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Poisson Match Predictor

If a team usually creates chances worth 1.6 goals, how often will it actually score none, one, two or three? The Poisson distribution answers that, and two of them together give a whole match.

Expected goals from 0.1 to 5.

Home win
Draw
Away win

Each cell is the chance of that exact score, in percent. The outlined cell is the most likely score.

Most likely score
Over 2.5 goals
Under 2.5 goals
Both teams score

Win, draw and loss are summed over every score up to 15 goals each, not only the cells shown.

How it works

Each team's goal count is treated as a Poisson random variable. The only input is its average, the expected goals. The chance of exactly k goals is:

$$P(X = k) = \frac{\lambda^{k}\, e^{-\lambda}}{k!}$$

Multiply the home and away chances for each pair of scores and you get the grid.

In plain football

  • \(\lambda\) is the home side's expected goals, set above to . The away side gets its own.
  • \(k\) is the number of goals we are asking about: 0, 1, 2 and so on.
  • \(e^{-\lambda}\) is the chance of a blank, with no goals at all.
  • \(\lambda^{k}\) is the scoring rate, counted once for each of the \(k\) goals.
  • \(k!\) means \(1 \times 2 \times \dots \times k\). The same goals can be counted in that many orders, so we divide to count them only once.
  • Each cell in the grid is the home chance multiplied by the away chance for that score.

Assumptions

  • Goals arrive independently and at a steady rate through the match.
  • The two teams' scores are independent of each other.
  • You supply the expected goals. The model is only as good as those two numbers.

Where it goes wrong

  • It tends to underestimate 0–0 and 1–1 draws. Real matches are not independent: a team a goal up often sits back. Dixon-Coles adjusts for this.
  • Red cards, injuries and game state change the scoring rate mid-match. A single λ cannot.

These probabilities come from a statistical model and are for analysis and education. Football remains uncertain and model predictions will frequently be wrong.

Read the full explanation: How many goals will we score? The Poisson distribution