Enter expected goals (xG), runs, or points per team. The calculator runs a Poisson model to derive win/draw/loss probabilities, over/under fair lines for any total, and the most likely scoreline. Built for soccer, hockey, baseball, and any low-scoring sport.
The Poisson distribution describes the number of independent rare events in a fixed time window. For sports where scoring events happen rarely and roughly independently (soccer goals, hockey goals, baseball runs), it's a remarkably good fit. Given an expected scoring rate λ, the probability of scoring exactly k goals is:
P(X = k) = (e−λ × λk) / k!
To model a match, we treat each team's score as an independent Poisson random variable. The joint distribution over (home score, away score) is the product of the two team Poissons. From that grid, we sum the cells to get win/draw/loss probabilities, total-goal probabilities for any line, and the most likely individual scorelines.
Poisson is most accurate for soccer — scoring is rare, events are nearly independent, and the long-run distribution of goals matches Poisson tightly. It also works well for hockey (with a small adjustment for empty-net goals in tight late games) and reasonably for baseball runs (where independence is weaker because innings are sequential).
Poisson is less accurate for high-scoring sports like basketball or American football, where possessions are correlated and scoring events come in clusters (a single touchdown is 6-8 points, not 1). For those sports, normal-distribution models work better — see the Point Spread Calculator.
The model also assumes the two teams' scoring rates are independent, which is approximately true for soccer/hockey but fails when one team's defense systematically suppresses the other. Sophisticated models add a Dixon-Coles correction for low-score correlations (0-0, 1-0, 0-1, 1-1). This calculator uses the basic Poisson; add ~1-2 points of probability mass to draws in tight low-scoring matches if you're using it for soccer betting.