How the Poisson Distribution Predicts Soccer Scores — and Frequently Asked Questions
How the model calculates scoreline probabilities
The Poisson Distribution describes the probability of a given number of random events occurring in a fixed interval. In soccer, the goals scored by each side in a match approximately follow a Poisson distribution. The calculation on Poisson Football runs in five steps:
Step 1: Establish the data base
Each team's recent matches are used as the calculation base: the last 30 matches for overall attacking and defensive strength, and the last 10 matches for current form. Match data is updated daily, and the model always runs on the latest completed fixtures.
Step 2: Compute expected goals λ
By analysing the change in each team's attacking and defensive output relative to the league average, the model derives a theoretical average number of goals for the home and away sides — the expected goals λ. Note that λ is a theoretical indicator: it does not equal the team's actual goals, but measures the team's scoring tendency in the fixture.
Step 3: Apply the Poisson formula for goal probabilities
The Poisson formula is P(k) = e^(-λ) · λ^k / k!, where λ is the expected goals and k is the number of goals. Feeding each side's λ into the formula yields the probability of scoring anywhere from 0 to 7 goals.
Step 4: Compute joint scoreline probabilities
The probability of the home side scoring i goals multiplied by the probability of the away side scoring j goals gives the joint probability of the i:j scoreline. For example, P(2:1) = P(home scores 2) × P(away scores 1).
Step 5: Sum up to win / draw / loss probabilities
Adding the probabilities of all home-win scorelines (e.g. 1:0, 2:1, 2:0, 3:1) gives the home-win probability; adding draw scorelines (0:0, 1:1, 2:2, 3:3…) gives the draw probability; the away-win probability follows the same logic. The site also outputs derived indicators such as the expected-goals sum and the expected-goals difference to support the analysis.
Free leagues and what is included
The basic analysis features for the following 5 leagues are permanently free — no registration required to view complete score and probability data:
The free scope covers basic analysis features only, specifically: league fixture lists, home and away expected goals (λ), win / draw / loss probabilities, goal-count distributions and exact scoreline probabilities.
The following are not part of the free basic scope and belong to the site's separate paid modules: half-time score predictions, total-goals position stats, similar-probability historical results, composite team points, same-points-difference stats, and match analysis for competitions beyond these 5 leagues.
| League |
Sport |
Predictions |
Entry |
| Premier League |
Football |
Win / draw / loss probabilities, expected goals, goal-count distribution, scoreline probabilities |
Premier League analysis |
| Serie A |
Football |
Win / draw / loss probabilities, expected goals, goal-count distribution, scoreline probabilities |
Serie A analysis |
| Bundesliga |
Football |
Win / draw / loss probabilities, expected goals, goal-count distribution, scoreline probabilities |
Bundesliga analysis |
| LaLiga |
Football |
Win / draw / loss probabilities, expected goals, goal-count distribution, scoreline probabilities |
LaLiga analysis |
| Ligue 1 |
Football |
Win / draw / loss probabilities, expected goals, goal-count distribution, scoreline probabilities |
Ligue 1 analysis |
Frequently asked questions
Q: How accurate are the predicted probabilities? Can you guarantee match results?
A: No, and we make no promises. A probability only expresses the relative likelihood of an outcome — a high probability means the outcome is relatively more likely, not that it is certain to happen; a low probability means it is relatively less likely, not that it cannot happen. Poisson Football provides statistical analysis data for research and reference by football fans. It does not constitute any decision-making advice. Please make sure you understand what probability means before using this tool.
Q: What is expected goals (λ)?
A: Expected goals is a theoretical average number of goals, weighted from the team's recent home / away attacking and defensive data. It does not equal the team's actual goals; it measures the team's scoring tendency in the fixture. If the difference between actual goals and expected goals falls within the normal range of variance, the team's performance is broadly in line with its recent form.
Q: How do I use the Poisson probabilities to judge a match?
A: A common approach is to compare the model's win / draw / loss probabilities with the implied probabilities derived from European odds averages. When the two differ significantly, the market pricing and the model's judgement disagree, and such fixtures deserve closer attention. When the home-win and away-win probabilities are close while the draw probability stands out, the draw is worth considering. All judgements are probabilistic references only, never certainties. See the draw-identification method.
Q: How often is the data updated?
A: Historical match data used for the calculations is updated daily, and the European odds averages on the fixture lists are refreshed every 2 hours. For newly promoted teams that lack recent match data in their league, the model flags the probability data as reference-only — using lower-division historical data would be inaccurate, and this situation usually occurs early in the season. For national-team competitions such as the World Cup, qualifiers plus finals data are used as the calculation base.
Q: What data and analysis features does the site provide?
A: For football: win / draw / loss probabilities, expected goals, goal-count probability distributions, scoreline probability distributions, half-time score probabilities, total-goals position stats, similar-probability historical results, and an interactive Poisson calculator. Extended modules covering more competitions and advanced analysis are offered separately as paid services.
Q: What exactly is included in the free scope?
A: Free means the basic analysis features for the 5 leagues listed above — Premier League, Serie A, Bundesliga, LaLiga and Ligue 1 — including fixture lists, expected goals (λ), win / draw / loss probabilities, goal-count distributions and exact scoreline probabilities. All of it is viewable without registration.
To be clear: the free scope does not include half-time score predictions, total-goals position stats, similar-probability historical results, composite team points, same-points-difference stats, or analysis of competitions beyond these 5 leagues. These are separate paid modules, independent from the free basic features — please do not read "free leagues" as "every feature included".
Disclaimer: Poisson Football provides statistical football analysis tools built on the Poisson distribution and expected goals. All outputs are data statistics and probability inferences based on historical data, published for browsing and research by sports fans. Poisson Football makes no promises about actual match results, and none of the data constitutes decision-making advice. All content is provided for educational and statistical-analysis purposes. This is not betting, gambling, or financial advice. Poisson Football does not operate a sportsbook and does not accept or facilitate wagers. You must be 18 or older to use this site. Always comply with the laws and regulations that apply in your jurisdiction.