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.
- Home win
- Draw
- Away win
Each cell is the chance of that exact score, in percent. The outlined cell is the most likely score.
- Home win
- Draw
- Away win
- 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 to read it
- Expected goals are each side's average goals in a match like this. The lines under them turn that into a season's goals.
- The three big numbers are the chances of a home win, a draw and an away win. They add up to 100%.
- The grid gives every exact score a chance: home goals down the side, away goals across the top. The outlined cell is the most likely score.
- The most likely score is still unlikely. With these starting values it happens about one match in eight.
- It assumes goals come at a steady rate, each side's independent of the other's. The Dixon-Coles predictor asks whether that gets 0–0s and 1–1s wrong.
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