Poisson Projections
Predict match scores and outcomes based on historical goal averages and team strength.
Score Matrix
| H\A | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 6.7% | 8.1% | 4.8% | 1.9% | 0.6% | 0.1% |
| 1 | 10.1% | 12.1% | 7.3% | 2.9% | 0.9% | 0.2% |
| 2 | 7.6% | 9.1% | 5.4% | 2.2% | 0.7% | 0.2% |
| 3 | 3.8% | 4.5% | 2.7% | 1.1% | 0.3% | 0.1% |
| 4 | 1.4% | 1.7% | 1.0% | 0.4% | 0.1% | 0.0% |
| 5 | 0.4% | 0.5% | 0.3% | 0.1% | 0.0% | 0.0% |
Bet Lab workflow
Turn this result into a saved betting scenario
Save the inputs, compare against previous edges, copy a compact brief, then continue into the next calculator without rebuilding the bet from scratch.
Inputs locked
homeExpectedGoals
1.5
awayExpectedGoals
1.2
Result snapshot
homeWin
44.1%
draw
25.5%
awayWin
30.3%
18+ where legal. Educational calculator only. Bet sizing outputs are not financial advice.
Poisson Distribution in Soccer Betting
The Poisson distribution is a probability formula that models the number of events occurring in a fixed interval, given a known average rate. In soccer betting, goals scored by each team follow a near-Poisson distribution — making this one of the most mathematically rigorous tools available for pricing match outcomes independently of bookmaker lines.
The formula: P(k goals) = (λᵏ × e⁻λ) / k! where λ (lambda) is the expected number of goals. If a team averages 1.5 goals per game, the probability of scoring exactly 2 goals is (1.5² × e⁻¹·⁵) / 2! = (2.25 × 0.2231) / 2 ≈ 25.1%. Building a full probability matrix for all score combinations (0-0 through 6-6+) lets you calculate win/draw/loss probabilities and price any scoreline bet.
To set your lambda values, use expected goals (xG) data from the current season. xG adjusts for shot quality, giving a more accurate picture of a team's true attacking output than raw goals. A team with 1.8 xG per game but only 1.2 actual goals is likely to regress upward — the Poisson model using xG captures this where raw goal counts don't.
The critical limitation: Poisson assumes statistical independence between home and away goals. In reality, game state affects scoring — a team leading 2-0 often defends, reducing late goals. This correlation means Poisson slightly overestimates draw probabilities. Professional models adjust with a Dixon-Coles correction, but raw Poisson still outperforms most intuitive approaches to soccer probability estimation.
Poisson Formula
P(k goals) = (λᵏ × e⁻λ) / k! λ = expected goals (lambda) k = number of goals (0, 1, 2, 3...) e = Euler's number ≈ 2.71828 Score probability: P(Home=h, Away=a) = P_h(h goals) × P_a(a goals) Home win = Σ P(h,a) where h > a
Poisson Examples
Home λ=1.8, Away λ=1.1. Poisson gives: Home win ≈ 51%, Draw ≈ 25%, Away win ≈ 24%. Most likely score: 1-1 (≈10.9%), then 2-1 (≈10.7%).
Your Poisson model says Away wins 30%. Bookmaker prices Away at 3.50 (IP=28.6%). Your model edge: +1.4%. Bet if you trust your lambda estimates. Combine with CLV tracking to validate model quality over time.
Frequently Asked Questions
What is the Poisson distribution in soccer betting?
The Poisson distribution models the probability of a specific number of goals occurring, given an expected average. By computing Poisson probabilities for each team independently, you can build a full score matrix and derive win/draw/loss probabilities — creating your own market prices.
Where do I get lambda (expected goals) values?
Use Expected Goals (xG) data from FBref, Understat, or WhoScored. xG weights shots by quality and gives a truer picture than raw goals. For each team, calculate average xG per game over the last 10–15 matches, adjusted for home/away split and opponent quality.
How accurate is the Poisson model?
Against the market, Poisson alone is not enough to beat sharp bookmakers — they use the same model. Its value is in finding discrepancies: your lambda estimates vs. the market's implied lambdas. Combined with team news, recent form, and motivation factors, Poisson provides a rigorous quantitative baseline.
What are the limitations of Poisson for soccer?
Poisson assumes independent scoring, which breaks down when game state affects play (a team sitting on a lead reduces attacking output). It also doesn't capture match-specific factors like red cards, injuries, or tactical changes. Dixon-Coles correction addresses the low-score correlation issue.