PSxG Model — Post-Shot Expected Goals for Goalkeeper Evaluation

Logistic regression model estimating the probability that an on-target shot becomes a goal, given its goalmouth position. Trained on ~15K StatsBomb on-target shots. Used to compute goals prevented (PSxG − actual goals conceded) as the primary shot-stopping pillar of the goalkeeper evaluation framework.

Part of the (Right! Luxury!) Lakehouse soccer analytics platform.

Model Description

PSxG (Post-Shot Expected Goals) conditions on the observed shot destination — where the ball was headed when it crossed the goalline plane — rather than the shooter's location. This gives a fairer evaluation of the goalkeeper: a shot headed for the top corner is harder to save than one at chest height in the center, regardless of where on the pitch the shot was taken.

Features

Feature	Range	Description
`end_location_y`	[0, 1]	Normalized horizontal goalmouth position (0 = left post, 1 = right post)
`end_location_z`	[0, 1]	Normalized vertical goalmouth position (0 = ground level, 1 = crossbar)

Both features are normalized to [0, 1] from StatsBomb's raw coordinate system (y: 36–44 yards, z: 0–2.44m).

Architecture

Component	Detail
Model class	`sklearn.linear_model.LogisticRegression`
Solver	`lbfgs`
Max iterations	1000
Feature scaling	`StandardScaler` (fit on training set, serialized with model)
Serialization	JSON (coefficients + intercept + scaler params — zero pickle surface)

Logistic regression with just two spatial features intentionally keeps the model transparent and auditable. The goalmouth coordinate surface is low-dimensional and near-linear in log-odds space, making logistic regression the appropriate choice. No tree-based or neural models are needed for this feature set.

Model Output

Field	Type	Description
`psxg`	float64	Probability that the shot becomes a goal (0 = certain save, 1 = certain goal)

Goals prevented = sum(PSxG over shots faced) − actual goals conceded. Positive = better than average, negative = worse than average.

Training Data

Source	On-Target Shots	License
StatsBomb Open Data	~15K	CC-BY 4.0

Training data is published as luxury-lakehouse/statsbomb-shots-on-target on HF Hub.

Only shots with shot_outcome in {Saved, Goal, Post} are included (blocked shots and wayward shots are excluded, as they do not reach the goalkeeper).

How to Use

Load and Run Inference

import json
import numpy as np
from huggingface_hub import hf_hub_download

# Download model coefficients
config_path = hf_hub_download("luxury-lakehouse/psxg-model", "psxg_model.json")

with open(config_path) as f:
    model = json.load(f)

# Extract logistic regression parameters
coef = np.array(model["coefficients"])  # shape (2,)
intercept = np.array(model["intercept"])  # shape (1,)
scaler_mean = np.array(model["scaler_mean"])
scaler_scale = np.array(model["scaler_scale"])

def predict_psxg(end_location_y_norm: float, end_location_z_norm: float) -> float:
    """Predict PSxG from normalized goalmouth coordinates."""
    x = np.array([[end_location_y_norm, end_location_z_norm]])
    x_scaled = (x - scaler_mean) / scaler_scale
    log_odds = x_scaled @ coef.T + intercept
    return float(1.0 / (1.0 + np.exp(-log_odds)))

# Example: shot aimed center-right, mid-height
psxg = predict_psxg(end_location_y_norm=0.65, end_location_z_norm=0.45)
print(f"PSxG: {psxg:.3f}")  # e.g. 0.312

Load Pre-Computed Predictions

from datasets import load_dataset

ds = load_dataset("luxury-lakehouse/psxg-predictions")
df = ds["train"].to_pandas()

# Goals prevented per keeper (positive = better than average)
gp = df.groupby("player_id").agg(
    psxg_sum=("psxg", "sum"),
    goals_conceded=("is_goal", "sum"),
).assign(goals_prevented=lambda d: d["psxg_sum"] - d["goals_conceded"])
print(gp.sort_values("goals_prevented", ascending=False).head())

Intended Use

Goalkeeper evaluation: Primary shot-stopping metric for fct_goalkeeper_stats
Benchmarking: Compare GK shot-stopping performance against PSxG expectations across seasons
Research: Transparent two-feature PSxG baseline for goalkeeper analytics research
Downstream: Input to the composite goalkeeper score (Lamberts 2025 framework)

EU AI Act — Intended Use and Non-Use

This model is published for research and reproducibility purposes on public, open-licensed match data. It is not intended for, not validated for, and not supplied to any use that would fall within Annex III §4 (Employment, workers management and access to self-employment) of Regulation (EU) 2024/1689 — including recruitment or selection of natural persons, decisions affecting work-related contractual relationships, promotion, termination, task allocation based on individual traits, or the monitoring and evaluation of performance and behaviour of workers for employment decisions. In particular, "goals prevented" (PSxG − actual goals conceded) is not a fit-for-purpose metric for goalkeeper contract decisions without full Article 14 human oversight by the deploying organisation.

Any deployer who wishes to use this model for such a purpose is responsible for performing their own conformity assessment under Article 43, for drawing up the technical documentation required by Article 11 and Annex IV, for implementing the human oversight measures required by Article 14, for declaring accuracy metrics under Article 15, and for ensuring the data governance obligations of Article 10 are met. Note specifically that the training data contains no protected attributes and therefore cannot support the group-fairness audits required by Article 10(2)(g) without ingesting additional personal data.

See the AI_GOVERNANCE.md gap analysis in the source repository for the project's full risk classification, re-classification triggers, and governance posture.

Limitations

Two features only: The model uses only goalmouth coordinates. Shot speed, trajectory, deflections, and defensive pressure are not captured.
Open data only: Trained on StatsBomb open data (~15K shots). Commercial datasets with larger coverage may yield different calibration.
StatsBomb coordinate system: end_location_z is available only in StatsBomb 360 data. Models trained on providers without z-coordinate data will require a 2D fallback.
No freeze-frame context: PSxG does not model the goalkeeper's starting position or movement. See the xG v2 model for freeze-frame-conditioned expected goals.

Model Files

psxg_model.json      -- LogisticRegression coefficients, intercept, and scaler params (JSON)

Model parameters use JSON serialization — a text-only format with zero pickle surface and no code execution capability. Predictions are delivered as Parquet (non-executable).

Citation

@article{butcher2025xgot,
  title={An Expected Goals On Target (xGOT) Model},
  author={Butcher, J. and others},
  journal={Big Data and Cognitive Computing},
  volume={9},
  number={3},
  pages={64},
  year={2025},
  publisher={MDPI},
  url={https://www.mdpi.com/2504-2289/9/3/64}
}

@software{nielsen2026psxg,
  title={PSxG Model: Post-Shot Expected Goals for Goalkeeper Evaluation},
  author={Nielsen, Karsten Skytt},
  year={2026},
  url={https://github.com/karsten-s-nielsen/luxury-lakehouse}
}

Companion Resources

Resource	Description
On-Target Shot Data	Training data: ~15K StatsBomb on-target shots with goalmouth coordinates
PSxG Predictions	Per-shot PSxG predictions with player and match identifiers
xG Shot Data	Full shot dataset (pre-shot xG features, StatsBomb + Wyscout)
xG Model v2	Deep Sets xG with freeze-frame context and MC Dropout uncertainty

Demo

Try the interactive Soccer Analytics App — explore goalkeeper shot-stopping metrics on the Defensive Impact page.

Explore interactively: HF Space demo

More Information

License: CC-BY-NC 4.0
Methodology: Butcher et al. (2025) xGOT framework
Platform: Luxury Lakehouse Soccer Analytics
Workflow card: workflow-cards/wf-goalkeeper.yaml

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