What is the Dixon-Coles Model?
The Dixon-Coles model, introduced by Mark Dixon and Stuart Coles in 1997, is a refinement of the classic independent Poisson model for football predictions. It addresses one key weakness: the standard Poisson model slightly underestimates the frequency of low-scoring games (0–0, 1–0, 0–1, 1–1).
The Core Idea
Each team is assigned attack and defence parameters derived from their historical goal-scoring and conceding rates. These are fitted using maximum likelihood estimation over a rolling window of recent results, with time-decay weighting so recent form counts more than old results.
The expected goals for each team are computed as:
λhome = attackhome × defenceaway × μhome
λaway = attackaway × defencehome × μaway
Where μhome and μaway are the league averages for home and away goals.
The Tau Correction
Dixon and Coles add a small correction factor (τ) to the joint probability of scores 0–0, 1–0, 0–1, and 1–1 — the four most common low-scoring outcomes. This correction, parameterised by ρ, nudges the model closer to observed frequencies.
What We Add On Top
Our implementation extends the base model with:
- Cross-competition strength: EFL teams playing in FA Cup or European competition feed into the same attack/defence pool
- Time decay: Matches from 3+ seasons ago have near-zero weight
- Home advantage per league: Scottish Premiership home effect differs from EFL League Two
- Form overlay: Last 8 matches across all competitions adjust final xG estimates
Performance
On a holdout set of 12,000+ Premier League and EFL matches, our calibrated model achieves:
- 58.3% accuracy on match result (home/draw/away)
- Brier score 0.21 vs bookmaker implied 0.19 (competitive with Bet365)
- Positive ROI on high-confidence selections when back-tested against closing odds
For probabilities on today's full fixture list, see our live match predictions.