Ghost-GK v1 — Conditional Density Estimation for Goalkeeper Positioning
Predicts where a league-average goalkeeper would position themselves given the current game state. Uses RFCDE (Random Forest Conditional Density Estimation) over HistGradientBoostingRegressor leaf assignments with weighted 2D kernel density estimation.
Part of the silly-kicks soccer analytics library (GKDV research program, TF-18, Layer 2).
Rest-defense / high sweeper? The default/full variants here train on a fixed x ∈ [0, 30] m goal-relative box and saturate at 30 m — they cannot place an in-possession keeper who has pushed up to 30–45 m. For that regime, see the separate extended-grid (x_max = 52.5 m) model ghost-gk-sweeper-v1 (and its velocity-less companion ghost-gk-sweeper-position-only-v1) — TF-60, ADR-083.
Model Description
Standard goalkeeper evaluation metrics (xGOT, save percentage, goals prevented) measure what happens after a shot is taken. Ghost-GK addresses the upstream question: given the current game state, where should the goalkeeper be standing?
The model learns a league-average positional density from thousands of match frames across multiple tracking data providers. For any given frame, it outputs a full 2D probability distribution over the goal-relative region, not just a point estimate. This enables downstream metrics like the GK Deterrent Value (GKDV) — comparing the actual GK position against the ghost position to quantify positioning-as-deterrent.
Key properties:
Density estimation, not regression: Outputs a 60×64 probability grid (3,840 cells at 0.5m resolution), not a single (x, y) point. Captures multimodal positioning (e.g., split between near-post and central when the ball is wide).
No pickle: Serialized as npz (NumPy arrays) + JSON (metadata) + SHA-256 integrity sidecar. No pickle anywhere in the load/save path.
Vectorized inference: Tree traversal uses NumPy array operations (no sklearn at inference time). Batch prediction of 1,000 frames completes in under 1 second.
Two variants: "default" (approx. 1.0 MB, 36k-frame subsample) ships bundled in the wheel; "full" (approx. 2.4 MB, 179-match corpus) downloads from this Hub repo on first use. Both are parameters-only artifacts — the two trained tree ensembles and their baselines, with no per-sample training data (silly-kicks 4.54.0; ADR-044).
Architecture
The model implements RFCDE (Pospisil & Lee 2018) adapted for goalkeeper positioning:
Feature extraction: 26 goal-relative features per frame (ball state, defensive geometry, game context). phase is trained numerically (not categorical) so the pickle-free numeric tree traversal matches sklearn exactly (4.14.0; ADR-016).
Leaf assignment: HistGradientBoostingRegressor (500 trees, max depth 8) trained on GK x-coordinate; leaf assignments partition the feature space
Co-occurrence weighting: Training frames sharing leaf assignments with the query frame receive higher weight (Dutta et al. 2024 NFL Ghosts approach)
2D KDE: Weighted Gaussian KDE over (x, y) positions of weighted training frames produces the density surface (mode, mean). This step needs the per-sample training positions, so it runs only on a locally fit model — the distributed artifact is parameters-only and does not carry them (silly-kicks 4.54.0; ADR-044).
Served point estimate: a second HistGradientBoostingRegressor is trained on GK y-coordinate; ghost_gk_x/y serve the exact boosted mean of both ensembles, reconstructed pickle-free as baseline + Σ_trees leaf_value (no sklearn at inference). 4.14.0; ADR-016.
All coordinates are goal-relative: the defending goal is at x=0, pitch center at y=34.
Hyperparameters
Parameter
Value
Algorithm
HistGradientBoostingRegressor
Number of trees
500
Max depth
8
Grid resolution
0.5m (60×64 cells)
Grid coverage
x: [0, 30]m from goal line, y: [18, 50]m across pitch
Variants
Variant
Training corpus
File size
Source
default
36k-frame subsample
~1.0 MB
Bundled in pip install silly-kicks
full
179 matches / ~1.04M frames
~2.4 MB
Downloaded from this HF repo via pip install silly-kicks[ghost-gk]
Both variants are parameters-only artifacts (no per-sample training data is stored or redistributed). They serve identical point-estimate machinery (ghost_gk_x/y); the full variant is trained on the larger corpus. The KDE density read-out (predict_density) is available only on a locally fit model — see Usage.
Training Data
Trained on licensed tracking data from professional football matches:
Provider
Competitions
Notes
Sportec (DFL)
Bundesliga
Native GK identification
SkillCorner
Multiple leagues
Derived GK identification (ADR-007)
Gradient Sports
FIFA World Cup 2022
Owner-tier source — only the trained model weights are distributed here; the underlying raw tracking data is not redistributed
The full variant is trained on 179 matches / ~1.04M frames across all three providers above (the SkillCorner cohort was expanded to include owner-tier matches — silly-kicks 4.51.0 / TF-19 PR-2); the default variant is a lighter 36k-frame subsample. Only the learned model parameters are published: the two gradient-boosted tree ensembles (split thresholds, feature indices, leaf values) and their additive baselines. No per-sample training data and no raw provider tracking data is redistributed (parameters-only artifact, silly-kicks 4.54.0 — the per-sample density arrays were removed; see ADR-044).
Training targets are restricted to a fixed goal-relative box — x ∈ [0, 30] m from the defended goal line, y ∈ [18, 50] m — a purely geometric filter with no action or possession condition. A keeper that has rushed far upfield (a sweeper action) falls outside this box and is naturally excluded, so the model represents normal in-goal positioning; the exclusion is geometric, not action-based.
Label domain: GK (x, y) position in goal-relative coordinates, filtered to the grid region [0, 30] × [18, 50].
Usage
python
1import silly_kicks.tracking as tracking
23# Default variant (bundled, works offline)4densities = tracking.compute_ghost_gk(frames, model="default")56# Full variant (downloads from HF Hub on first use)7densities = tracking.compute_ghost_gk(frames, model="full")89# Action-coupled aggregator for VAEP integration10actions = tracking.add_ghost_gk(actions, frames, model="full")1112# Direct model loading — served POSITIONS (works on the distributed parameters-only artifact)13model = tracking.GhostGkModel.from_variant("full")14positions = tracking.compute_ghost_gk(frames, model=model, home_team_id=1)# ghost_gk_x / ghost_gk_y1516# The KDE density read-out (predict_density / GhostGkDensity) requires a LOCALLY FIT model:17# distributed artifacts are parameters-only and do not carry the per-sample data the density18# needs (silly-kicks 4.54.0, ADR-044). On a loaded artifact predict_density raises.19local = tracking.GhostGkModel(n_estimators=500).fit(features, labels)20density = local.predict_density(feature_vector)21print(f"Mode: ({density.mode_x:.1f}, {density.mode_y:.1f})")22print(f"Spread: {density.spread:.2f}")
Output
Each prediction returns a GhostGkDensity frozen dataclass:
Field
Type
Description
mode_x
float
Joint 2D mode x (argmax), goal-relative meters
mode_y
float
Joint 2D mode y (argmax), goal-relative meters
mean_x
float
Density-weighted (grid) mean x
mean_y
float
Density-weighted (grid) mean y
spread
float
Effective area (entropy-based density dispersion measure)
probabilities
ndarray (60, 64)
Full density grid
grid_x
ndarray (60,)
X-axis cell centers
grid_y
ndarray (64,)
Y-axis cell centers
The served point estimate (ghost_gk_x/y, model.predict()) is the exact boosted HGBR
predict_mean (below), reconstructed pickle-free — it is not a field of GhostGkDensity.
Served point estimate (v4.14.0)
ghost_gk_x/y and model.predict() serve the exact sklearn HistGradientBoostingRegressor boosted
mean — the same estimator the old card's ≈1.1 m number measured, but now reconstructed pickle-free
(baseline + Σ_trees leaf_value) so it survives load() and is actually served. This closes a
pre-existing integrity gap: the card reported ≈1.1 m for an estimator that save()/load() discarded,
while production served the KDE mode (≈4.65 m):
Estimator
Held-out euclidean MAE
Served?
old card number (predict_mean, sklearn, phase-categorical)
≈1.1 m
never served (unavailable after load())
KDE mode (≤ v4.12)
≈4.65 m
served through 4.12
boosted mean (reconstructed pickle-free)
1.13 m (current full re-fit, 5-fold aggregate; per-provider GS 1.08 / SkillCorner 1.18 / Sportec 1.67)
served now
The 4.14.0 number is re-measured at re-fit on the same held-out split as the mode (not copied from the
old ≈1.1 m card, which was a different, phase-categorical model). An intermediate design that served
the leaf-weighted conditional mean (no re-fit) was empirically rejected — it measured ≈7.0 m, worse
than the mode, because the conditional density is broad + multimodal. The boosted mean is a structurally
stronger estimator and is the only candidate that beats the mode. The mode remains available via
predict_density(...).mode_x/mode_y. See ADR-016.
Weights re-fit + re-published (4.14.0). This is an artifact-format change (the npz now carries the
gk_y tree ensemble + baselines for the reconstruction; serve_estimator = "boosted_mean"), and fit()
now trains phase numerically (closing a latent KDE categorical-routing capability gap). Both the
bundled default and this Hub full model are re-fit; old-format artifacts fail closed on load with a
clear "re-fit required" error.
Parameters-only (4.54.0; ADR-044). The artifact format is now metadata.version = 1.3.0
(stores_training_data = false): the per-sample density arrays (training_gk_x/y, training_leaves)
are no longer stored or distributed. The served point estimate (ghost_gk_x/y via predict_mean) is
byte-identical. The emitted ghost_gk_density_spread column (renamed from ghost_gk_spread in 4.14.0)
is retired from compute_ghost_gk / add_ghost_gk / ghost_gk_xfns; the KDE density read-out now
requires a locally fit model.
Serialization Format
model_dir/
rfcde_weights.npz # NumPy arrays: gk_x + gk_y gradient-boosted tree nodes + additive baselines (parameters only; no per-sample data)
metadata.json # Feature names, grid spec, hyperparameters, version, corpus provenance, chirality fingerprint
SHA256SUMS # Integrity checksums (CRLF-normalized for cross-platform safety)
No pickle is used anywhere in the serialization or deserialization path.
Coordinate System
Input frames must be in LTR-normalized convention (home team attacks right in all periods — the standard silly-kicks tracking output after play_left_to_right normalization).
Features are extracted in goal-relative coordinates:
Origin: defending goal center (x=0, y=34)
The defending goal is inferred per (game_id, period_id, team_id) from mean GK x position
Limitations
League-average ghost: The model predicts where an average goalkeeper would stand, not where a specific goalkeeper would stand. Stylistic differences (sweeper-keeper vs. line-keeper) are averaged out.
No shot-stopping ability: Ghost-GK models positioning, not reactions. It does not predict save probability or diving reach.
Tracking data quality: Predictions inherit noise from the underlying tracking system. SkillCorner broadcast-derived coordinates are noisier than optical systems (Sportec DFL).
LTR normalization required: Input frames must be LTR-normalized. Feeding raw provider coordinates produces incorrect goal-relative features.
Static density: Each frame produces an independent density estimate. Temporal smoothing is not built into the model (apply externally if needed).
References
bibtex
1@inproceedings{le2017ghosting,
2 title={Data-Driven Ghosting Using Deep Imitation Learning},
3 author={Le, Hoang M. and Yue, Yisong and Carr, Peter and Lucey, Patrick},
4 booktitle={MIT Sloan Sports Analytics Conference},
5 year={2017}
6}
bibtex
1@article{dutta2024nflghosts,
2 title={NFL Ghosts: A framework for evaluating defender positioning
3 with conditional density estimation},
4 author={Dutta, Rishav and Yurko, Ronald and Ventura, Samuel},
5 journal={arXiv preprint arXiv:2406.17220},
6 year={2024}
7}
bibtex
1@article{pospisil2018rfcde,
2 title={RFCDE: Random Forests for Conditional Density Estimation},
3 author={Pospisil, Taylor and Lee, Ann B.},
4 journal={arXiv preprint arXiv:1804.05753},
5 year={2018}
6}
bibtex
1@software{nielsen2026ghostgk,
2 title={Ghost-GK: Conditional Density Estimation for Goalkeeper Positioning},
3 author={Nielsen, Karsten Skyt},
4 year={2026},
5 url={https://github.com/karsten-s-nielsen/silly-kicks}
6}
