Model

Poisson calculator (football)

The Poisson distribution is the simplest model for estimating how goals are distributed in a football match. From each team's expected goals (xG, adjusted goal average), it produces the probability of every scoreline — and therefore of every market derived from it.

xG or adjusted goal average

Result

It is the starting point of most home-grown models. It won't beat the market on its own, but it gives an honest basis for judging a price.

The formula

P(k goals) = e^(−λ) × λ^k / k!

where λ is the number of expected goals. Crossing the two teams' distributions gives the probability of every exact score, then those of the 1X2, the goal totals and “both teams to score”.

Estimating expected goals

The quality of the output depends entirely on λ. A simple, robust method:

  1. Compute the team's attacking strength: its goals scored relative to the league average.
  2. Do the same for the opponent's defensive weakness.
  3. Multiply both by the league's goal average, then apply home advantage (around +15% at home in Ligue 1).

Public xG data generally gives a better basis than raw goals, especially on small samples.

The model's limits

  • Independence of the attacks. Poisson assumes the two teams score independently of each other. That is false: an open game benefits both.
  • Draws underestimated. The plain model gives too little weight to level scores; serious models apply a correction (Dixon-Coles) on low scorelines.
  • Context. Red cards, rotation before a European tie, end-of-season stakes: none of that enters λ.

Always compare the model's output with the market's fair odds. A 30% gap almost always signals a mistake on your side, not an opportunity.

Frequently asked questions

Do you need to build your own model to win?

It is not the fastest route. Starting from the devigged reference line gives a more reliable estimate than a home-grown model on a small sample, and that is the approach Stats&Bet uses to detect value bets on French bookmakers.

Can the Poisson model beat the bookmakers?

On its own, no. Bookmakers use comparable models fed with far richer data and betting flow. It remains very useful for testing a hunch, pricing a thinly followed market, or spotting an obviously off price on a secondary competition.

Should you use xG or goals scored?

xG, as soon as the sample is small. Goals scored are noised by finishing, which swings wildly from match to match, whereas xG measures chance creation, far more stable over time.

Does the model work for other sports?

Yes for sports with rare, independent events: ice hockey, handball to some extent. It is unsuited to basketball (too many possessions, normal distribution) and to tennis, which is modelled point by point.

Find value bets without hunting for them

Stats&Bet continuously compares the odds of ANJ-licensed French bookmakers with the market's fair odds and alerts you on Telegram, suggested stake included. The real results are public.

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