Gut feelings do not beat bookmakers; better probability work does. In low-scoring sports like soccer, Poisson Distribution is one of the most durable ways to turn historical scoring rates into scoreline, total-goals, and match-odds probabilities that you can compare against the market.
Poisson Distribution estimates the probability of a team scoring exactly x goals in a fixed match window when you know its expected goal rate, usually written as lambda.
Probability of scoring exactly x goals.
Expected number of goals for that team.
Euler's number, approximately 2.71828.
Factorial of the goal count, such as 3! = 3 * 2 * 1.
Before you can run Poisson, you need a realistic scoring rate for each team. That starts with league averages, then compares each side to that baseline.
First, calculate the average home goals and average away goals in the league. Then measure how each team scores and concedes relative to those league numbers.
Suppose your numbers say Arsenal should score 1.6 goals at home and Chelsea should score 1.2 away. Those become the two lambda inputs that power the rest of the model.
Arsenal expected scoring rate.
Chelsea expected scoring rate.
Run the Poisson formula for 0, 1, 2, 3, and 4 goals for each team. Then multiply the home-team probability by the away-team probability to get the chance of each exact scoreline.
If your modeled probability for a 1-1 draw is 11.52%, the fair decimal odds are 1 / 0.1152 = 8.68. If a sportsbook is offering 10.00, that is a positive EV price because the market is paying you as though the outcome is less likely than your model suggests.