Using Poisson Distribution to Predict Soccer Scores
Poisson Distribution is a mathematical method that allows us to translate averages into probabilities, making it a useful tool for predicting soccer scores. By using teams' average scoring rates, along with their Attack Strength and Defence Strength, we can calculate potential score outcomes for a match. This article breaks down how Poisson Distribution works, the steps to apply it, and how to convert these probabilities into odds for smarter betting.
How to Apply Poisson Distribution in Soccer Betting
Understanding Poisson Distribution
In basic terms, Poisson Distribution calculates the probability of an event happening a certain number of times over a given period. In soccer, this can translate to predicting how many goals a team might score in a match. For example, if Manchester City has an average goal rate of 1.7 per game, we can use Poisson Distribution to determine the likelihood of them scoring 0, 1, 2, or more goals in a specific match.
Using Attack Strength and Defence Strength
Before calculating score probabilities, we need two key factors: Attack Strength and Defence Strength. Attack Strength measures a team's scoring ability relative to the league average, while Defence Strength assesses their ability to prevent goals. These strengths are determined using recent goal data, as explained below.
Calculating Attack Strength
To determine a team’s Attack Strength, calculate the league’s average goals scored per game for both home and away matches. Then, divide a team’s average goals per game by the league average to get their Attack Strength.
For example, in the 2015/16 English Premier League season:
- Average goals scored at home: 1.492
- Average goals scored away: 1.207
Example:
Tottenham Hotspur scored an average of 1.842 goals per home game. Dividing this by the league average of 1.492 gives Tottenham an Attack Strength of 1.235.
Calculating Defence Strength
Similarly, calculate Defence Strength by finding the league average of goals conceded and comparing a team’s defensive record to it. For instance, Everton conceded an average of 1.315 goals away from home. Dividing this by the league average of 1.492 gives a Defence Strength of 0.881.
Predicting Scores Using Poisson Distribution
Step-by-Step Calculation
To predict the number of goals Tottenham might score against Everton:
- Multiply Tottenham’s Attack Strength (1.235) by Everton’s Defence Strength (0.881) and the league’s average home goals (1.492):
Result: 1.235 x 0.881 x 1.492 = 1.623 goals
This calculation suggests that Tottenham is likely to score around 1.6 goals in the game. For Everton, use the same process with their Attack Strength and Tottenham’s Defence Strength.
Applying Poisson Distribution to Predict Multiple Outcomes
Since no game score ends exactly at 1.623, Poisson Distribution helps distribute probabilities across various outcomes. Use the formula:
P(x; μ) = (e-μ * μx) / x!
For practicality, many bettors use online Poisson calculators to get the probability of each team scoring 0, 1, 2, or more goals based on their calculated expected goals.
Example Probabilities
For a hypothetical Tottenham vs. Everton match:
| Goals | Tottenham | Everton |
|---|---|---|
| 0 | 19.73% | 43.86% |
| 1 | 32.02% | 36.14% |
| 2 | 25.99% | 14.89% |
| 3 | 14.06% | 4.09% |
| 4 | 5.07% | 0.84% |
These probabilities can help estimate the most likely scorelines. By multiplying probabilities, you can find the probability of specific results, such as a 1-0 win for Tottenham.
Converting Estimated Chances into Betting Odds
Calculating True Odds for Scorelines
To convert your probabilities into odds, take the inverse of the probability for each scoreline. For example, if the probability of a 1-1 draw is 11.53%, the true odds would be 1 / 0.1153, or 8.67. Compare these calculated odds to bookmaker odds to find potential value bets.
Combining Draw Probabilities
To calculate the total odds for a draw outcome, add up the probabilities for all possible draw scorelines (e.g., 0-0, 1-1, 2-2). This will give you the overall probability of a draw, which you can then convert into odds.
Limitations of Poisson Distribution in Soccer
While Poisson Distribution is a helpful tool, it doesn’t account for situational factors like team tactics, injuries, or coaching changes. Additionally, it doesn’t consider correlations, such as certain teams performing better or worse on specific pitches. For higher accuracy, combine Poisson insights with subjective factors and real-world data.
Despite its limitations, Poisson Distribution remains a valuable approach for spotting trends and finding betting value, especially when used alongside other metrics.
