Poisson Distribution

The Poisson distribution is a probability model that estimates how likely a given number of independent, evenly-paced events are to occur in a fixed period, and in betting it is used to predict how many goals a football team will score and convert that into odds. It needs only one input per team: the expected number of events, usually the projected goals (an expected-goals figure). From that single average it produces a full probability for every possible scoreline, from 0-0 upward. Bookmakers feed each team's expected goals into the formula, calculate the chance of every scoreline, then group those chances into markets such as correct score, over/under totals and both teams to score, before adding a margin to set the final price. Worked example: suppose the model expects the home team to score 1.5 goals and the away team 1.1. Poisson says the chance the home side scores exactly 1 is about 33%, exactly 2 is about 25%, and zero is about 22%. Combining both teams' curves, a 1-1 draw comes out near 11%, which as fair odds is roughly 1/0.11 = 9.1, or about 8.10 (7/1) once the bookmaker's margin is applied. The model's weakness is its core assumption that goals are independent and occur at a steady rate. Real matches break that: red cards, momentum shifts and defensive game states distort scoring, so sharp compilers adjust the raw Poisson output rather than trust it blindly. For bettors, understanding Poisson helps you judge whether a correct-score or totals price looks fair, and where a bookmaker's line may have drifted from the underlying probabilities.