How to use the poisson scoreline probability calculator
- Enter the expected goals for each team: the average number you expect each to score.
- Set the total goals line, such as 2.5, if you want over and under chances.
- Read the chance of a win, a draw and a loss, the most likely score and the clean-sheet chances.
- Study the scoreline grid to see the chance of every result from 0-0 up to 6-6.
Formula
P(k goals) = e^(-m) m^k / k!, with m the expected goals
P(scoreline h-a) = P(h goals for team 1) x P(a goals for team 2)
Win = sum of cells with h > a; draw = cells with h = a; loss = cells with h < a
Clean sheet for team 1 = P(team 2 scores 0) = e^(-m2)
The two goal counts are treated as independent Poisson counts. The page sums the grid up to the cutoff you choose and reports the small probability left beyond it.
1.6 expected goals against 1.1
With expected goals of 1.6 and 1.1, the most likely score is 1-1 at 11.83 percent. The first team wins 48.96 percent of the time, the match is drawn 24.89 percent and the second team wins 26.15 percent. More than 2.5 goals happen 50.64 percent of the time and both teams score 53.24 percent. The first team keeps a clean sheet when the other scores nothing, e^-1.1 = 33.29 percent, and the second team 20.19 percent.
With 1.0 against 1.0 the most likely score is 0-0 at 13.53 percent, wins are each 34.57 percent and the draw is 30.85 percent. With 2.8 against 2.2 and a line of 4.5 total goals, the first team wins 51.44 percent and more than 4.5 goals have 55.95 percent.
What the model assumes
A Poisson count suits events that occur at an average rate and independently of each other, such as goals in a low-scoring sport. Real matches have slightly more draws and more high-scoring games than two independent Poisson counts predict, so the model is a starting point, not a forecast. The expected goals are your own input, and the output is only as sound as that input.
For a single Poisson distribution use the Poisson distribution calculator, for averages of uncertain outcomes see the expected value calculator, and for general probability see the probability calculator.
Totals, both teams to score and the grid
The over and under chances add the grid cells whose two scores sum above or below your line. Both teams to score adds every cell where each team has at least one goal. The grid shows scores up to 6-6 to stay readable, while the calculation itself runs up to the cutoff you set, with a note of the tiny probability beyond it.
Assumptions and limits
- Each team's goals follow a Poisson distribution and the two counts are independent.
- Expected goals are above 0 and up to 20 per team. They are your own estimates, not published data.
- The cutoff counts goals per team from 5 to 30, with 12 as the default, and the probability beyond it is reported.
- Results are shown as percentages to two decimals and are model outputs, not betting advice.
Frequently asked questions
How do I turn expected goals into win probabilities?
Compute each team's chance of scoring 0, 1, 2 and so on with the Poisson formula, multiply the two chances for each scoreline, and add the scorelines where the first team leads, ties or trails. The page does all of this.
Why does the model give a draw so often at low scoring?
When both teams score few goals, 0-0 and 1-1 are individually likely and they add up. With 1.0 against 1.0, the draw is 30.85 percent. Higher scoring spreads the probability over more results.
What does over 2.5 goals mean?
It means three or more goals in total, counting both teams. A half-goal line removes the possibility of a tie on the line, so the over and under chances add to 100 percent.
Is the Poisson model accurate for real matches?
It is a reasonable approximation for rare events but not exact. Goals are slightly related, and teams change their play when ahead. Treat the results as a reference model rather than a prediction.