Home Expected Goals
Away Expected Goals
Max Goals (per team)
Match Outcome
Over / Under Goals
Both Teams to Score
Score Probability Matrix
What Is It?
The Poisson Distribution is a probability distribution that models the likelihood of a given number of events occurring in a fixed interval, given a known average rate. In football (soccer) betting, it’s used to predict the probability of specific scorelines based on expected goals (xG) for each team.
The calculator takes the expected goals for the home and away teams and generates a full probability matrix: the chance of every possible scoreline (e.g., 0-0, 1-0, 1-1, 2-1, etc.). From this matrix, it derives probabilities for key markets: Match Result (Home/Draw/Away), Over/Under goals, and Both Teams to Score (BTTS).
This tool is essential for bettors who use statistical models. By comparing the Poisson-derived probabilities to the bookmaker’s implied probabilities, you can identify value bets across multiple markets from a single analysis.
How to Use
Formulas & Data Sources
Poisson Probability:
Where: lambda = expected goals for the team, k = number of goals (0, 1, 2, 3, …), e = Euler’s number (approximately 2.71828), k! = factorial of k.
Score Matrix:
Derived Markets:
Expected goals (lambda) must be supplied by you. The Poisson assumption is that goals are independent events ā a simplification, but one that works well in practice.
Real-World Scenarios
Home xG: 1.50, Away xG: 1.10. Total xG: 2.60. The Poisson model might show Over 2.5 probability at 52.3%. If a bookmaker offers Over 2.5 at 2.05 (implied 48.8%):
The matrix shows 1-1 as the most likely scoreline at 11.2% probability. A bookmaker offers 1-1 at 6.50 (implied 15.4%). This actually overprices the outcome ā no edge here. But 2-1 at 9.8% probability is offered at 12.00 (implied 8.3%).
With Home xG: 1.80 and Away xG: 0.70, the BTTS Yes probability might be 55.8% but BTTS No at 44.2%. If a bookmaker offers BTTS No at 2.40 (implied 41.7%):
Frequently Asked Questions
QWhere do I get expected goals (xG) data?
Free sources include FBref, Understat, and FotMob. Paid services like StatsBomb and Opta offer more granular data. You can also calculate a simple average from recent match data (e.g., average goals scored/conceded over the last 10 home/away games).
QDoes Poisson work for all sports?
Poisson works best for low-scoring sports where goals/points are independent events: football (soccer), hockey, and baseball. It’s less accurate for high-scoring sports like basketball or American football.
QWhy doesn't the matrix always add up to exactly 100%?
The matrix is truncated at a maximum number of goals (e.g., 5). The tiny remaining probability of 6+ goals per team accounts for the difference. With max goals set to 5, the total typically exceeds 99.5%.
QCan I use season averages instead of xG?
Yes. A simple approach: Home lambda = (Team’s avg home goals scored + Opponent’s avg away goals conceded) / 2. This is less precise than xG models but works as a starting point.
QDoes this account for red cards, injuries, or form?
No. Poisson uses the expected goals you provide. Adjusting lambda up or down based on team news, form, or conditions is your responsibility as the analyst.
