The Math Behind Match Predictions: Poisson Distribution Explained

# The Math Behind Match Predictions: Poisson Distribution Explained

Every AI match prediction starts with one fundamental idea: goals are rare, random events.

The Poisson distribution — named after 19th-century French mathematician Siméon Denis Poisson — models exactly this. And it's the backbone of modern football prediction.

What is the Poisson Distribution?

In plain English: the Poisson distribution tells you how many times a rare event is likely to happen in a fixed time period, given an average rate.

Examples:

• Number of emails you receive per hour
• Number of cars passing a point per minute
• Number of goals a team scores per match

Why Football?

Football goals have three key properties that make Poisson modeling work:

1. Goals are discrete (0, 1, 2, 3... never 2.5 goals)
2. Goals are independent (one goal doesn't directly cause the next — mostly)
3. Goals occur at an average rate (a team averaging 1.8 goals/game tends to score around that)

From Goals to Probabilities

Here's how Sezi uses Poisson:

1. Estimate goal expectancy — based on team strength (ELO), recent form, home/away, and league averages
2. Run the Poisson formula — for each possible score (0-0, 1-0, 2-1... up to ~10 goals)
3. Sum the probabilities — home win = sum of all home > away scorelines, draw = tied scores, away win = away > home scorelines

Example: If Team A is expected to score 1.8 goals and Team B 0.9 goals, the model might output:

• Home win: 52%
• Draw: 26%
• Away win: 22%

Beyond Basic Poisson

Pure Poisson has limitations. Sezi's Dixon-Coles variant adds:

• Low-score correction — 0-0 and 1-0 happen more often than basic Poisson predicts
• Team-specific attack/defense parameters — every team has unique scoring and conceding characteristics
• League effects — Serie A has different scoring patterns than the Bundesliga

Why This Matters

Understanding the math helps you understand why the model makes certain predictions. Sezi isn't a black box — it's probability theory, applied honestly.