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Sports Models

Poisson Calculator

A Poisson model estimates the probability of a number of events occurring from an assumed average rate. Real games may violate its independence and constant-rate assumptions.

Inputs

Live

Common Uses

  • • Soccer goals per game
  • • Hockey goals per game
  • • Baseball runs per game
  • • Touchdowns per game

Results

Live
Under 3
54.38%
Exactly 3
21.38%
Over 3
24.24%

Probability Distribution

0:
8.21%
1:
20.52%
2:
25.65%
3:
21.38%
4:
13.36%
5:
6.68%
6:
2.78%
7:
0.99%
Mean2.50
Variance2.50

Method and assumptions

How to use this calculator

The Poisson distribution models the probability of a given number of events occurring in a fixed interval. It's perfect for sports betting markets involving counts like goals, runs, or touchdowns.

When to Use Poisson

Use Poisson when events are independent, occur at a constant average rate, and two events can't happen at exactly the same time. Soccer goals are a classic example.

Inputs

  • Expected Value: The average number of events (e.g., average goals per game = 2.5)
  • Target Value: The number you're calculating probability for (e.g., exactly 3 goals)

Betting Applications

  • Calculate over/under probabilities for totals
  • Price exact score markets in soccer
  • Find value in prop markets
  • Model team and player scoring rates

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Calculator results are informational estimates based on the values entered. They do not guarantee an outcome. Confirm current prices, rules, fees, liquidity, limits, and eligibility on the relevant platform.