What is the Poisson distribution in football betting?

The Poisson distribution models the probability of a given number of goals occurring in a match, based on an expected goals (xG) estimate. P(X=k) = (λ^k × e^−λ) ÷ k!, where λ is the expected goals and k is the number of goals you are calculating the probability for.

How do you use Poisson to find betting value?

Estimate xG for each team independently, use the Poisson formula to derive probabilities for each scoreline, combine home and away scorelines into match outcome probabilities (home win, draw, away win), then compare to bookmaker implied probabilities to find value.

What are the limitations of Poisson modelling?

Poisson assumes goals are independent events. In reality, teams adjust tactics after goals are scored, creating score-based correlations. The Dixon-Coles adjustment corrects for this low-scoring match bias. Additionally, xG inputs must come from reliable data sources.

Poisson Distribution for Football Betting

Why Poisson Fits Football Scoring

The Poisson distribution models the probability of a given number of independent events occurring in a fixed time period — and goals in football fit this pattern reasonably well: relatively rare, roughly independent events occurring over 90 minutes.

Step 1: Estimate Expected Goals (xG)

You need an expected goals figure for each team in the specific matchup, typically derived by combining their attacking strength with the opponent's defensive strength relative to league averages.

        Team A Expected Goals = Team A Attack Strength × Team B Defence Weakness × League Average Goals
      

Step 2: Apply the Poisson Formula

P(X = k) = (λ^k × e^−λ) ÷ k!

λ (lambda) = expected goals for that team
k = the specific number of goals you're calculating the probability for
e = Euler's number (≈2.71828)

Worked Example

Team A has an expected goals (λ) of 1.8. The probability of Team A scoring exactly 2 goals:

P(X=2) = (1.8² × e^−1.8) ÷ 2! = (3.24 × 0.1653) ÷ 2 ≈ 26.8%

Repeat this for every goal count (0, 1, 2, 3, 4+) for both teams, then combine the two independent distributions to calculate the probability of every possible scoreline (0-0, 1-0, 2-1, etc.).

Step 3: Derive Market Probabilities

Once you have a full scoreline matrix, you can sum across it to get probabilities for any market:

Match result: Sum all scorelines where Team A's goals > Team B's (Home win), etc.
Over/Under 2.5: Sum all scorelines where total goals ≥ 3 (Over) vs ≤ 2 (Under).
BTTS: Sum all scorelines where both teams have 1+ goals.
Correct score: Read directly off the matrix for any specific score.

Comparing Your Model to the Bookmaker

Once you have your own probabilities for a market, convert the bookmaker's odds to implied probability and compare. A meaningful gap in your favour — beyond what could be explained by margin or model error — is a candidate value bet.

Limitations

Basic Poisson assumes goal-scoring is independent between teams and over time, which isn't perfectly true — game state (a team leading 2-0 plays differently than at 0-0) and red cards break this assumption. Advanced models add corrections like the Dixon-Coles adjustment for low-scoring game correlation, but basic Poisson remains a strong, accessible starting point.