Poisson Distribution Calculator
Calculate football match probabilities using Poisson distribution. Get expected goals, scoreline probabilities, and fair odds for all betting markets based on team statistics.
Team Statistics
Home Team
Average goals scored per game
Average goals conceded per game
Away Team
Average goals scored per game
Average goals conceded per game
Advanced Options (Optional)
Typically 1.0-1.3 (1.0 = neutral)
Optional: total goals per game in league
What is Poisson Distribution in Football?
Poisson distribution is a statistical model that predicts the probability of events occurring within a fixed time period. In football, it's used to calculate the likelihood of teams scoring different numbers of goals based on their historical performance.
Named after French mathematician Siméon Denis Poisson, this distribution is particularly suited to football because:
- Goals are relatively rare events (typically 0-5 per team per match)
- Goals occur independently throughout the 90 minutes
- The average goal rate can be estimated from team statistics
- It provides probabilities for all possible scorelines
Professional bettors and football analysts use Poisson distribution to generate fair odds for matches, identify value bets, and predict correct scores more accurately than simple intuition.
How to Use the Poisson Calculator
Step-by-Step Guide
1. Enter Home Team Statistics
- Attack Strength: Average goals scored per game (e.g., 1.8)
- Defense Strength: Average goals conceded per game (e.g., 1.2)
2. Enter Away Team Statistics
- Attack Strength: Average goals scored per game (e.g., 1.5)
- Defense Strength: Average goals conceded per game (e.g., 1.4)
3. Optional: Fine-Tune Your Prediction
- Home Advantage: Typically 1.0-1.3 (use 1.15 as a good default)
- League Average: Total goals per game in the league (helps normalize across competitions)
4. Review Results
The calculator instantly shows expected goals, most likely scores, probability grid, and fair odds for all major betting markets.
Example: Liverpool vs Brighton
Home Team (Liverpool)
- Attack: 2.1 goals/game
- Defense: 0.9 goals/game
Away Team (Brighton)
- Attack: 1.4 goals/game
- Defense: 1.3 goals/game
With home advantage of 1.15, this gives Liverpool 2.49 expected goals and Brighton 1.04 expected goals, making Liverpool heavy favorites.
Understanding Your Results
Expected Goals (xG)
The average number of goals each team is predicted to score. This is calculated using team attack/defense strengths and home advantage. Higher expected goals indicate stronger attacking threat.
Most Likely Scores
The top 10 scorelines ordered by probability. Even the most likely score typically has only 8-12% probability. Use this to identify correct score betting value.
Probability Grid
A 6×6 matrix showing probabilities for all scorelines from 0-0 to 5-5. Darker cells indicate higher probabilities. Use this to visualize score distribution.
Fair Odds
What the odds should be based on Poisson probabilities (with no bookmaker margin). If bookmaker odds are higher than fair odds shown here, that may represent value. Add 5-10% margin when comparing.
Market Odds Coverage
The calculator provides probabilities and fair odds for: Match Result (1X2), Over/Under Goals (0.5 to 4.5), Both Teams to Score, Double Chance, and Draw No Bet.
How to Calculate Team Statistics
Accurate input statistics are crucial for reliable Poisson predictions. Here's how to calculate each value:
Attack Strength (Goals Scored)
Formula: Total Goals Scored ÷ Games Played
Example: Manchester City scored 28 goals in 15 games = 28 ÷ 15 = 1.87 goals/game
Tip: Use recent form (last 10-15 games) rather than full season for more accurate predictions, especially if team form has changed significantly.
Defense Strength (Goals Conceded)
Formula: Total Goals Conceded ÷ Games Played
Example: Arsenal conceded 12 goals in 15 games = 12 ÷ 15 = 0.80 goals/game
Tip: Lower values indicate stronger defense. Elite defensive teams concede <1.0 goals/game.
Home Advantage Multiplier
Typical Range: 1.10 to 1.30
Common Values:
- 1.15-1.20: Premier League, La Liga, Bundesliga
- 1.20-1.25: Serie A, Ligue 1
- 1.25-1.30: Lower leagues with stronger home support
- 1.00: Neutral venue matches
League Average Goals
Formula: Total Goals Scored in League ÷ Games Played
Typical Values:
- Bundesliga: 3.0-3.2 goals/game (high scoring)
- Premier League: 2.6-2.8 goals/game
- La Liga: 2.5-2.7 goals/game
- Serie A: 2.4-2.6 goals/game (lower scoring)
Limitations and Pro Tips
Known Limitations
- Underestimates draws: Poisson typically shows draws 3-5% less likely than reality due to tactical factors
- Assumes independence: Doesn't account for teams changing tactics when ahead/behind
- Ignores context: Doesn't factor in injuries, motivation, weather, or tactical matchups
- Best for mid-range scoring: Less accurate for very defensive (<0.5 goals/game) or attacking (>3.5 goals/game) teams
- Static model: Doesn't adapt during match (less useful for live betting)
Pro Tips for Better Predictions
- Use recent form: Last 10-15 games gives better predictions than full season averages
- Adjust for injuries: Reduce attack strength if key striker injured, increase defense weakness if key defender out
- Separate home/away stats: Calculate attack/defense separately for home and away performance
- Add 3-5% to draw probability: Compensate for Poisson's draw underestimation
- Compare to bookmaker odds: Add 5-10% margin to fair odds before comparing to bookmaker prices
- Combine with other analysis: Use Poisson alongside form analysis, head-to-head records, and team news
- Track your accuracy: Record predictions vs actual results to calibrate your inputs
Frequently Asked Questions
What is Poisson distribution in football betting?
Poisson distribution is a statistical method used to predict the probability of different scorelines in football matches. It calculates expected goals for each team based on their attack and defense strength, then uses these to generate probabilities for all possible scores and betting markets.
How do you calculate expected goals using Poisson?
Expected goals are calculated by multiplying team strengths: Home Expected Goals = Home Attack × Away Defense × Home Advantage. Away Expected Goals = Away Attack × Home Defense. These values are then used in the Poisson probability formula to calculate scoreline probabilities.
How accurate is Poisson distribution for football predictions?
Poisson distribution is reasonably accurate for predicting goal probabilities in football, with typical accuracy of 50-55% for match outcomes. It works best for matches between evenly-matched teams scoring 1-3 goals per game. Accuracy decreases for very low-scoring (<0.5 goals/game) or high-scoring (>3 goals/game) teams.
Where do I find team attack and defense statistics?
Calculate attack strength as average goals scored per game (total goals scored ÷ games played). Defense strength is average goals conceded per game. Use recent form (last 10-15 games) for more accurate predictions. Websites like FBref, Understat, and official league sites provide detailed statistics.
What is home advantage in football betting?
Home advantage is a multiplier (typically 1.0-1.3) applied to home team expected goals. Research shows home teams score approximately 10-30% more goals than they would away. A value of 1.15-1.20 is common across major leagues, though this varies by league and team.
How do you use Poisson calculator results for betting?
Compare the calculator's fair odds to bookmaker odds. If bookmaker odds are higher than fair odds calculated by Poisson, that represents potential value. Focus on markets where you have significant edge (10%+ higher odds). Remember to account for bookmaker margin when comparing.
What markets can you predict with Poisson distribution?
Poisson distribution can predict: Match Result (1X2), Over/Under Goals (all lines), Both Teams to Score (BTTS), Correct Score, Double Chance, Draw No Bet, and Asian Handicap markets. It generates probabilities for all scorelines from 0-0 to 5-5 and beyond.
Should I use league average goals in the calculator?
Using league average goals (optional field) helps normalize predictions across different leagues. Some leagues average 2.5 goals/game while others average 3.5. Including league average (total goals per game) improves accuracy when comparing teams from different competitions or eras.
Why does Poisson underestimate draws in football?
Poisson assumes goals are independent events, but football has tactical factors (teams defending leads, settling for draws) that increase draw probability. Advanced bettors adjust Poisson predictions by increasing draw probability by 3-5% and reducing home/away win probabilities proportionally.
Can Poisson distribution be used for live betting?
Yes, but you must adjust expected goals based on current score, time remaining, and match context. A team leading 1-0 after 70 minutes may defend rather than attack, changing their effective attack strength. Poisson works best for pre-match predictions with full match duration.