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Poisson Distribution Calculator
Predict soccer and hockey scores with the Poisson distribution. Enter team scoring stats to get expected goals, match outcome probabilities, BTTS, over/under lines, most likely scorelines, and the fair odds behind every market.
Home Team
Away Team
Auto-filled from the sport preset. Soccer ≈ 1.4, Hockey ≈ 3.0. Adjust for your specific league.
How the Poisson Distribution Works for Score Predictions
The Poisson distribution is a statistical model that predicts the probability of a given number of events occurring in a fixed interval. In betting, it's used to predict how many goals each team will score based on their historical scoring and conceding rates.
Attack Strength measures how many goals a team scores compared to the league average. Defense Strength measures how many goals they concede. By combining these metrics, we calculate the expected goals (lambda) for each team, then spread that across every possible scoreline.
This calculator accounts for home advantage (a 10%boost to the home team's expected goals in Soccer) and converts every probability into fair, no-vig odds. Compare those fair odds to your sportsbook to spot value in 1X2, correct score, BTTS, and over/under markets.
Poisson Calculator FAQ
What is a Poisson distribution in sports betting?
The Poisson distribution models how likely a team is to score 0, 1, 2, 3 or more goals in a match given their expected goals (lambda). Because goals are discrete, independent, low-frequency events, Poisson is an excellent fit for soccer and hockey scoring and lets you build probabilities for win/draw/loss, correct score, BTTS, and totals.
How do I calculate expected goals for each team?
Divide each team's goals scored and conceded by the league average to get attack and defense strengths. Multiply the home team's attack strength by the away team's defense strength and the league average (plus a home-advantage boost) to get home expected goals, and vice versa for the away team. This calculator does that automatically.
What league average should I use?
Use the average goals scored per team per game in the specific competition. Top European soccer leagues sit around 1.4, while the NHL is closer to 3.0. The sport preset fills in a sensible default, but adjusting it to your exact league improves accuracy.
How do I turn Poisson probabilities into betting value?
Each output includes fair, no-vig American odds. Compare them to the price your sportsbook offers. If the book's payout is longer than the fair odds (for example, the book offers +180 when fair value is +150), the bet carries positive expected value.
Does the Poisson model account for correlated scoring?
The basic model treats each team's goals as independent. Real matches have some correlation (game state, red cards, tactics), so Poisson tends to slightly underrate very high-scoring and 0-0 outcomes. Use it as a strong baseline, then adjust for context like injuries, weather, and motivation.
Master Poisson Betting
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This calculator is for informational and educational purposes only. Results should be verified with your sportsbook before placing any wagers. All betting carries risk. Full Disclaimer
Frequently Asked Questions
What is the Poisson distribution in soccer betting?
The Poisson distribution models the probability of a team scoring 0, 1, 2, 3+ goals given its expected goals rate. Multiplying two teams' distributions produces a scoreline matrix used to price 1X2, totals, and correct-score markets.
How accurate is Poisson for predicting soccer scores?
Poisson is a solid baseline but slightly underestimates draws and low-scoring games because goals are not fully independent. Adjustments like Dixon-Coles correct the 0-0 and 1-1 probabilities that pure Poisson underrates.
What inputs do I need for a Poisson betting model?
You need each team's expected goals (attack strength times opponent defensive weakness, adjusted for home advantage and league average). Using xG-based inputs rather than raw goals scored improves predictive accuracy meaningfully.
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