Soccer analytics / Probability guide

How is BTTS probability calculated?

BTTS means both teams to score: an outcome is “Yes” if each side scores at least one goal, and “No” otherwise. A pre-match probability is an estimate, not a prediction that a goal must occur.

What is the event?

A 1–1 score is BTTS Yes; 2–0 and 0–0 are BTTS No. The result depends on goals scored by both sides, not on which team wins.

Where do inputs come from?

Goal-rate estimates may use historical team strength, venue, recent matches or squad information. Good models must avoid using information that became available after kickoff.

1. Start with expected scoring rates

An independent Poisson model assumes the home and away goal totals each follow a Poisson distribution with their own mean rates, commonly written as λhome and λaway. These are assumed future scoring rates, not the actual match score or measured post-match shot xG.

In a Poisson distribution, the chance of scoring zero is exp(−λ). Therefore the chance of scoring at least one goal is 1 − exp(−λ).

2. Multiply, but only under independence

If the two teams' goal totals are independent, BTTS Yes can be written as:

P(BTTS Yes) = (1 − exp(−λhome)) × (1 − exp(−λaway)).

The BTTS No probability is one minus that result. The independence assumption is an approximation: tactics, game state, red cards and other shared influences can create dependence between scores.

3. Example using hypothetical match inputs

Suppose a fictional home side has a modeled goal rate of 1.5 and the fictional away side has a rate of 1.1. Under independence, the home side's probability of at least one goal is approximately 77.7%, and the away side's is approximately 66.7%. Multiplying gives about 51.8% BTTS Yes.

These rates were chosen to illustrate the calculation; they are not observed or published probabilities for any real clubs. A different pair of rates, or a model with dependence, will produce a different answer.

4. Why model outputs can disagree

Different models can estimate different team goal rates from the same historical matches. A Dixon–Coles-style adjustment can also change probabilities for common low-scoring results. To obtain BTTS under a dependent model, sum the probabilities of all scorelines where both sides score, or subtract the probabilities of the complementary events using a valid joint score distribution.

Compare the independent Poisson and Dixon–Coles approaches to see why a simple product formula is not universally applicable.

5. How to evaluate a BTTS forecast

A 60% forecast should not be judged correct or incorrect solely because one match ends 0–0. Across many truly out-of-sample matches, well-calibrated 60% forecasts should be followed by BTTS Yes roughly 60% of the time. Calibration plots, Brier scores and log loss help evaluate probabilistic forecasts against outcomes and baselines.

Odds are a separate quantity: even a well-calibrated probability does not establish a profitable opportunity without reliable, contemporaneous prices, costs and uncertainty estimates.

Go deeper

Read what xG actually measures, the Poisson and Dixon–Coles comparison, and Cateo's evaluation principles.

All numeric examples above are hypothetical. Cateo's fictional model research is not a live selection, validated track record or betting recommendation.