Poisson football calculator

What it is doing

The home side’s expected goals sets the mean of one Poisson distribution and the away side’s sets another. The probability of any scoreline is the product of the two, adjusted by the Dixon–Coles term for the low-scoring cells and renormalised. Adding up the cells where the home side scores more gives the home win; the cells with three or more goals in total give over 2.5; the cells where both score give both teams to score.

Because every market comes from one table, the numbers cannot contradict each other: home, draw and away sum to 100%, over and under sum to 100%, and the correct-score probabilities add up exactly to the result probabilities.

What it cannot do

The calculator is only as good as the two numbers you give it, and it assumes the two sides’ goals are independent beyond the Dixon–Coles adjustment — no side sitting on a lead, no side chasing a game. It knows nothing about who is playing. On this site the expected goals come from a model fitted on results and expected goals over the last two seasons, shrunk toward the league average, and even so the how-it-works page lists what the model misses.

Questions

What does a Poisson model do in football?

It treats each side’s goals as a Poisson-distributed count with a mean equal to its expected goals, and multiplies the two distributions to get a probability for every scoreline. Every market — result, totals, both teams to score, correct score — is then read off that table.

What is the Dixon–Coles adjustment?

A correction for the low-scoring draws that plain Poisson gets wrong. Independent Poisson distributions under-rate 0-0 and 1-1 and over-rate 1-0 and 0-1; Dixon and Coles (1997) introduced a parameter, rho, that nudges those four cells. This calculator uses the site’s fitted value.

Where do I get expected goals for each side?

From a model, ideally. A rough version: the home side’s attack rate times the away side’s defence rate times the league average, with a home-advantage factor; the site’s league and team pages have the season rates. The match pages show the model’s own expected goals for every fixture.

Why do the probabilities not match the bookmaker’s?

The bookmaker’s prices reflect line-ups, injuries, motivation and the weight of money, none of which a goal expectation carries. Where a well-built model and the market disagree by a lot, the market is usually right. The gap is information, not a recommendation.

The same numbers on real fixtures

• The model’s expected goals and probabilities for today’s fixtures
• Season goal rates for every league and team
• The model in full, including its limits