Betting 101

First team to score betting: the formula that prices the market

Published 2026-09-04

First team to score is one of the few football markets whose fair price collapses to a single fraction. Most markets need a full grid of scorelines before you can read a number off them. This one does not: given a goal model, the entire first team to score market falls out of one ratio and one exponential, and the arithmetic is short enough to do on a phone. That makes it an unusually good place to see where a bookmaker’s margin actually sits, because you can compute the truth in ten seconds and compare.

The market has three outcomes, not two. Home scores first, away scores first, or No Goal — the match finishes 0–0 and every team selection is settled as a loser. That third leg is where the interesting behaviour lives.

The one-line formula behind first team to score betting

Start from the standard treatment of goals as a Poisson process: each side scores at some constant rate, and the model’s expected goals for the match, λ_home and λ_away, are those rates integrated over ninety minutes.

Two facts do all the work.

First, at least one goal has to be scored for a team selection to win at all. The probability that nobody scores is the Poisson probability of zero goals from the combined rate:

P(No Goal) = e^(−(λ_home + λ_away))

Second — and this is the part that surprises people — given that a goal is scored, the probability it belongs to the home side is simply that side’s share of the combined rate:

P(home scores first | someone scores) = λ_home / (λ_home + λ_away)

No time term appears. Two competing Poisson processes race, and the winner of the race is decided by the ratio of their rates alone. Whether the first goal arrives in the eighth minute or the eighty-first, the split is identical, because the exponential waiting times involved are memoryless — having waited an hour tells you nothing about who is due.

Put together:

P(home first) = λ_home/(λ_home + λ_away) × (1 − e^(−(λ_home + λ_away)))

Pricing the three outcomes from a goal rate

Take a modest home favourite in a normal top-division scoring environment: the model expects 1.55 goals from the home side and 1.15 from the away side. Combined rate 2.70.

• P(No Goal) = e^(−2.70) = 0.0672 → 6.72%
• Home’s share of the rate = 1.55 / 2.70 = 57.41%
• P(home first) = 0.5741 × 0.9328 = 53.55%
• P(away first) = 0.4259 × 0.9328 = 39.73%

The three sum to 100% exactly, which is the sanity check worth running every time.

Now compare that with the match result priced off the same two numbers: home win 46.5%, draw 25.2%, away win 28.3%. The favourite is 1.64 times more likely than the underdog to win the match, but only 1.35 times more likely to score first. First team to score is a systematically flatter market than 1X2, and the reason is structural. Scoring first is a single event decided by one race. Winning the match requires the stronger side’s advantage to compound across every goal in the game. One roll of the dice separates fewer teams than ninety minutes of them.

That has a practical consequence: pricing this market by eyeballing the 1X2 odds will overrate the favourite every single time.

Why the No Goal price moves and the split does not

Because the split depends only on the ratio of the two rates, changing the scoring environment while holding the balance of the fixture constant leaves the team prices almost untouched and moves only the third leg. Three fixtures with identical 57.4 / 42.6 strength ratios, at low, normal and high total goal expectancy:

Every row splits the “someone scores” probability 57.4 / 42.6. All the movement is in the No Goal column, which swings by a factor of six across a plausible range of scoring environments. If you are going to be wrong about a fixture, being wrong about how open it is costs you far more here than being wrong about who is stronger.

An 8% book on a three-way market

Here is why the market is worth reading closely. Suppose a book offers 1.79 / 2.41 / 9.00 on the three outcomes above. Converting each to implied probability gives 55.87%, 41.49% and 11.11%, summing to 108.47% — an 8.5% book, entirely unremarkable.

But an aggregate figure hides the distribution. Compare each implied probability against the fair one:

The two selections nearly everyone backs carry about four percent of margin each. The one almost nobody backs carries sixty-five. The headline 8.5% is an average across outcomes that are not charged remotely alike — the same asymmetry described in our note on the favourite-longshot bias, showing up in a three-way market instead of a price ladder.

This also exposes a common mistake in removing margin. Dividing each implied probability by the 108.47% total — proportional de-margining — returns 51.50%, 38.25% and 10.24%. The No Goal figure is still half as large again as the fair value, because the distortion was never proportional to begin with. On markets containing a genuine longshot, that shortcut does not recover the true price.

What the model cannot see

The formula assumes each side’s scoring rate is constant across the match. It is not, and the failure mode is specific: the split survives anything that scales both rates together, and breaks on anything that moves them differentially. Goals arriving more often late in matches than early changes the No Goal probability and leaves the 57.4 / 42.6 split alone. A red card, or a leading side dropping deep to protect a scoreline, changes one rate without the other — and only then does the split shift.

The same memorylessness makes the formula reusable in running. “Next team to score” from any point in a match uses the identical ratio, with only the No Goal leg rescaled to the minutes remaining. That is a rare piece of pre-match arithmetic that does not go stale at kick-off.

None of this tells you which team will score first in a given match; it tells you what a stated pair of goal expectancies implies, and what a posted price is charging on top. Whether a set of goal expectancies is any good is a separate question, and the only honest answer to it is a record kept in public — which is why every probability we publish is scored against what actually happened on our track record.