Model Validation

Model Performance Metrics and Diagnostics on Out-of-Sample Data

15.3%

Better than Player Historical Avg

2.5x

Top vs Bottom Decile Lift

42824

Player Appearances

0.153

Prediction Correlation

Methodology: All metrics use multi-class Brier score comparing full goal distributions (0, 1, 2, 3+ goals) on held-out test data (42824 player appearances). The Naive model uses each player's Poisson distribution derived from their historical scoring rate in the training data. Both SFM and Naive are evaluated on the same task: predicting the complete goal probability distribution, not just "score vs not score."
Calibration: Predicted vs Actual Scoring Rates

When we predict a 30% chance of scoring, does it happen ~30% of the time? Perfect calibration follows the diagonal line.

Ranking Performance: Scoring Rate by Prediction Decile

Players ranked in the top decile by our predictions score 27.5% of the time, compared to 11.0% for the bottom decile - a 2.5x lift.

Brier Score Comparison

Lower is better. Brier Score measures the accuracy of probabilistic predictions.

Model Brier Score vs SFM
SFM 0.0598 -
Naive 0.0706 +15.3%

Naive: Poisson distribution using each player's historical scoring rate from training data.

Based on 27599 player appearances with training history.

Performance by League

SFM consistently outperforms the Naive model across all 5 major European leagues.

League Impr. SFM Naive Apps
Premier League +11.5% 0.0608 0.0687 9260
La Liga +19.7% 0.0572 0.0713 8393
Serie A +16.0% 0.0561 0.0668 8287
Bundesliga +10.9% 0.0632 0.0709 7062
Ligue 1 +16.8% 0.0635 0.0763 6993
Champions League +22.9% 0.0575 0.0746 2829
Detailed Decile Analysis

Players sorted by predicted scoring probability, split into 10 equal groups.

Decile Predicted Actual Avg Goals Apps
1 (Bottom) 8.0% 11.0% 0.119 4282
2 10.7% 12.1% 0.131 4282
3 12.2% 11.0% 0.123 4282
4 13.1% 8.9% 0.097 4282
5 13.9% 12.1% 0.137 4282
6 15.2% 12.1% 0.135 4282
7 16.5% 12.5% 0.138 4282
8 17.5% 12.9% 0.145 4282
9 19.8% 18.6% 0.217 4282
10 (Top) 28.6% 27.5% 0.332 4286
Performance by Season

SFM maintains strong performance across different seasons.

Season Impr. SFM Score Rate Apps
2025/26 +24.3% 0.0513 11.4% 23932
2024/25 +2.4% 0.0706 17.0% 18892