Poisson Distribution Calculator
Updated:Calculate exact score probabilities, over/under odds, and win/draw/loss chances for soccer, hockey, and low-scoring sports using expected goals (xG)
Match Probability Analysis
Home vs Away
Home Goals
Away Goals
What is Poisson Distribution?
Poisson distribution is a statistical model that predicts the probability of a certain number of events occurring within a fixed interval, given a known average rate. In sports betting, it's used to model goal-scoring or point-scoring patterns.
The formula calculates the likelihood of each team scoring exactly 0, 1, 2, 3, or more goals based on their expected goals (xG). By combining both teams' distributions, we can predict:
- Exact score probabilities — The chance of any specific scoreline (e.g., 2-1, 0-0)
- Match outcomes — Win, draw, or loss probabilities
- Over/Under totals — Probability of total goals exceeding or falling below a line
- Both Teams to Score (BTTS) — Likelihood of both teams finding the net
Where: λ = expected goals, k = number of goals, e ≈ 2.71828
How to Use This Calculator
- Enter team names — Optional, for easier reference in results
- Set expected goals (xG) — Input each team's expected scoring rate based on your analysis
- Review probabilities — Results update automatically as you type
- Compare to bookmaker odds — Use the fair odds to identify value bets where your probability exceeds the implied odds
- Copy results — Share your analysis with the copy button
How to Estimate Expected Goals
The accuracy of Poisson predictions depends on your expected goals estimates. Here are reliable methods:
- Historical averages — Use team's average goals scored/conceded over the last 10-20 matches
- Home/away adjustments — Home teams typically score ~0.3 goals more than away
- Head-to-head records — Factor in specific matchup history
- Advanced xG metrics — Use expected goals data from providers like Opta, FBref, or Understat
- Market-implied totals — Derive from over/under betting lines (e.g., O/U 2.5 at even odds ≈ 2.5 total expected goals)
Frequently Asked Questions
What is Poisson distribution in sports betting?
Poisson distribution is a mathematical formula used to calculate the probability of a specific number of events (like goals or points) occurring in a fixed period. In sports betting, it helps predict exact scores, over/under totals, and win probabilities based on teams' expected scoring rates.
How accurate is the Poisson distribution for predicting sports scores?
Poisson distribution is reasonably accurate for low-scoring sports like soccer and hockey where goals are relatively rare and independent events. Studies show it predicts around 30% of exact scores correctly. However, it assumes goals are independent events and doesn't account for game state changes, injuries, or tactical adjustments.
How do I find the expected goals (xG) for each team?
Expected goals can be derived from: historical head-to-head records, team's average goals scored/conceded, home/away performance adjustments, advanced xG metrics from stats providers, or betting market implied totals. Many bettors use a combination of these factors to estimate each team's expected goals.
What sports work best with Poisson distribution?
Poisson works best for soccer (football), ice hockey, and field hockey where scoring is relatively rare (typically 1-4 goals per team). It's less accurate for high-scoring sports like basketball or American football where scores follow different distributions and dependencies between possessions matter more.
How do I use Poisson for over/under betting?
To bet overs/unders with Poisson: 1) Calculate each team's expected goals, 2) Use the calculator to find probabilities for all score combinations, 3) Sum up probabilities where total goals exceed or fall below the bookmaker's line, 4) Compare your calculated probability to the implied probability from the odds to find value.
What is the formula for Poisson distribution?
The Poisson probability formula is: P(k) = (λ^k × e^(-λ)) / k! where λ (lambda) is the expected number of events (goals), k is the actual number of events you're calculating probability for, and e is Euler's number (≈2.71828). For example, if Team A has λ=1.5 expected goals, P(2 goals) = (1.5² × e^(-1.5)) / 2! = 25.1%.