Free Poisson Distribution Calculator

This Poisson Distribution Calculator helps you estimate sports match outcome probabilities using expected scores, most commonly expected goals (xG) in football.

By entering the expected number of goals for the home and away team, the calculator generates score probabilities, match outcome probabilities, and implied odds. These results can be used for match analysis, AI predictions, and betting odds comparison.

Our model is based on an enhanced Poisson distribution calibrated for football statistics and historical match trends. Compared to the classic Poisson model, it better reflects real-world match behavior, including draw frequency and favorite team performance.

Enter expected goals

1. Enter the expected goals (xG) for the home team
2. Enter the expected goals (xG) for the away team
3. Click "Calculate"
4. Review score probabilities and match outcome distributions

This tool is ideal for analysts, bettors, and anyone interested in data-driven football predictions.

Using xG instead of historical goals allows predictions to reflect chance quality, not just past results.

Benefits include:

• Reducing randomness caused by finishing variance
• Aligning predictions with underlying performance
• Creating fair odds from statistical probabilities
• Identifying value bets by comparing model odds with bookmakers

This is why Poisson-based models are commonly used in AI football prediction systems.

While powerful, the Poisson model has limitations:

• Assumes goal events are independent
• Does not account for red cards or game state changes
• Less accurate in very low or very high xG matches

For best results, Poisson models should be combined with team strength adjustments, home advantage, and recent form analysis.