Over/Under 2.5 and Both Teams to Score (BTTS), Straight From the Score Matrix

To calculate Over 2.5, add the probabilities of all scorelines with at least three total goals. To calculate both teams to score (BTTS) Yes, add every scoreline where each team scores at least once. Both probabilities come from the same score matrix, but they include different outcomes.

A 3–0 result is Over 2.5 and BTTS No. A 1–1 result is Under 2.5 and BTTS Yes. Below are the formulas, a worked example and the calculation for Over 2.5 and BTTS together.

Open the football score calculator →

Let p(h, a) be the probability of a score with h home goals and a away goals. Each market selects a set of those cells. If you need help with the axes and percentages, start with how to read a score probability map.

ImpliedScore first removes margin from the supplied odds, then fits expected home and away goals to those market probabilities. Removing margin and fitting goal rates are separate steps. Once the score matrix is built, totals and BTTS are obtained by summing its cells.

• Under 2.5: 0–0, 1–0, 0–1, 2–0, 1–1 and 0–2. These are all scores with zero, one or two total goals.
• Over 2.5: every score with three or more total goals.

P(Under 2.5) = p(0,0) + p(1,0) + p(0,1) + p(2,0) + p(1,1) + p(0,2)

For the full probability distribution, P(Over 2.5) = 1 − P(Under 2.5). The half-goal line has no push because the total number of goals is an integer.

Under an independent Poisson model, total goals follow a Poisson distribution with mean s = λhome + λaway. This gives a shortcut:

P(Under 2.5) = e−s × (1 + s + s2/2)
P(Over 2.5) = 1 − e−s × (1 + s + s2/2)

Other half-goal lines use the same counting rule: Over 1.5 needs at least two goals; Over 3.5 needs at least four.

BTTS Yes adds every cell with h ≥ 1 and a ≥ 1. BTTS No adds every cell where at least one team finishes on zero, counting 0–0 once.

For independent Poisson goals, multiply the probabilities that each team scores at least once:

P(BTTS Yes) = (1 − e−λhome) × (1 − e−λaway)
P(BTTS No) = 1 − P(BTTS Yes)

This product assumes the two team goal counts are independent. For a model with dependence, sum the relevant cells of its joint distribution or use that model's specific formula.

Use an independent Poisson model with λhome = 1.83 and λaway = 0.58. Expected total goals are 2.41. You can reproduce this example in the Poisson football calculator.

• Over 2.5: 43.29%; Under 2.5: 56.71%.
• BTTS Yes: 36.95%; BTTS No: 63.05%.

The away team has a 44.01% probability of scoring at least once. BTTS cannot exceed that probability because both teams scoring requires the away team to score.

For orientation: 2–1 belongs to Over + BTTS Yes, 3–0 to Over + BTTS No, 1–1 to Under + BTTS Yes, and 1–0 to Under + BTTS No.

Calculated from unrounded probabilities and displayed to two decimal places. The inputs are illustrative goal rates, not a claim about a named fixture.

Add cells where both teams score and the total is at least three: 2–1, 1–2, 2–2 and all other qualifying scores. Among BTTS Yes outcomes, only 1–1 is Under 2.5. Therefore, for any valid score distribution:

P(Over 2.5 and BTTS Yes) = P(BTTS Yes) − p(1,1)

In the example, BTTS Yes is 36.95% and 1–1 is 9.53%, giving 27.42% for the combination. Multiplying the separate Over and BTTS probabilities would give about 16.00%, which is wrong for this model. These two events are dependent even when the teams' goal counts are modelled as independent.

The other combinations can also be read from the table. Under 2.5 + BTTS Yes is exactly the 1–1 cell. Over 2.5 + BTTS No contains results such as 3–0, 0–3 and higher wins to nil.

The standard Dixon-Coles correction changes 0–0, 1–0, 0–1 and 1–1. Of these, only 1–1 contributes to BTTS Yes. At fixed goal rates, the corrected probability is:

PDC(BTTS Yes) = PPoisson(BTTS Yes) − ρλhomeλawaye−(λhome+λaway)

With the same 1.83 and 0.58 rates and an illustrative valid ρ = −0.10, BTTS Yes increases from 36.95% to 37.90%. This is an example assumption, not a recommended rho value for every match. BTTS + Under 2.5 rises from 9.53% to 10.49%, while BTTS + Over 2.5 stays at 27.42% because its scorelines are not among the four corrected cells.

Over/Under 2.5 remains unchanged at fixed rates. All four corrected cells are under 2.5, and their adjustments cancel in that total. If a calculator refits the goal rates when the model changes, its totals can move because the new rates differ.

For a standard Asian total of 2.0, exactly two goals returns the stake on both Over and Under. Over wins at three or more goals; Under wins at zero or one. Win, push and loss probabilities must be kept separate. For this win/push/loss structure with no fees, fair decimal odds are (1 − P(push)) / P(win) when P(win) > 0. For half-goal lines without pushes, this reduces to 1 / P(win).

A quarter-goal line such as 2.25 splits the stake between 2.0 and 2.5. It can produce a half-win or half-loss, so the simple two-outcome treatment used for 2.5 does not describe every settlement. Use the same scoring period for all markets being compared.

A small visible heatmap can omit high-scoring outcomes. The formulas above refer to the full distribution; a truncated grid may sum to slightly less than 100%. Use the calculator's full computational grid and account for its omitted tail rather than treating everything outside the displayed cells as zero.

Markets derived from one valid score distribution follow the same probability rules. That internal consistency does not establish accuracy or guarantee an exact fit to the input odds. The methodology explains fitting residuals; how accurate betting odds are addresses comparison with actual results.