Calculator

Poisson calculator: correct score, result and totals probability

Enter the expected goals of the home and away sides and the calculator uses the Poisson distribution to work out the probability of every score, the match result, totals and both teams to score.

Home expected goals Away expected goals

For example, the teams' average xG for this matchup or your own estimate of expected goals. Values from 0 to 10.

Most likely score: 1:1 (12.3%)

Outcome	Probability	Fair odds
Home win (1)	46.4%	2.15
Draw (X)	25.8%	3.88
Away win (2)	27.8%	3.60
Both teams to score — yes	51.8%	1.93
Both teams to score — no	48.2%	2.08

Goal totals

Line	Over	Under
0.5	92.6%	7.4%
1.5	73.3%	26.7%
2.5	48.2%	51.8%
3.5	26.4%	73.6%
4.5	12.3%	87.7%

Correct score probability

Home \ away	0	1	2	3	4	5
0	7.4%	8.2%	4.5%	1.6%	0.5%	0.1%
1	11.1%	12.3%	6.7%	2.5%	0.7%	0.1%
2	8.4%	9.2%	5.1%	1.9%	0.5%	0.1%
3	4.2%	4.6%	2.5%	0.9%	0.3%	0.1%
4	1.6%	1.7%	0.9%	0.3%	0.1%	0.0%
5	0.5%	0.5%	0.3%	0.1%	0.0%	0.0%

How the Poisson calculator works

Goals in football are rare events, and the number of goals one team scores in a match is described well by the Poisson distribution. If a team's expected goals are λ, the probability of exactly k goals is:

P(k) = λ^k × e^(−λ) / k!

The calculator builds that distribution for each team, multiplies the probabilities to get every scoreline and adds the scorelines up into the result, totals and both teams to score. Fair odds are one divided by the probability.

Where to get expected goals

The teams' xG over recent matches — steadier than goals scored, and quicker to show the real level of attack and defence.
The home side's home games and the away side's away games separately: many teams play differently at home and away.
The league's scoring average: it differs noticeably between competitions.

Limits of the model

A plain Poisson model treats the two teams' goals as independent, although the score changes tactics during a match, and it usually misjudges the frequency of draws and low scores slightly. The result is a guide, not a guarantee: its accuracy depends above all on how well the expected goals are estimated.

Frequently asked questions

How do you calculate the probability of a correct score in football?

Estimate each team's expected goals, use the Poisson distribution to get the probability of the required number of goals for each side, and multiply the two.

How do you calculate the probability of over 2.5 goals?

Add up the probabilities of every scoreline with two goals or fewer and subtract the sum from one. The calculator does this for lines from 0.5 to 4.5.

How do you calculate the probability of both teams to score?

Multiply the probability that the home side scores at least once by the probability that the away side does: (1 − home P0) × (1 − away P0).

How accurate is a Poisson prediction?

It is a simplified model: it ignores how goals depend on the score and usually misjudges the frequency of draws slightly. The main source of error is an inaccurate estimate of expected goals.

More on the blog

The xG.Football model calculates result, totals and both-teams-to-score probabilities for the day's matches — handy to compare with the odds.

Football predictions →

The content of this site is informational and is not an invitation to gamble. Betting carries a risk of losing money and is for adults only (18+). Please play responsibly.