Poisson Distribution Calculator

Use a Poisson model for football goal probabilities

The Poisson distribution is a common baseline model for estimating the probability that a team scores a particular number of goals when you have an expected-goals rate (lambda). Enter separate home and away expected-goal values and a target scoreline.

The calculator returns the probability of each team scoring the target number of goals, the joint exact-score probability and model estimates for home win, draw, away win, Over 2.5 goals and Both Teams To Score.

Where the model is useful

Poisson probabilities are useful as a transparent starting point for score and totals analysis because the assumptions are explicit. They can help you compare a model probability with prices from the betting tools section.

Important limitations

• The basic model treats each team’s goals as independent Poisson processes.
• Expected goals must be estimated well; poor lambda inputs produce poor outputs.
• Red cards, game state, tactical changes and correlated scoring are not captured by the simple model.
• Use it as one analytical input rather than a guaranteed score predictor.