Poisson Football Calculator
Turn expected goals into probabilities for the result, the score, the totals and both teams to score.
Poisson Football Calculator
Turn expected goals into probabilities for the result, the exact score, totals and both teams to score.
Home win
47.80 %
Draw
24.81 %
Away win
27.39 %
Both score
54.54 %
Most likely scores
| Score | Chance | Fair odds |
|---|---|---|
| 1 – 1 | 11.76 % | 8.50 |
| 1 – 0 | 10.23 % | 9.78 |
| 2 – 1 | 9.41 % | 10.63 |
| 2 – 0 | 8.18 % | 12.22 |
| 0 – 1 | 7.35 % | 13.60 |
| 1 – 2 | 6.76 % | 14.79 |
| 0 – 0 | 6.39 % | 15.64 |
| 2 – 2 | 5.41 % | 18.48 |
Markets
| Market | Chance | Fair odds |
|---|---|---|
| Over 0.5 | 93.61 % | 1.07 |
| Over 1.5 | 76.03 % | 1.32 |
| Over 2.5 | 51.85 % | 1.93 |
| Over 3.5 | 29.70 % | 3.37 |
| Under 0.5 | 6.39 % | 15.64 |
| Under 1.5 | 23.97 % | 4.17 |
| Under 2.5 | 48.15 % | 2.08 |
| Under 3.5 | 70.30 % | 1.42 |
| Both teams to score | 54.54 % | 1.83 |
Scores above 10–10 are ignored; they account for 0.0001 % of the distribution here. Poisson also assumes the two teams score independently, which understates draws and 0–0 slightly in real football.
Why Poisson Fits Football
Goals are rare, roughly independent events spread over a fixed period — the situation the Poisson distribution was built for. Give it one number per team, the expected goals (λ), and it returns the chance of that team scoring exactly 0, 1, 2 and so on.
Multiply the two teams' distributions together and you get a grid of every scoreline. Adding up the right cells then answers every common market: home win, draw, over 2.5, both teams to score.
The Formula
- Chance of exactly k goals: P(k) = (λ^k × e^−λ) ÷ k!
- Chance of a given score: P(i, j) = P_home(i) × P_away(j)
- Any market: add the cells that satisfy it — home win is every cell with i > j
The calculator builds the series iteratively — P(k) = P(k−1) × λ ÷ k — rather than computing λ^k and k! separately, which overflow long before the probabilities become negligible.
Example
A home side expected to score 1.60 against an away side expected to score 1.15:
- Home win 47.80 %, draw 24.81 %, away win 27.39 % — fair odds of 2.09, 4.03 and 3.65
- Most likely score 1–1 at 11.76 %, then 1–0 at 10.23 %
- Over 2.5 goals 51.85 %, both teams to score 54.54 %
Note how flat the exact-score distribution is: the single most likely result happens barely one time in eight. That is a genuine property of football, not a weakness of the model — and a good reason to be sceptical of anyone confidently predicting a scoreline.
Where λ Comes From
The output is only as good as the input, and there is no way around that. Two workable approaches:
- Published xG. Average each team's expected goals for and against over the last five to ten matches, adjusting for opponent quality if you can.
- Strength indices. Attack and defence ratings relative to the league average, multiplied by the league's average home and away goals. The second input mode does this for you.
What the Model Does Not Know
Poisson assumes the two teams score independently. They do not: a goal changes the game state, and both sides respond. The practical effect is that plain Poisson slightly understates draws and low scores — the reason professional models apply a correction to the 0–0, 1–0, 0–1 and 1–1 cells.
It also has no idea about red cards, injuries, or a team with nothing to play for in May. Treat the output as a baseline to compare against the market, not as a forecast to bet blindly.
Frequently Asked Questions
How accurate is a Poisson forecast?
Good enough to be useful, not good enough to beat a sharp market on its own. Poisson gets the shape of football scoring roughly right, but it assumes the two teams score independently — in reality a goal changes how both sides play. That understates draws and 0–0 by a couple of points, which is why serious models apply a correction to the low-score cells.
Where do I get the expected goals from?
Three common sources: published xG for recent matches, averaged over five to ten games; a strength model built from goals scored and conceded relative to the league average, which the second input mode implements; or the bookmaker’s own totals market, worked backwards. The first two are independent of the price, which is what makes them worth using.
How does the team strengths mode work?
It multiplies three numbers: the home side’s attack index, the away side’s defence index, and the league average of home goals. An index of 1.00 means league average, 1.20 means 20 % better than average. The away λ is built the same way from the away attack, home defence and the league average of away goals.
What does the model miss?
Red cards, injuries, motivation, weather and any in-match dynamic. It also treats every goal as equally likely at any moment, and cannot know that a team already 3–0 up stops attacking. Use it to price a market before kick-off, not to follow a game.
Related Tools
- Value Bet / EV Calculator — test the probabilities this produces against a bookmaker’s price.
- Asian Handicap Calculator — settle the handicap lines these probabilities price.
- Implied Probability Calculator — convert the market’s prices into the same units for comparison.