How to use
- 1Choose a method: goal averages or expected goals (xG) entered directly.
- 2Enter the home side’s home scoring and conceding averages, the away side’s away averages, and the league’s home and away goals per match.
- 3Read the 1X2 percentages and fair odds, then the over/under and BTTS tables.
- 4Check the 10 most likely scores and the 0–6 score-matrix heatmap.
How the Poisson model works
Goals are rare and fairly independent events, so the number a team scores in a match is well approximated by a Poisson distribution. First each side’s expected goals (λ) is estimated from attack and defence strength: home λ = (home team’s home goals scored per game × away team’s away goals conceded per game) ÷ league average home goals. The away λ uses the away and home-defence figures with the league average away goals. Every scoreline’s probability is then P(home = i) × P(away = j), and summing the grid gives 1X2, over/under and BTTS.
Worked example: 1.8 v 0.9 expected goals
With 1.8 expected goals for the home side and 0.9 for the visitors, the model gives about 58.6% home win, 22.9% draw and 18.5% away win. Over 2.5 goals is about 50.6%, both teams to score 49.5%, and the single most likely score is 1-0 at 12.1%. Fair odds are 1 ÷ probability (58.6% → 1.71). Averages over the last 10–20 matches work better than a whole-season figure once form or squads change, whether it is the Premier League or a Sunday league.
Limits of the model and 18+ note
An independent Poisson model tends to slightly under-rate draws, especially 0-0 and 1-1, and it knows nothing about injuries, rotation, weather or motivation. Treat the output as a statistical estimate, not a tip or a guaranteed result. Betting is for adults (18+, or 21+ in some US states) only; never stake money you cannot afford to lose, and contact a gambling-support service such as GamCare (UK) or 1-800-GAMBLER (US) if it stops being fun.
Frequently asked questions
How do you predict football scores with the Poisson distribution?
Estimate each team’s expected goals, compute the probability of 0, 1, 2… goals with e^−λ × λ^k ÷ k!, and multiply the two teams’ probabilities for every scoreline. Sum the scores where the home side leads for 1, level scores for X and the rest for 2.
Should I use xG or actual goal averages?
xG is usually more stable because it strips out finishing luck. If you don’t have xG, home/away goal averages combined with league averages are a solid starting point.
How is over 2.5 goals calculated?
Add the probabilities of every score with 0, 1 or 2 total goals – that is under 2.5. Over 2.5 = 1 − under 2.5.
What are fair odds?
Odds with no bookmaker margin: 1 ÷ probability. A 40% chance equals fair decimal odds of 2.50. Market prices are shorter because they include a margin.
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