From expected goals to fair odds: the Poisson model for one football match
Odds and margins
With 1.5 expected goals for the home side and 1.1 for the visitors, the Poisson model gives a home win 46.4% of the time, a draw 25.8% and an away win 27.8%: fair odds of 2.15 for the home win.
- 46.4%home win
- 25.8%draw
- 48.2%over 2.5 goals
Calculating Match Probabilities
The Poisson model converts expected goals into specific outcome chances. With higher expected goals for the home side, the model assigns the largest probability to a home win. The table below lists the chance for each result. A draw holds the middle position, while the away win has the smallest share among the three main outcomes. These figures reflect the relative strength implied by the expected goal inputs. The home advantage in scoring expectation directly translates to a higher win probability. Readers should note that these percentages represent long-term averages rather than guarantees for any single match.
| Score | Chance |
|---|---|
| 1-1 | 12.3% |
| 1-0 | 11.1% |
| 2-1 | 9.2% |
| 2-0 | 8.4% |
| 0-1 | 8.2% |
| 0-0 | 7.4% |
From Chances to Fair Odds
Fair odds are derived by dividing one by the probability of the outcome. For the home win, the resulting fair price is higher than the expected goal figures themselves. This inverse relationship means that more likely outcomes receive lower numerical odds. The fair odds for a home win exceed the expected goals for both teams. This calculation removes the bookmaker's margin to show the true mathematical value. The fair price reflects the balance between risk and reward inherent in the specific probability.
Model Assumptions and Realities
The standard Poisson model assumes that home and away goals are scored independently. In practice, real football matches often feature slightly more draws than this independence assumption predicts. The model treats each goal as a separate event without considering how one team's scoring might influence the other's tactics. Despite this simplification, the method provides a consistent baseline for evaluation. The likelihood of the most common scoreline, a one-one draw, is lower than the overall probability of any draw occurring. This distinction highlights the difference between specific score predictions and general outcome forecasts.
Understanding Total Goals
The probability of scoring over two and a half goals is higher than the chance of a home win. This total goals market aggregates various scorelines that meet the threshold. It demonstrates how combining multiple outcomes can create a higher probability event. The over two and a half goals chance exceeds the likelihood of both individual win outcomes. This aggregation effect is useful for comparing different types of bets. The key figures show that total goals markets often have higher hit rates than match result markets. If gambling stops being fun, free help is available through support services.
Questions
Why do fair odds differ from expected goals?
Fair odds are the reciprocal of probability, while expected goals are a count of average scores. Higher expected goals lead to higher win probabilities, which result in lower numerical fair odds.
Does the model account for team interaction?
No, the basic Poisson model assumes independent scoring. Real matches often show correlated scoring patterns, particularly in draws, which the simple model may underpredict.
Is the home win the most likely outcome?
Yes, with higher expected goals, the home win has the largest probability among the three match results. The table confirms this ranking based on the input figures.
How does the margin affect odds?
Bookmakers add a margin to fair odds to ensure profit. The fair odds shown here exclude this margin to reflect the pure mathematical probability of the event.
Every figure on this page is computed by code from exact fractions for odds, margins and parlays, and closed-form Kelly growth, each checked by a seeded simulation. See the methodology.