What is the Poisson distribution?

The Poisson distribution gives the probability of something happening 0, 1, 2, 3… times when you know the average. In football, it turns a team's xG into the probability of it scoring each number of goals.

The formula is P(k) = e^(−λ) × λ^k ÷ k!, where λ is the xG and k is the number of goals. With λ = 1.62, the chance of the team not scoring is about 20%, and of scoring exactly 1 goal, about 32%.

xG PRO uses independent Poisson: it models each team separately and multiplies the probabilities to build the scoreline matrix. Its known weak spot is the draw, which this model tends to underestimate; the public calibration shows by how much.

See also

• xG (expected goals)
• Scoreline matrix
• Model calibration
• How xG PRO calculates every match