Poisson Distribution, coupled with historical data, provides a simple and reliable method for calculating the most likely score in a soccer match which can be applied to betting. This simple walk-through shows how to calculate the necessary Attack/Defence Strength measures along with a handy shortcut to generate the Poisson Distribution values. In no time you’ll be predicting soccer scores using the Poisson Distribution.
Poisson Distribution is a mathematical concept for translating mean averages into a probability for variable outcomes across a distribution. For example, if we know Manchester City average 1.7 goals per game, so by putting the Poisson Distribution formula tells us that this average equates to Manchester City scoring 0 goals 18.3% of the time, 1 goal 31% of the time, 2 goals 26.4% of the time and 3 goals 15% of the time.
Calculating score-line probabilities
Before we can use Poisson to calculate the most likely score-line of a match, we need to calculate the average number of goals each team is likely to score in that match. This can be calculated by determining the “Attack Strength” and “Defence Strength” for each team and comparing them.
Selecting a representative data range is vital when calculating Attack Strength and Defence Strength – too long and the data will not be relevant for the team’s current strength, while too short may allow outliers to skew the data. The 38 games played by each team in the 2015/16 EPL season will provide a sufficient sample size to apply the Poisson Distribution.
How to calculate Attack Strength
The first step in calculating Attack Strength based upon last season’s results is to determine the average number of goals scored per team, per home game, and per away game.
Calculate this by taking the total number of goals scored last season and dividing it by the number of games played:
- Season total goals scored at home / number of games (in season)
- Season total goals scored away / number of games (in season)
In 2015/16 English Premier League season, there were 567/380 at home and 459/380 away, equalling an average of 1.492 goals per game at home and 1.207 away.
- Average number of goals scored at home: 1.492
- Average number of goals scored away: 1.207
The ratio of a team’s average and the league average is what constitutes “Attack Strength”.
How to calculate Defence Strength
We’ll also need the average number of goals an average team concedes. This is simply the inverse of the above numbers (as the number of goals a home team scores will equal the same number that an away team concedes):
- Average number of goals conceded at home: 1.207
- Average number of goals conceded away from home: 1.492
The ratio of a team’s average and the league average is what constitutes “Defence Strength”.
We can now use the numbers above to calculate the Attack Strength and Defence Strength of both Tottenham Hotspur and Everton (as of 1st March 2017).
The limits of Poisson Distribution
Poisson Distribution is a simple predictive model that doesn’t allow for numerous factors. Situational factors – such as club circumstances, game status etc. – and subjective evaluation of the change of each team during the transfer window are completely ignored.
In this case, the above Poisson formula calculation fails to quantify any effect Everton’s new manager (Ronald Koeman) might have had on the team. It also fails to take Tottenham’s potential fatigue into consideration now that they are playing close to a Europa League fixture.
Correlations are also ignored; such as the widely recognised pitch effect that shows certain matches have a tendency to be either high or low scoring.
These are particularly important areas in lower league games, which can give bettors an edge against bookmakers. It is harder to gain an edge in major leagues such as the Premier League given the expertise and resources that modern bookmakers have at their disposal.
Last, but not least, these odds do not factor in the margin a bookmaker charges which are hugely important to the whole process of finding value.