How many goals in the next Real Madrid – Barcelona? The question looks impossible to put a number on. Yet one mathematical tool handles it remarkably well: the Poisson distribution. Here is how football scorelines get predicted, without a crystal ball.
Why Poisson works for football
Goals tick every box the law requires: they are rare (about 2.5 per match), they come in whole numbers (0, 1, 2…), and above all they are roughly independent — a goal in the 30th minute does not make another one likelier in the 31st. That is exactly Poisson's home ground.
What it gives you in practice
The idea: start from the average number of goals a team scores, and the Poisson law derives the probability of every possible score.
Example: Real average 2.1 goals at home. Poisson then gives 0 goals ≈ 12%, 1 goal ≈ 26%, 2 goals ≈ 27%, 3 goals ≈ 19%, 4 or more ≈ 16%. One useful bet falls out immediately: Real have about a 62% chance of scoring at least twice.
The secret: expected goals (xG)
That leaves THE question: where does the "average number of goals" come from? The modern method leans on xG (expected goals). Rather than counting goals, xG measures the quality of the chances: a shot from five metres in front of goal is worth a lot (about 0.7), a 30-metre effort almost nothing (about 0.05).
Why is that better than raw goals? Because a lucky deflection or a goalkeeper having the night of his life does not distort the measurement. Over time, xG predicts future goals better than past goals do.
Two teams, one scoreline
For a match, you compute the expected goals of each side (from the strength of its attack and the weakness of the defence facing it). Crossing the two gives you the probability of every exact score, of the win, of the draw, and of the famous over/under 2.5 goals.
Where Poisson gets it wrong
Poisson assumes goals are independent, which is not always true. At 2-0 the leading team eases off and the other pushes; a red card changes everything; late on, matches open up. To correct those flaws — especially low scores like 0-0 and 1-1, which happen more often than the theory says — an improved version called Dixon-Coles is used.
That is the model, fed with recent xG and adjusted for form and absentees, that PROLIFICK runs across the dozens of football matches covered every day. The basis for then looking for value.