Poisson calculator for football
Football scoreline model — 1X2, totals and BTTS from expected goals
Enter what you expect each side to score. Get fair odds for every main market, all derived from one scoreline grid.
What the Poisson model does
A football match is a handful of rare events spread over 90 minutes, which is exactly what the Poisson distribution describes. Give each side an expected number of goals and it tells you how likely every scoreline is — 1-0, 2-1, 0-0 and the rest. Add up the cells where the home side scores more and you have the home win probability; add the cells where the total clears 2.5 and you have the Over price. Because every market comes off the same grid, the numbers agree with each other, unlike quoting 1X2 from one place and totals from another. Compare what comes out against the market with No-vig fair odds, and size the bet with Value bet finder.
See also: Value bet finder, No-vig (fair odds), Goal Line (Total)
How to use
- 1Enter the goals you expect the home side to score. A bookmaker's handicap and total imply these, and so do xG averages over recent matches.
- 2Do the same for the away side. Home advantage is already inside the number — you are not asked for it separately.
- 3Pick the totals line you care about.
- 4Read the fair odds. Anything the market prices above them is value; anything below is not.
Example: 1.60 against 1.20 expected goals
A home side expected to score 1.60, an away side 1.20. The grid gives home 46.7%, draw 24.7%, away 28.6% — fair odds of 2.14, 4.05 and 3.49. Over 2.5 lands at 53.1% (1.88), both teams to score at 55.8% (1.79), and the single most likely result is 1-1 at 11.7%. If a bookmaker offers 2.40 on the home win while your model says 2.14, that gap is the bet.
The formula
For one side with expected goals λ, the probability of scoring exactly k:
- P(k) = e^−λ × λ^k ÷ k!
- Both sides at once, assuming they score independently: P(i−j) = P(i) × P(j)
- Home win = every cell where i > j · Draw = where i = j · Away win = where i < j
- Over the line = every cell where i + j clears it · Both teams to score = where i ≥ 1 and j ≥ 1
- Fair odds = 1 ÷ probability
The grid runs to 15 goals a side and is renormalised, so the three 1X2 prices always imply exactly 100% between them.
What this model does not know
Poisson assumes the two sides score independently of each other. Real matches do not quite work that way: 0-0 and 1-1 come up slightly more often than the model says, lopsided scorelines slightly less. The Dixon-Coles correction exists for exactly this, but fitting it needs a database of results that this calculator does not have — so what you get is the plain model, said plainly. Treat it as a baseline to price against, not a forecast. And it is only ever as good as the two numbers you feed it: careless expected goals produce confident, precise, wrong odds.
When to use
- Turning an xG view — or a bookmaker's handicap and total — into a full set of prices
- Checking whether one bookmaker's 1X2, totals and BTTS prices are consistent with each other
- Pricing both teams to score and correct score, which few calculators cover
- Building your own number before you look at the market, so the market does not anchor you
Frequently asked questions
What is the Poisson calculator calculator?
A football match is a handful of rare events spread over 90 minutes, which is exactly what the Poisson distribution describes. Give each side an expected number of goals and it tells you how likely every scoreline is — 1-0, 2-1, 0-0 and the rest.
How does the Poisson calculator calculator work in practice?
A home side expected to score 1.60, an away side 1.20. The grid gives home 46.7%, draw 24.7%, away 28.6% — fair odds of 2.14, 4.05 and 3.49. Over 2.5 lands at 53.1% (1.88), both teams to score at 55.8% (1.79), and the single most likely result is 1-1 at 11.7%. If a bookmaker offers 2.40 on the home win while your…
What is the most common mistake with the Poisson calculator calculator?
Poisson assumes the two sides score independently of each other. Real matches do not quite work that way: 0-0 and 1-1 come up slightly more often than the model says, lopsided scorelines slightly less. The Dixon-Coles correction exists for exactly this, but fitting it needs a database of results that this calculator…
When should I use the Poisson calculator calculator?
Turning an xG view — or a bookmaker's handicap and total — into a full set of prices. Checking whether one bookmaker's 1X2, totals and BTTS prices are consistent with each other. Pricing both teams to score and correct score, which few calculators cover.