Poisson Distribution Betting Calculator – convert goal expectancy into exact‑score, ‘at least’ and ‘at most’ probabilities in seconds
What does the Poisson model do?
The Poisson distribution assigns probabilities to independent events that occur at a known average rate. In football and many other low‑scoring sports, it lets you predict the chances of a team scoring 0, 1, 2 goals and so on, given an expected average (λ). When you turn those probabilities into odds, you can spot mis‑priced markets such as Correct Score, Both Teams to Score or Total Goals.
Inputs
- Expected average (λ) – the mean number of goals (or runs, points, etc.) you expect the team to score, e.g. 1.5.
- Proposition (k) – the specific outcome you want to price, e.g. exactly 1 goal.
Outputs
The calculator instantly shows three key probabilities:
- Exactly k – the likelihood the team scores the precise number you entered.
- At most k – the chance they score k or fewer.
- At least k – the chance they score k or more.
All percentages update as soon as you type, ready to compare with sportsbook prices.
Why bettors use the Poisson calculator
- Price niche markets – generate fair odds for Correct Score, Under/Over and team‑total lines.
- Identify value – if a bookmaker’s odds imply a lower probability than your Poisson output, you may have a positive‑EV wager.
- Model whole matches – combine separate home‑ and away‑team λ values to build a full score‑matrix and calculate match odds.
- Quick scenario testing – adjust λ up or down to see how team‑news or weather affects market prices.
How to operate the calculator
- Enter the expected average λ.
- Type the proposition k.
- Read the percentages for Exactly, At most and At least.
- Convert any percentage to decimal odds by dividing 100 by the probability.
- Compare with the sportsbook’s price to judge whether the market is over‑ or under‑valued.
Tip: For league football, λ often comes from historical goal averages adjusted for attacking and defensive strength, home‑advantage and injury news.
Probability of scoring k goals
P(k) = (e^(−λ) × λ^k) ÷ k!
No need to calculate by hand—the tool handles the math and displays the answer instantly.
Frequently asked questions
Do I need two averages for a full match?
Yes. Use one λ for the home team, another for the away team, then combine them to model scorelines like 2–1 or 0–0.
Does Poisson work for basketball or high‑scoring sports?
It loses accuracy when scores are high and events are not independent. Alternatives such as the negative binomial or normal distribution may fit better.
How do I convert the percentage to odds?
Decimal odds = 100 divided by the probability. For example, 33.3 % becomes 3.00. (Odds Converter Calcucator)
Can I use Poisson live, during a match?
Yes, but you need an updated λ that reflects game state—red cards, injuries, tempo—otherwise the probabilities will be off.