Poisson Calculator: Goal Odds and Scorelines
Goals in low-scoring sports are often modeled as Poisson counts: the chance a team scores k goals is e^(−λ) × λ^k ÷ k!, where λ is its expected goals. Multiply the two teams' chances for each scoreline, then add up the scorelines for each result.
Key facts
- The Poisson distribution gives the probability of a given number of events with a known average rate (Wikipedia, Poisson distribution).
- P(k goals) = e^(−λ) × λ^k ÷ k! for expected goals λ.
- Treating the two teams as independent Poisson counts is the standard simple model for soccer scores.
If you know roughly how many goals each team is expected to score, the Poisson model turns that into a full set of probabilities: who wins, how likely a draw is, how many goals to expect and which scorelines come up most. It's the standard first model for soccer and other low-scoring games. It runs in your browser, sends nothing anywhere and forgets your numbers when you close the page.
Poisson goals calculator
Turn on JavaScript to use the calculator. The worked example below shows the same math by hand.
What you enter and what you get
You enter
- Home expected goals: a number.
- Away expected goals: a number.
- Total goals line: For over/under, such as 2.5.
You get
- Home / draw / away
- Over 2.5 goals
- Under 2.5 goals
- Both teams score
- Most likely score
- Second
- Third
- Fair odds home / draw / away
How the calculator works
- For each team, the chance of k goals is e^(−λ) × λ^k ÷ k!.
- Multiply the two teams' chances to get each exact scoreline.
- Add the scorelines where home > away, equal, or home < away for the three results.
- Add the scorelines above the line for the over, and where both teams score for BTTS.
A worked example
Expected goals of 1.6 for the home team and 1.1 for the away team, with a 2.5 goal line.
| Item | Result |
|---|---|
| Home / draw / away | 49% / 25% / 26% |
| Over 2.5 goals | 50.6% |
| Under 2.5 goals | 49.4% |
| Both teams score | 53.2% |
| Most likely score | 1-1 (11.8%) |
| Second | 1-0 (10.8%) |
| Third | 2-1 (9.5%) |
| Fair odds home / draw / away | +104 / +302 / +282 |
What the calculator leaves out
- It treats the two teams' goals as independent, which understates low-scoring draws a little.
- Expected goals are your inputs; the model doesn't estimate them.
- It ignores red cards, game state and extra time.
How we checked it
Before it went on the page we checked it against a case worked by hand: two equal teams have to get equal win chances and the draw chance the model gives for that scoring rate. The calculator is also run against thousands of odd entries such as blanks, zeros and huge numbers, so a bad entry shows a plain prompt and never a wrong number. The worked example above comes from the same code the calculator runs.
At a sweepstakes sportsbook
Soccer markets at a sweepstakes sportsbook are priced by that site, so you can compare its prices with the fair odds this model produces. The model's output is a probability, not a recommendation. See Sweepstakes vs Social vs Real-Money Casinos for how these sites differ from regulated sportsbooks.
Betting math is not betting advice. Only play with money you can afford to lose, and if gambling stops being fun, call or text 1-800-GAMBLER.
Frequently asked questions
What are expected goals?
The average number of goals a team is expected to score in the match, from your own model or a published estimate.
Why do draws look higher in real matches?
Real matches have some dependence between the teams' goals. Adjusted models correct for it, and this simple one doesn't.
Can I use it for hockey?
Yes, for a rough view, using each team's expected goals. Hockey has more scoring, so check how well it fits your data.
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- Poisson distribution, Wikipedia (read 2026-10-05)
- Probability, Wikipedia (read 2026-10-05)
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