Most days you read Pinnacle's prices. Sometimes you want your own: a model that turns two expected-goals estimates into a full 1X2 price set, so you can compare your view with the market's. The smallest honest version of that model is a Poisson one, and it fits on a page.
From expected goals to probabilities
The model assumes each team's goals follow a Poisson distribution with its own rate: the home side at 1.4 expected goals, the away side at 1.1, say. The probability of any scoreline is then the product of the two Poisson probabilities, and the match outcomes are just sums over the grid: home win, draw and away win collect the cells where the home score is higher, equal or lower.
For those two rates, the grid sums to about 43.8% home, 26.6% draw and 29.6% away. Divided into 1, those are fair decimal prices of 2.28, 3.75 and 3.38.
Why your model has no margin
A model's probabilities sum to exactly 100% by construction, because they describe a complete set of mutually exclusive outcomes. The market's prices never do: the overround is the book's margin, as the site's pages define it. So the comparison is never your 2.28 against the market's posted price; it is your 2.28 against the market's fair price with the margin removed. The no-vig calculator does that removal on the market side, checked 2026-10-14.
Skip that step and you will read value into every favorite, because the raw market price always looks shorter than it should.
A worked reading
Say the market posts 2.10, 3.40 and 3.80 on home, draw and away. The implied probabilities sum to 104.0%, so the overround is 4.0%, and proportional removal gives fair prices of about 2.18, 3.54 and 3.96. Now the comparison is honest: your model is shorter on the home side, 2.28 against the market's 2.18, and longer on the away side, 3.38 against 3.96.
That disagreement is the model's whole output. Where you disagree, you either know something the market does not, or the market knows something you do not, and the second is the safer default.
Where the model stops
A two-parameter Poisson carries no team news, no motivation, no matchup history, and no correlation between the two scores. It is a teaching instrument and a baseline, not an oracle. The site's research page sets the standards for claims made from data, and a toy model's output belongs nowhere near a bet until it survives that kind of scrutiny.
Two rates, one grid, three fair prices. Build it once, and every match on the board becomes a comparison instead of a verdict.