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xG Poisson football calculator
Convert two user-supplied expected-goal rates into a complete score matrix—then pressure-test the assumptions behind the answer.
Canonical publication record
Abstract
A deterministic browser converter from user-supplied home and away expected-goal rates to an independent-Poisson score matrix, 1X2, BTTS and totals probabilities, with aggregated 7+ tails, numerical-mass audit and four-corner input stress scenarios.
- Author and publisher
- Football Proof AI
- Technical report
football-independent-poisson-scenario/1.0.0- Published
- Last modified
- Release status
- Current release
- Review status
- Editorial technical note; not externally peer reviewed
- Version history
football-independent-poisson-scenario/1.0.0: Initial public release.
Transparent scenario engine · Browser local
Turn two xG assumptions into a complete score world
Enter match-level expected goals. The tool applies two independent Poisson distributions, retains the 7+ goal tails, then shows how a small input perturbation changes every headline probability.
Model contractH ~ Pois(1.70) · A ~ Pois(1.10) · H ⟂ A
Independent goals. Fixed rates. No team model, form data or low-score correction.
Derived 1X2 probability
- BTTS · Yes
- 54.5%
- Over 1.5
- 76.9%
- Over 2.5
- 53.1%
- Under 2.5
- 46.9%
- Over 3.5
- 30.8%
- Expected total
- 2.80
Complete score matrix
Every cell is visible—including the 7+ tails
Rows are home goals; columns are away goals. The final row and column aggregate seven or more goals, so the displayed matrix retains 100.0% of the model probability.
| H \ A | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7+ |
|---|---|---|---|---|---|---|---|---|
| 0 | 6.1% | 6.7% | 3.7% | 1.3% | 0.4% | 0.1% | 0.0% | 0.0% |
| 1 | 10.3% | 11.4% | 6.3% | 2.3% | 0.6% | 0.1% | 0.0% | 0.0% |
| 2 | 8.8% | 9.7% | 5.3% | 1.9% | 0.5% | 0.1% | 0.0% | 0.0% |
| 3 | 5.0% | 5.5% | 3.0% | 1.1% | 0.3% | 0.1% | 0.0% | 0.0% |
| 4 | 2.1% | 2.3% | 1.3% | 0.5% | 0.1% | 0.0% | 0.0% | 0.0% |
| 5 | 0.7% | 0.8% | 0.4% | 0.2% | 0.0% | 0.0% | 0.0% | 0.0% |
| 6 | 0.2% | 0.2% | 0.1% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% |
| 7+ | 0.1% | 0.1% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% |
Assumption stress test
What changes if each xG input moves by ±0.25?
The band spans four corner scenarios: low/high home xG crossed with low/high away xG. It measures input sensitivity only. It is not sampled uncertainty and it does not validate the entered xG.
Short answer
Can xG be converted into football score probabilities?
Yes—conditionally. If the entered home and away rates are fixed match-level scoring means, and goals are treated as independent Poisson counts, each exact score gets a probability. Summing the relevant cells produces 1X2, BTTS and total-goal probabilities. The conversion cannot prove that the entered rates are good.
Independent score modelP(H=h, A=a) = e−(λH+λA) · λHh/h! · λAa/a!
1X2 is the sum over h > a, h = a and h < a—not the single largest cell.
Critical input boundary
This tool does not estimate xG
You supply λH and λA. They may come from a properly frozen pre-match model, a documented external source or a synthetic scenario. The calculator does not inspect shots, teams, form, injuries or odds, and it never turns post-match observed xG into pre-match evidence.
For honest model evaluation, preserve when each rate was available, score a complete out-of-sample history and inspect probability calibration—not only the modal score.
Assumption register
What a plain football Poisson model leaves out
The baseline is useful because it is legible, not because it is universally true. Each omitted mechanism can move the final distribution even when the two headline xG values stay fixed.
- 01
Score dependence
Independent home and away counts cannot represent correlation. Dixon–Coles and bivariate Poisson models address related low-score behaviour with extra fitted parameters.
- 02
Changing match state
A single full-match rate ignores red cards, substitutions, game state and time-varying tempo.
- 03
Rate uncertainty
λ is treated as known. The four-corner stress scenarios show input sensitivity, not a statistical confidence interval.
- 04
Information compression
Two aggregate rates do not preserve team identity, shot mix or how an upstream xG model was trained and calibrated.
Primary research trail
Why the baseline—and its warnings—are public
Maher formalised attack and defence strengths in Poisson football score models. Dixon and Coles introduced a low-score dependence adjustment; Karlis and Ntzoufras developed bivariate-Poisson alternatives. Later comparative work reinforces the need for time-aware validation rather than one attractive example.
Keep the workflow honest
Generate a baseline here. Test a real model elsewhere.
A transparent score generator is a useful benchmark, not a substitute for point-in-time features, walk-forward validation or a public prediction record.