Tool · Free, no sign-up
Both teams to score probability calculator
Turn two expected-goals figures into the chance that both teams score, a fair BTTS price, and the BTTS combinations bookmakers sell.
The short answer
If the home side is expected to score λ goals and the away side μ, and goals follow a Poisson distribution, the chance that both teams score is (1 − e−λ) × (1 − e−μ).
For 1.45 and 1.20 expected goals: 76.54% × 69.88% = 53.49%, a fair BTTS Yes price of 1.87 (about 5/6). BTTS No is the rest, 46.51%.
Type each side’s expected goals, add the Dixon-Coles correction if you use it, and optionally the bookmaker’s Yes and No prices. The calculator builds the full correct-score grid and reads BTTS and its combinations off it. Nothing is stored or sent.
Worked example
A home side expected to score 1.45 goals against an away side expected to score 1.20.
- Chance the home side fails to score: e−1.45 = 23.46%. So it scores at least once 76.54% of the time.
- Chance the away side fails to score: e−1.20 = 30.12%. So it scores at least once 69.88% of the time.
- Both, treating the two as independent: 0.7654 × 0.6988 = 0.5349, so BTTS Yes is 53.49% and the fair price is 1.87 (about 5/6).
- With a Dixon-Coles ρ of −0.10 the 1-1 cell grows and Yes rises to 54.72% (fair 1.83).
| Side | Price | Implied | Market, margin removed | Model | EV per £1 |
|---|---|---|---|---|---|
| Yes | 8/11 | 57.89% | 53.66% | 53.49% | −7.6p |
| No | evens | 50.00% | 46.34% | 46.51% | −7.0p |
Against a bookmaker offering Yes at 8/11 and No at evens, the two prices add to 107.89 per cent, a margin of 7.32 per cent. On this model neither side is worth backing: Yes is priced as if it were 57.89% likely, well above the model’s 53.49%, and No at evens needs 50% to break even. That is the normal result. A margin this size means you need a sizeable disagreement with the market before either side becomes value.
BTTS combinations: read them off the grid
BTTS and win, or BTTS and over 2.5, cannot be priced by multiplying the two chances, because they are connected: if both sides score, the match already has at least two goals. The calculator adds up the right cells of the correct-score grid instead.
| Market | From the grid | Multiplying the two separately |
|---|---|---|
| BTTS and home win | 19.81% | 22.93% |
| BTTS and over 2.5 goals | 41.20% | 26.43% |
Multiplying gets BTTS and over 2.5 badly wrong, 26.43% against the true 41.20%, because the two are so closely linked. Bookmakers price these combinations with their own correlation adjustments and their own margins, so compare the price with the grid figure, not with a product.
Where the simple model is weak
Plain Poisson treats the two sides’ goals as independent. Real matches have a little dependence at low scores, which is what the Dixon-Coles ρ corrects. Game state matters too: a side that goes a goal down tends to push forward, which can raise the chance of a reply. The inputs matter far more than either effect, so spend your effort on the expected goals. The Poisson match predictor builds them from league averages and team ratings and prices every other market from the same grid, and any other score uses the same grid for the correct score market.
Chapter 16 of The Stat Man, Poisson and Chips, builds the correct-score grid and reads BTTS, win to nil and the rest off it; the chapter 16 worked solutions and chapter 17 worked solutions cover Poisson and the Dixon-Coles correction.
Questions
Frequently asked questions
How do you calculate the probability of both teams scoring?
With expected goals λ for the home side and μ for the away side, and Poisson goals, the chance of both scoring is (1 − e^−λ) × (1 − e^−μ): the chance the home side scores at least once times the chance the away side does. For 1.45 and 1.20 that is 76.54% × 69.88% = 53.49%.
What expected goals figures should I use?
Your best estimate of how many goals each side will score in this match, not their season averages. League averages adjusted for each side’s attack and defence are a sound start, and the Poisson match predictor will build them from goals or xG for and against.
Why does the Dixon-Coles setting raise BTTS Yes?
A negative ρ moves probability onto 0-0 and 1-1 and away from 1-0 and 0-1. Only 1-1 is a BTTS Yes score, so the Yes figure rises by −ρ × λ × μ × e^−(λ+μ). With ρ = −0.10 on a typical match that is a bit over one percentage point.
Does the calculator store anything?
No. It runs in your browser, sets no cookies and sends nothing anywhere. The inputs live in the page address after the #, which never reaches a server.
Out now · free to read on Kindle Unlimited