A football match produces only a handful of goals, and each one is a surprise. That is exactly the kind of situation the Poisson distribution was built for: it describes how often a rare event happens in a fixed window of time when we know the average rate.
Why football suits a Poisson model
Goals are rare compared with the number of passes, shots and attacks in a match. They also arrive more or less independently: one goal does not mechanically cause the next. Real matches are messier, but as a first approximation the fit is surprisingly good.
The idea is simple. If you know a team is expected to score 1.5 goals in a match, the distribution tells you how likely it is that the actual number is 0, 1, 2, 3 or more. With 1.5 as the average, one goal is the single most common outcome, but zero goals and two goals are both very plausible, and four or five goals are rare but not impossible.
From expected goals to win, draw, loss
Predicta first estimates an expected number of goals for each side, using the attacking strength of one team and the defensive strength of the other, both measured relative to the league average. Each team's expected goals then feed their own Poisson distribution.
Next comes a simple grid. Imagine one row for every possible score of team A and one column for every possible score of team B. Each cell holds the probability of that exact scoreline, found by multiplying the two Poisson probabilities. Add up every cell where A has more goals than B and you get the probability of an A win. The diagonal gives the draw, and the cells where B leads give a B win. The most probable cell is the most likely scoreline.
The result is not a forecast of what will happen. It is a map of how likely each outcome is, given the inputs.
What the model cannot see
A Poisson model only knows what its inputs tell it. It does not know that a key striker is injured, that a coach was just replaced, or that a team has nothing left to play for. It also assumes goals are independent, which is not perfectly true: a team that goes behind often changes its approach. Very low scores are a known weak spot, and that is the reason Predicta applies a correction for them, covered in another article.
Treat the output as a structured estimate, not a verdict.
Key takeaways
- Goals are rare and roughly independent, which makes the Poisson distribution a sensible starting model.
- Expected goals for each team produce a grid of scoreline probabilities that can be summed into win, draw and loss.
- The model ignores injuries, tactics and motivation, so it estimates rather than predicts.
- A probability describes likelihood, never certainty.