Poisson Match Prediction: Modeling Scorelines, Spreads, and Totals

Why Poisson?

Goals in soccer, runs in baseball, goals in hockey — these are low-frequency events occurring over a fixed period. The Poisson distribution models exactly this: the count of independent events when you know the average rate.

$$P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!}$$

A team expected to score 1.4 goals has a 24.7% chance of scoring exactly 1, a 17.3% chance of exactly 2, and a 24.7% chance of being shut out. One parameter, the full range of outcomes.

Building the Score Matrix

The key assumption is independence: each team's scoring follows its own Poisson process. This lets us build a joint probability matrix where each cell is the product of two marginal probabilities:

$$P(\text{Home}=h, \text{Away}=a) = \frac{\lambda_H^h e^{-\lambda_H}}{h!} \cdot \frac{\lambda_A^a e^{-\lambda_A}}{a!}$$

For $\lambda_H = 1.6$ and $\lambda_A = 1.1$, the matrix (as percentages):

	0	1	2	3
0	6.7	7.3	4.0	1.5
1	10.7	11.7	6.4	2.4
2	8.5	9.4	5.1	1.9
3	4.6	5.0	2.8	1.0

Every cell is a tradeable scoreline. Sum the right cells and you get any market.

Deriving Market Probabilities

Moneyline — Sum all cells where home > away (home win), away > home (away win), and the diagonal (draw). For sports without draws, the draw probability redistributes proportionally.

Spreads — For a -1.5 spread, sum all cells where $h - a > 1.5$. The complement gives the other side.

Totals — For over 2.5, sum all cells where $h + a > 2.5$.

One model, every market. This is the power of the matrix approach.

Strengths

Poisson is the standard model for soccer and performs well for hockey and baseball — any sport where scoring events are relatively rare and roughly independent. The model requires just two inputs (expected goals for each team) and produces a complete probability distribution over all outcomes.

Limitations

• Independence — in practice, goals are not fully independent. A trailing team pushes forward, affecting both teams' rates
• Thin tails — Poisson constrains variance to equal the mean. Real scoring often has variance exceeding the mean, making blowouts more likely than the model predicts
• Draw inflation — soccer draws occur more often than independent Poisson processes predict, likely due to tactical effects

Practical Tips

• Use expected goals (xG) as inputs rather than raw goal totals — xG is less noisy
• Check your model against the totals market for calibration — if your model and the book agree, there is likely no edge
• Compare Poisson predictions to the Negative Binomial model for the same inputs — when they disagree, the truth is likely between them
• The Poisson Match Predictor builds the full score matrix and derives moneyline, spread, and total probabilities from your inputs