Beating Betting Odds with Dixon-Coles

The Dixon-Coles model (1997) is the standard approach for predicting football match outcomes. Rather than classifying matches into win/draw/loss directly, it models the number of goals each team will score using a modified bivariate Poisson distribution. Every other market (over/under, both teams to score, correct score, Asian handicaps) falls out of that same prediction for free.

Each team has two parameters: an attack strength (how good they are at scoring) and a defense strength (how leaky their backline is). These are estimated from historical match results via maximum likelihood estimation. A home advantage parameter captures the well-documented boost that home teams get.

The key innovation over standard independent Poisson is the correlation parameter ρ. In real football, low-scoring outcomes (0-0, 1-0, 0-1, 1-1) occur more often than independent Poisson predicts. The ρ parameter corrects for this by adjusting probabilities for these specific scorelines. This is especially important for predicting draws accurately — which is exactly where bookmakers tend to be weakest.

Matches are weighted using exponential time decay (half-life ≈ 138 days), so recent form matters more than results from two seasons ago. The model is re-fitted every 5 gameweeks using all available data up to that point, so predictions for GW 20 only use information from GW 1–19 and prior seasons. No data leakage.

For each match, the model outputs probabilities for home win, draw, and away win. We compare these to the implied probabilities from Bet365 odds (after removing the bookmaker's margin/overround). When the model assigns a probability more than 5 percentage points higher than the market, that's a value bet — the market is underpricing that outcome relative to our model.

This is a flat-stake simulation: $10 on every value bet, regardless of how large the edge is. No compounding, no Kelly criterion — just a clean test of whether the model identifies genuine mispricings. All odds are Bet365 closing odds from football-data.co.uk.

The model doesn't try to predict upsets or find longshots. It simply asks: is the market's probability wrong? Sometimes that means backing the favorite when the market isn't favoring them enough. Sometimes it means backing a draw that the market has underpriced. The math doesn't care about narratives.