Guide · updated 2026-10-15
How log loss and Brier score measure football predictions
Football matches have three outcomes—home win, draw and away win—and even the strongest favourite can drop points. Proper scoring rules such as log loss and the Brier score evaluate the exact probabilities a model published before kickoff, rather than reducing a forecast to a single tip.
Why “hit rate” is not enough
Suppose a model gives the home team 48%, the draw 27% and the away team 25%. Calling that match a “home win pick” throws away the 52% chance that the home side does not win. Over a season, two models can pick the exact same favourite in every match while one is well calibrated and the other is wildly overconfident.
How log loss works
For a single match, log loss is −ln(p), where p is the probability (between 0 and 1) given to the result that actually happened. Lower is better:
- If the winning outcome was given 60% (0.60), the log loss is
−ln(0.60) = 0.511. - If the winning outcome was given 33.3% (0.333), the log loss is
−ln(0.333) = 1.099. - If an upset happens that was given only 10% (0.10), the log loss is
−ln(0.10) = 2.303.
How the Brier score works
The multi-category Brier score adds the squared error across all three 1X2 probabilities: (p_home − y_home)² + (p_draw − y_draw)² + (p_away − y_away)², where the outcome that happened has y = 1 and the other two have y = 0. An equal 33.3% split on every outcome scores 0.667; lower numbers mean better calibration and sharper discrimination.
Model vs bookmakers' closing odds
Across 1,141 held-out Premier League matches, our Dixon–Coles model recorded a mean log loss of 0.991 (Brier 0.591) compared with 0.969 (Brier 0.577) for de-vigged closing prices. Bookmakers' closing odds have been more accurate than the model. See the full model performance record for league-by-league validation.
Common questions
What is a good log loss for Premier League 1X2 predictions?
A naive forecast that gives 33.3% to home, draw and away scores 1.099. A historical league-average baseline scores around 1.05, while sharp closing bookmaker odds and well-calibrated statistical models typically score between 0.94 and 1.01 over large multi-season samples (lower is better).
Why not judge a football model only by how often its top pick wins?
In a three-outcome sport with frequent draws, the most likely result happens only about half the time. Accuracy percentage ignores how confident the forecast was and gives zero credit when a 32% draw or 28% away win happens.
What is the difference between log loss and Brier score?
Log loss takes the negative natural logarithm of the probability assigned to the actual result, heavily penalising confident wrong calls. Brier score sums the squared errors across all three outcomes (home, draw, away), making it more forgiving of rare upsets.
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