Soccer goals are commonly modeled with a Poisson distribution. Enter a team's expected goals (sometimes called xG) and get the probability of every exact scoreline from 0 to 5, plus over/under probabilities, each converted to fair sportsbook-style American odds.
The formula
P(goals = k) = (e−λ × λk) / k!
P(goals = k) = (e−1.5 × 1.5k) / k!
Plugged in for each row below:
P(0) = (e−1.5 × 1.5⁰) / 0!
P(1) = (e−1.5 × 1.5¹) / 1!
P(2) = (e−1.5 × 1.5²) / 2!
P(3) = (e−1.5 × 1.5³) / 3!
P(4) = (e−1.5 × 1.5⁴) / 4!
P(5) = (e−1.5 × 1.5⁵) / 5!
P(goals = k) = (e^−λ × λ^k) / k!, where λ is expected goals
P(under line) = sum of P(goals = k) for k = 0 up to floor(line)
P(over line) = 1 − P(under line)
American odds: if probability ≤ 50%, odds = (1 − p) / p × 100 (shown as +); if probability > 50%, odds = −p / (1 − p) × 100 (shown as −)
These are fair, no-margin odds implied by the model. Real sportsbooks shade both sides to bake in their profit margin (the vig).