How Our Models Work: Poisson, Dixon-Coles and Elo

Every probability on Tofiko starts life in one of three models. They are deliberately simple, published methods — no black boxes — and understanding them takes about three minutes.

The goals family

Poisson

Football scoring is rare and bursty, which happens to be exactly what the Poisson distribution describes. The model estimates each team's goal expectancy for the fixture — say 1.8 for the home side, 1.1 for the away side — from their attacking and defensive records, adjusted for home advantage and opposition quality.

Given those two numbers, Poisson prices every possible scoreline: the chance of 2-1, of 0-0, of 4-2. Sum the scorelines where the home side wins and you have P(home win); likewise for the draw and the away win. The same machinery prices Over/Under 2.5 and Both Teams To Score — that's why those markets come from this family.

Dixon-Coles

Plain Poisson has one known blind spot: it treats the two teams' goal counts as independent, which slightly underprices 0-0 and 1-1. Real football produces more tight, low-scoring stalemates than independence allows. The Dixon-Coles correction — from the 1997 paper that founded modern football modelling — adjusts precisely those scorelines.

The consequence: Dixon-Coles and Poisson agree almost everywhere else. On our data they pick the same 1X2 outcome in ~98% of matches. That is why we present them as one family with one vote — calling them two independent opinions would be counting the same evidence twice.

The ratings model: Elo

Elo ignores goals entirely. Every team carries a strength rating that rises when it beats expectations and falls when it disappoints — the same system chess uses. A win over a strong side moves your rating more than a win over a weak one; ratings carry across seasons and adjust for home advantage.

For a fixture, the rating gap converts into win/draw/loss probabilities. Elo knows nothing about scorelines — but it has a long memory of who actually keeps winning, which the goals family can miss when a team's underlying numbers and results diverge.

The ensemble — and the family split

The probabilities you see are the average of the available models. Where you used to see "3/3 models agree" we now show the honest version:

• Model families agree — the goals family and Elo point at the same outcome. Two genuinely different methods reaching one conclusion.
• Model families split — they disagree. Not a malfunction: it usually marks matches where recent results and underlying performance tell different stories. Treat the forecast more loosely.