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Most likely result
44.15%
Home win Most likely score 1–1 (12.10%)
Home win44.15%Fair +127
Draw25.48%Fair +292
Away win30.37%Fair +229
Both teams score54.29%Fair −119
Home clean sheet30.12%Away held to 0
Away clean sheet22.31%Home held to 0
No goals6.72%A 0–0 final
Correct score
Rows are Home goals, columns Away goals. Draws on the outlined diagonal.
0
1
2
3
4
5
6
0
6.7
8.1
4.8
1.9
0.6
0.1
<0.1
1
10
12
7.3
2.9
0.9
0.2
<0.1
2
7.6
9.1
5.4
2.2
0.7
0.2
<0.1
3
3.8
4.5
2.7
1.1
0.3
0.1
<0.1
4
1.4
1.7
1.0
0.4
0.1
<0.1
<0.1
5
0.4
0.5
0.3
0.1
<0.1
<0.1
<0.1
6
0.1
0.1
0.1
<0.1
<0.1
<0.1
<0.1

Scores beyond 6 goals for either side: 0.12%.

Total goals
2.7 expected in all
LineOverUnder
0.593.28%6.72%
1.575.13%24.87%
2.550.64%49.36%
3.528.59%71.41%
4.513.71%86.29%
5.55.67%94.33%
6.52.06%97.94%
LineOverUnder
7.50.66%99.34%
8.50.19%99.81%
9.50.05%99.95%
10.50.01%99.99%
11.50.00%100.00%
12.50.00%100.00%
13.50.00%100.00%
How it's worked out

Goals in low-scoring sports like soccer and hockey arrive roughly at random, so the number a team scores follows a Poisson distribution: give it the average (λ, the expected goals) and it gives the chance of 0, 1, 2 and so on.

Each team's goals are treated as independent, so the chance of a score is the two teams' chances multiplied. Adding up the scores where the home side is ahead gives the home win, and so on. Total goals is itself Poisson with λ = home λ + away λ. Fair odds are the prices with no vig.

P(x goals) = e−λ × λx ÷ x!
P(home h, away a) = Phome(h) × Paway(a)
Both score = (1 − e−λ home) × (1 − e−λ away)
Real matches show a few more draws and low scores than independence predicts, so treat close calls with care.

Using the poisson calculator

Turn each team's expected goals into probabilities for every score, the match result, total goals and both teams to score, with fair odds for each.

  1. 1Pick the sport and name the teams if you like.
  2. 2Enter each team's expected goals (λ), or start from an example.
  3. 3Read the most likely result, win-draw-win and fair odds, the correct-score grid and the total-goals lines.

Questions bettors ask

What is the Poisson distribution in betting?

A way to model goals, which arrive roughly at random in low-scoring sports. Give it a team's expected goals and it gives the chance of 0, 1, 2 and more. With 1.5 expected, a team is held scoreless 22.3% of the time.

How do I find each team's expected goals?

Start from goals (or xG) scored and conceded per game, adjusted for the opponent's strength and home advantage. Market totals help too: a 2.5 total priced near even suggests about 2.6 goals between the two teams.

How do I turn a probability into odds?

Fair decimal odds are 1 ÷ the probability: a 25% chance is 4.00, or +300. A book's price longer than that has value, if your expected goals are right.

How accurate is a Poisson model?

It's a good start but treats the two teams' goals as independent. Real matches have slightly more draws and low scores than it predicts, and in hockey empty-net goals and overtime bend the numbers, so treat close calls with care.