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 (expected goals among them), adjusted for home advantage and opposition quality.

Given those two numbers — try your own in the Poisson calculator — 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.