xG v2 — Context-Aware Expected Goals with Freeze-Frame Set Encoding
Context-aware expected goals (xG) model that conditions on the visible player positions at the moment of each shot. Trained on ~131K shots from StatsBomb Open Data and Wyscout. Includes MC dropout uncertainty quantification — every prediction comes with a 95% confidence interval.
Part of the (Right! Luxury!) Lakehouse soccer analytics platform.
Model Description
Standard xG models treat each shot in isolation: distance, angle, body part, and a handful of tabular features. xG v2 adds spatial context by encoding the positions of all visible players from StatsBomb 360 freeze frames into a fixed-length context vector using a Deep Sets architecture (Zaheer et al. 2017).
The model answers the question: given where the shooter is, where the defenders are, and where the goalkeeper is, what is the probability this shot results in a goal?
Key properties:
Permutation-invariant: Handles any number of visible players in any order. There is no fixed roster slot or player identity assumption.
Graceful degradation: When no freeze-frame data is available, the context vector is zeroed out and the model degrades to tabular-only prediction — identical in structure to the v1 XGBoost baseline.
Uncertainty-aware: MC dropout produces a mean xG estimate plus a 95% confidence interval, quantifying model confidence per shot rather than collapsing to a single scalar.
Serverless-compatible: Pure NumPy inference. No PyTorch, no ONNX, no GPU. The JSON-serialized weight file is under 100 KB and loads on Databricks serverless executors.
Architecture
The model combines a set encoder that processes freeze-frame player positions with a prediction MLP that fuses tabular shot features:
Set Encoder (per-player, shared weights):
Input: N players x 4 features (x_norm, y_norm, is_keeper, is_teammate)
Sum aggregation (permutation invariant) → context vector (16-dim)
Prediction MLP:
Concatenate: context vector (16-dim) + tabular features (13+ dim)
Linear(→ 64) → ReLU → Dropout
Linear(→ 32) → ReLU → Dropout
Linear(→ 1) → Sigmoid → xG score in [0, 1]
Set Encoder Hyperparameters
Parameter
Value
Player feature dim
4 (x_norm, y_norm, is_keeper, is_teammate)
Encoder hidden dim
32
Context dim (output)
16
Aggregation
Sum (permutation invariant)
Prediction MLP Hyperparameters
Parameter
Value
Hidden layer 1
64 units, ReLU
Hidden layer 2
32 units, ReLU
Output
1 unit, Sigmoid
Dropout rate
0.1
MC dropout samples
50
Uncertainty Quantification
xG v2 uses MC Dropout (Gal & Ghahramani 2016) as a practical Bayesian approximation. Dropout is active at inference time, and 50 stochastic forward passes are run per shot:
Each prediction returns a 4-tuple: (mean, std, ci_lower, ci_upper).
Interpretation: A narrow CI (e.g., xG = 0.72 ± 0.03) indicates the model is confident. A wide CI (e.g., xG = 0.35 ± 0.18) signals high uncertainty — typical for partially occluded freeze frames or unusual shot geometries.
Freeze-frame coverage comes from StatsBomb 360 data: approximately 15.58M freeze-frame rows across 323 matches, embedded inline within the events JSON (shot_freeze_frame field). Wyscout shots contribute tabular features only — no freeze frames.
Coverage includes the Premier League, La Liga, Serie A, Bundesliga, Ligue 1, Champions League, World Cup, and more.
Training is performed on Hugging Face Jobs using PyTorch. Inference uses the pure NumPy forward pass exported from the trained weights.
Features
Tabular Features (13)
These features are the same as the v1 XGBoost baseline:
Feature
Type
Description
distance_to_goal
Numeric
Euclidean distance from shot location to goal center (yards)
shot_angle
Numeric
Angle subtended by the goal from the shot location (radians)
From Counter, From Keeper, From Free Kick, From Corner, etc.
Set Encoder Input (variable-length, per visible player)
Feature
Type
Description
x_norm
Float [0, 1]
Player x-position normalized from StatsBomb 120m pitch
y_norm
Float [0, 1]
Player y-position normalized from StatsBomb 80m pitch
is_keeper
Binary
1 if this player is the goalkeeper, 0 otherwise
is_teammate
Binary
1 if this player is on the shooter's team, 0 for opponent
Player identity is never used. The set encoder sees only spatial position and role.
Performance
Model
ROC-AUC
Brier Score
Log Loss
v1 XGBoost + Isotonic Calibration (13 features)
0.825
0.057
1.212
v2 Set Encoder (raw, pre-calibration)
0.901
0.061
—
v2 Set Encoder + Isotonic Calibration + MC Dropout
0.915
0.060
0.200
ROC-AUC improved by +0.090 over the v1 XGBoost baseline (0.825 → 0.915) — a large gain in discrimination for xG models, where +0.02 is typically meaningful. Isotonic calibration closed the Brier score gap to 0.003 while reducing log loss sixfold (1.212 → 0.200). MC dropout 95% CI coverage: 95.1% (properly calibrated).
Training: 153 seconds on HF Jobs A10G-small. MC dropout z-multiplier: 4.2, inference dropout rate: 0.30 (3× training dropout of 0.10).
Evaluation protocol: 80/20 train/test split by competition. Metrics computed on held-out test set.
Coordinate System
All spatial features use the StatsBomb coordinate system:
This normalization ensures that the per-player MLP receives consistent scale inputs regardless of pitch dimension conventions.
Inference
The model is serialized as a JSON file with base64-encoded NumPy arrays — no pickle, no PyTorch dependency at inference time.
Output mart: predictions are persisted to {catalog}.dev_gold.fct_xg_predictions_v2 as a dbt-built mart with contract: enforced: true, inheriting Kimball surrogate FKs (match_key, team_key, player_key, competition_key) via INNER JOIN to fct_shots on shot_id per ADR-013 (consumer-side ML inference output). PR 7 (2026-04-27) extended the inheritance with team_key + player_key.
No pickle is used anywhere in the serialization or deserialization path (banned by project security policy).
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.
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
Anonymous freeze frames: The set encoder receives only position and role (keeper/teammate flag). Player identity, stamina, height, dominant foot, and tactical assignment are not encoded. Two players in identical positions produce identical context contributions.
Missing freeze-frame coverage: Only StatsBomb 360 matches include freeze frames (~323 of ~3,000 StatsBomb matches). All Wyscout shots and non-360 StatsBomb shots fall back to the zero context vector.
Partial occlusion: StatsBomb 360 freeze frames capture only visible players. Players behind the camera or in crowded areas may be absent. The set encoder handles this gracefully (sum over fewer players), but predictions may underestimate defensive pressure when multiple defenders are occluded.
Open data only: Trained on publicly available StatsBomb and Wyscout data. Models trained on full broadcast-quality tracking data with complete visibility would likely produce narrower uncertainty intervals and higher discrimination.
Static snapshot: The freeze frame captures player positions at the instant of the shot only. Prior positioning (run-up angle, off-ball movement, pressing intensity) is not encoded.
No player clustering or identity: The set encoder cannot distinguish a massed low block from an isolated goalkeeper. Tactical shape is implicit in the aggregate position distribution, not explicit.
Model Files
The model is published to three destinations, all in sync:
Logged via mlflow.pyfunc.log_model; the @Champion alias points at
the latest version. The raw weights are also logged as an artifact
(model_weights.json) so the consumer can download them byte-for-byte.
model_weights.json — identical bytes to the HF Hub copy
model_weights.json.sha256 — hex SHA-256 sidecar for SEC2 integrity verification
The Databricks serverless inference pipeline ingestion.xg_model_v2 tries
MLflow @Champion first, then falls back to the UC Volume copy; the sidecar
lets the consumer detect tampering without trusting the MLflow registry
metadata alone.
Citation
If you use this model, please cite the Deep Sets architecture and the MC Dropout method:
bibtex
1@inproceedings{zaheer2017deep,
2 title={Deep Sets},
3 author={Zaheer, Manzil and Kottur, Satwik and Ravanbakhsh, Siamak
4 and P{\'o}czos, Barnab{\'a}s and Salakhutdinov, Ruslan
5 and Smola, Alexander J.},
6 booktitle={Advances in Neural Information Processing Systems (NeurIPS)},
7 volume={30},
8 year={2017}
9}
bibtex
1@inproceedings{gal2016dropout,
2 title={Dropout as a Bayesian Approximation: Representing Model Uncertainty
3 in Deep Learning},
4 author={Gal, Yarin and Ghahramani, Zoubin},
5 booktitle={International Conference on Machine Learning (ICML)},
6 pages={1050--1059},
7 year={2016}
8}
bibtex
1@software{nielsen2026xgv2,
2 title={xG v2: Context-Aware Expected Goals with Freeze-Frame Set Encoding},
3 author={Nielsen, Karsten Skyt},
4 year={2026},
5 url={https://github.com/karsten-s-nielsen/luxury-lakehouse}
6}
