score ordering is not a validated player-value ranking, and its sum is not team scoring value.The nine players discussed in the main text had at least five qualifying picks; all others had at most one.Source: C Complete Attribution Roster · p. 37, Table 10 · p. 38

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