Poisson Calculator for Sports Betting

Updated: 07.09.2026

The Poisson distribution calculator lets you predict the correct score of a football match from each team's average goals (xG). Enter the expected goals of the home and away teams — the calculator will build a probability matrix of every scoreline, show the chances of a home win, draw and away win, and the probabilities of the totals and both teams to score.

Correct score probability matrix

1X2 outcome probabilities

Market probabilities

What is the Poisson distribution

The Poisson distribution is a mathematical model that describes the probability of a certain number of events occurring within a fixed interval, provided those events happen independently of each other at a constant average rate. In football betting the "event" is a goal, and the "average rate" is the team's expected goals (xG).

The model is named after the French mathematician Siméon Denis Poisson. It works well for predicting goals because goals in football are relatively rare, discrete events that, to a first approximation, can be treated as independent.

The Poisson formula

The probability of exactly k goals with a mean value of λ:

P(k) = (λk × e−λ) / k!

Where:

λ — the team's expected goals (xG)

k — the specific number of goals (0, 1, 2, 3...)

e — Euler's number (≈ 2.71828)

k! — the factorial of k

To predict the correct score, the goal probabilities of the home and away teams are calculated independently and then multiplied. For example, the probability of a 2:1 scoreline is Phome(2) × Paway(1).

Example: with a home xG of 1.5, the probability of exactly 2 goals:

P(2) = (1.52 × e−1.5) / 2! = (2.25 × 0.2231) / 2 = 0.2510 = 25.1%

How to use Poisson in betting

The Poisson distribution lets you build your own outcome probabilities and compare them with the odds of Fonbet, Winline or any other bookmaker. If your calculated probability is higher than the probability implied by the odds, the bet may be a value bet.

Workflow:

  1. Determine each team's xG. Use data from statistical services (Understat, FBRef) or calculate the average goals scored over the last 5–10 matches.
  2. Enter the values into the calculator above.
  3. Get the probability matrix and the market figures (1X2, totals, BTTS).
  4. Compare the calculated probabilities with the odds in the line. Use the margin calculator to find the bookmaker's real probabilities.
  5. If the calculated probability is significantly higher than the implied one — this is a potential value bet. Double-check it with the value bet calculator.

Limitations of the Poisson model

For all its usefulness, the Poisson distribution has significant limitations that need to be kept in mind when using it for betting:

  • Independence of goals. The model assumes that home and away goals are independent. In reality, after one team scores, the tactics change, which affects the probability of further goals.
  • Constant scoring rate. The model treats the rate of goals as constant throughout the match. In practice, the probability of a goal is higher late in each half and after red cards.
  • Quality of the input data. The result depends entirely on the accuracy of the xG. A simple average over recent matches may not reflect current form, injuries or motivation.
  • No context. Derbies, relegation battles, a gap in class — none of these factors enter the model directly.
  • Draws are underestimated. The classic Poisson model slightly underestimates the probability of draws. Advanced models apply the Dixon–Coles adjustment.

The Poisson model is a starting point for analysis, not a ready-made solution. Combine the mathematical calculations with an understanding of the bookmaker margin and your own expertise.

The Poisson model does not account for the variance of a specific team's results: it works with average figures over the season. Over a run of 10+ matches a favorite may post a strike rate below expectation due to random factors (injuries, red cards). Losing a bet on a "calculated" total or outcome is normal; the model is profitable only over a large sample. For underdogs Poisson often underestimates the probability — keep this in mind when analysing the line.

Other calculators

Also read: Betting Strategies — detailed material on analysis and bankroll management.

Frequently asked questions about the Poisson calculator
🙋 What is the Poisson distribution in simple terms?
💁 The Poisson distribution is a mathematical formula that shows the probability of a specific number of events occurring within a fixed period. For football: if a team scores 1.5 goals per match on average, the formula calculates the probability of 0 goals, 1 goal, 2 goals and so on. This makes it possible to predict the correct score and compare your own calculations with the bookmaker's line.
🙋 Where do I get xG for a Poisson calculation?
💁 xG (expected goals) data is available from open statistical services: Understat, FBRef, WhoScored. You can also use a simple average of goals scored over the last 5–10 matches as an approximation. It is important to consider home and away figures separately, as well as the strength of the opponents in those matches.
🙋 How accurate is the Poisson calculator?
💁 The Poisson model gives acceptable accuracy for most football matches, especially in mid- and top-tier leagues with a large data sample. However, the model slightly underestimates the probability of draws and does not account for the correlation between the teams' goals. To improve accuracy, professionals apply the Dixon–Coles adjustment and dynamic xG models.
🙋 Can Poisson be used for hockey or basketball?
💁 Formally, the model can be applied to any sport with a points tally, but the accuracy will vary. For hockey Poisson works reasonably well (goals are also rare events). For basketball the model is unsuitable — there are too many points per game, and a normal distribution will be more accurate. Tennis and volleyball require specialised set and game models.
🙋 How do I find a value bet with Poisson?
💁 Calculate the probability of the outcome you are interested in with the calculator. Then convert the bookmaker's odds into the implied probability (1 / odds). If your calculated probability is higher than the implied one, the bet is potentially a value bet. For example, if Poisson gives 35% on a home win while odds of 3.20 imply 31.3%, you have an edge of 3.7 percentage points in your favour.
🙋 Why does the Poisson model underestimate draws?
💁 The classic Poisson model assumes that home and away goals are independent. In reality there is a weak positive correlation: in open matches both teams score more, in tight matches both score less. This increases the probability of level scorelines (0:0, 1:1, 2:2). The Dixon–Coles adjustment adds a correlation parameter for low-scoring outcomes (0:0, 1:0, 0:1, 1:1) and improves the model's accuracy.