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

Robert Jimerson

cs.LGSep 6, 2026

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

Authors: Robert Jimerson

Organizations: Independent Researcher

Abstract

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.

Figures & tables

Date	Opponent	Site	Result
Jan. 3, 2026	Colorado Mammoth	Away	L, 13–18
Jan. 9, 2026	Philadelphia Wings	Away	W, 16–13
Jan. 10, 2026	Buffalo Bandits	Home	W, 12–9
Jan. 17, 2026	Toronto Rock	Home	L, 10–11
Jan. 31, 2026	Vancouver Warriors	Home	L, 6–16
Feb. 7, 2026	Vancouver Warriors	Away	L, 15–16

Table 1: Rochester Knighthawks games included in the frozen analysis dataset. Scores are shown from Rochester’s perspective; OT denotes overtime.

Characteristic	Value
Season	2025–2026
Team	Rochester Knighthawks
Games	13
Shot attempts	1,006
Goals	151
Saved shots	587

Table 2: Summary of the Rochester Knighthawks shot dataset.

Figure 1: Illustration of coordinate normalization into a common attacking direction before distance and angle are calculated.

Feature group	Variables
Baseline numeric	Quarter, time remaining, shot-clock seconds, shot-clock-disabled indicator, passer-present indicator, normalized $X$ , $Y$ , distance, angle, and behind-goal indicator
Baseline categorical	Strength state, offense type, swing state, shot type, off-pass state, score differential, and pulled-goalie state
Two-man extension	Baseline plus two-man-action role
Pick-type extension	Two-man extension plus qualifying pick type
Outcome	Goal, saved, blocked, or missed

Table 3: Feature groups used to represent each shot attempt.

Figure 2: Data-preparation and modeling workflow. Manually annotated events undergo feature engineering, validation, and encoding before model development and downstream offensive analysis.

Feature set	Model	Log Loss	$\Delta$ LL	Brier	ROC AUC	AP	ECE
Baseline	Random forest	0.4189	$+1.22\%$	0.1260	0.604	0.214	0.026
$+$ two-man action	Random forest	0.4195	$+1.07\%$	0.1261	0.603	0.215	0.019
$+$ pick type	Random forest	0.4197	$+1.03\%$	0.1260	0.604	0.216	0.019
Baseline	Extra Trees	0.4219	$+0.51\%$	0.1268	0.569	0.207	0.030
$+$ two-man action	Extra Trees	0.4256	$-0.37\%$	0.1277	0.557	0.195	0.027
$+$ pick type	Extra Trees	0.4269	$-0.66\%$	0.1276	0.553	0.204	0.035

Table 4: Complete out-of-fold comparison against a base-rate benchmark. Lower log loss, Brier score, and ECE are better; higher ROC AUC and average precision (AP) are better.

\Delta

LL is the percentage reduction in log loss relative to the benchmark, with negative values indicating performance worse than predicting the training-fold goal rate.

Statistic	Observed	Null mean	Null 95% interval	Diagnostic count
Mean $\|$ xPV $\|$	0.0222	0.0236	$[0.0181,\ 0.0306]$	74/200 below observed
Fraction positive	0.822	0.551	$[0.391,\ 0.707]$	0/200 at or above observed

Table 5: Exploratory counterfactual xPV diagnostic in which the pick fields are permuted jointly across rows within each training fold. Two hundred replicates, seed 20251214. The permutation does not preserve game-level pick composition; comparison counts are descriptive rather than confirmatory

p

values.

Player (No.)	Rank	Shots	xG/shot	xG	xA	xPV	$\mathbf{OI^{expl}}$
Ryan Lanchbury (7)	1	131	0.144	18.83	45.27	0.21	64.32
Connor Fields (10)	2	233	0.140	32.56	27.59	0.15	60.30
Ryan Smith (43)	3	194	0.160	31.12	12.46	0.76	44.34
Thomas McConvey (12)	4	165	0.161	26.57	10.91	1.16	38.64
Zed Williams (28)	5	93	0.156	14.47	6.58	0.71	21.76
Kyle Waters (42)	6	43	0.144	6.18	4.39	0.62	11.20

Table 6: Exploratory augmented Offensive Impact for the nine Rochester players credited with at least five qualifying picks. Rank is calculated among all 25 players in the attribution dataset (Appendix C ). xG/shot is observed-state out-of-fold xG divided by attempts;

\mathrm{OI}^{\mathrm{expl}}

equals xG

+

+

xPV. Because xPV magnitudes are not distinguishable from model noise, neither the xPV column nor the augmented ranking is a validated goal-equivalent player comparison.

Player (No.)	Expl. rank	Shots	Goals	Assists
Ryan Lanchbury (7)	1	131	22	40
Connor Fields (10)	2	233	31	24
Ryan Smith (43)	3	194	27	17
Thomas McConvey (12)	4	165	24	12
Zed Williams (28)	5	93	18	4
Kyle Waters (42)	6	43	4	6

Table 7: Shots, goals, and recorded final-pass assists for the same nine players.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Variable	Role	Definition
source_file , source_row	Audit	Original CSV filename and one-based source row.
game_id , shot_id	Grouping/identifier	Game key for LOGO folds and unique event identifier.
Quarter	Baseline numeric	Regulation quarter or overtime period, with overtime encoded as 5.
Time In Qtr	Raw	Display clock retained as entered.
time_remaining_seconds	Baseline numeric	Period clock converted to seconds, including fractional seconds.
shot clock	Raw/sentinel	Recorded shot clock; $-1$ denotes disabled.

Appendix

Table 8: Variables in the corrected processed dataset.

Model	Settings
Logistic regression	$C=1.0$ ; maximum 3,000 iterations; no class weighting; standardized numeric inputs
Random forest	500 trees; minimum leaf size 5; max_features=sqrt ; no class weighting; parallel fitting
Extra Trees	500 trees; minimum leaf size 5; max_features=sqrt ; no class weighting; parallel fitting

Appendix

Table 9: Fixed estimator settings in the corrected experiment.

Rank	No.	Shots	Goals	xG/shot	xG	xA	Picks	xPV	$\mathbf{OI^{expl}}$
1	7	131	22	0.144	18.83	45.27	7	0.211	64.32
2	10	233	31	0.140	32.56	27.59	6	0.154	60.30
3	43	194	27	0.160	31.12	12.46	42	0.756	44.34
4	12	165	24	0.161	26.57	10.91	60	1.159	38.64
5	28	93	18	0.156	14.47	6.58	35	0.709	21.76
6	42	43	4	0.144	6.18	4.39	39	0.622	11.20

Appendix

Table 10: Complete attribution roster, ordered by exploratory augmented Offensive Impact. xPV magnitudes are not distinguishable from model noise (Section 6.4 ) and are reported for completeness only; the ordering is not a validated player-value ranking.

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