Free · browser-local · two xG inputs
BTTS probability calculator from xG
Calculate Both Teams to Score Yes and No, isolate each side's zero-goal risk, then inspect how BTTS overlaps with Over 2.5.
No sign-upNo data uploadVisible formulaNot betting advice
Your inputs
Enter home and away xG
Use two full-match scoring means. Results update on this device as you type.
Free, browser-local calculationNo account, upload or server request. The page does not know which match—if any—the numbers describe.
Independent-Poisson result
BTTS, blank-score risk and its Over 2.5 overlap
“Both teams to score” is one event. The joint table then separates it from a different question: how that event intersects with the 2.5-goal line.
- Home scores zero
- 21.2%
- Away scores zero
- 33.3%
- 0–0 probability
- 7.1%
| Question | Probability | What is counted |
|---|---|---|
| BTTS Yes ∩ Over 2.5 | 40.5% | Both score and at least 3 total goals |
| BTTS Yes ∩ Under 2.5 | 12.0% | Exactly the 1–1 scoreline |
| Over 2.5 | BTTS Yes | 77.1% | Among BTTS Yes outcomes |
| BTTS Yes | Over 2.5 | 82.0% | Among Over 2.5 outcomes |
| BTTS No ∩ Over 2.5 | 8.9% | 3–0, 0–3 and higher one-sided scores |
Exact formulaP(BTTS Yes) = (1 − e−λH)(1 − e−λA)
BTTS Yes ∩ Under 2.5 is only 1–1, so its probability is e−(λH+λA)λHλA. Subtract that one scoreline from BTTS Yes to obtain BTTS Yes ∩ Over 2.5.
Method
How is BTTS probability calculated from xG?
For a Poisson count with mean λ, the probability of zero goals is e−λ. Therefore the probability that a team scores at least once is 1 − e−λ. If the home and away goal counts are independent, multiply those two “at least one” probabilities to obtain BTTS Yes.
BTTS No is the complement. It includes 0–0 and every scoreline where exactly one team scores. The calculator exposes both team-zero probabilities and 0–0 so the overlap is visible rather than added twice.
Joint-event insight
Why 1–1 is the special BTTS / Under 2.5 case
Both teams must score at least once, so two is the smallest possible total. Under 2.5 permits no more than two goals. Consequently, BTTS Yes and Under 2.5 can only be 1–1. Every other BTTS Yes scoreline—2–1, 1–2, 2–2 and beyond—is Over 2.5.
Conditional probabilities answer different questions. “Over 2.5 given BTTS Yes” divides the joint event by all BTTS Yes outcomes. “BTTS Yes given Over 2.5” divides the same joint event by all Over 2.5 outcomes. Their numerators match; their denominators do not.
Scope and limits
What the result assumes—and cannot prove
- Home and away goals are independent Poisson counts.
- The entered xG values are fixed full-match means, not observed post-match xG.
- No red cards, game state, team identity, injuries or low-score dependence correction is modelled.
- The calculation transforms inputs; it does not establish that those inputs are accurate or available before kick-off.
Fair odds are a mathematical reciprocal, not a price prediction.
A fair decimal odd of 1 ÷ p contains no margin, liquidity, model error or uncertainty allowance. It is not a bet, stake, value claim or recommendation.
Research trail
The baseline is transparent; real validation is separate
- Maher (1982), Modelling association football scores
- Dixon & Coles (1997), Modelling association football scores and inefficiencies
These papers ground football score modelling and explain why a simple independent baseline has known limits. They do not certify a user-entered xG scenario or this site's future model.
Canonical publication record
Abstract
A browser-local independent-Poisson calculator for BTTS Yes and No, team zero-goal risk, zero-margin fair odds, and the joint and conditional relationship between BTTS and Over 2.5 from two user-supplied expected-goal rates.
- Author and publisher
- Football Proof AI
- Technical report
football-btts-independent-poisson/1.0.0- Published
- Last modified
- Release status
- Current release
- Review status
- Editorial technical note; not externally peer reviewed
- Version history
football-btts-independent-poisson/1.0.0: Initial public release.