Using Poisson Distribution to Predict Football Scores for Betting

Sharp football bettors and traders are always looking for a new edge. That appetite to learn new strategies and methods is what often separates long-term winning bettors from losers!

In today’s article, we are going to look at using Poisson distribution to predict football scores, covering how we can use this in the football betting markets.

What is Poisson Distribution?

Poisson distribution is a probability distribution that expresses the given number of events occurring in a fixed interval. When we look at using it for football, the event we are interested in is goals and the interval is over a 90 minute period.

To calculate this we first to need to assess the attacking strength of a team alongside its defensive strength.

Calculating Attacking Strength

The first step for calculating the attack strength of a team is based on last season’s results. First off we need to determine the average number of goals scored per team. Covering goals scored per home game, and per away game.

We can 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 2023/2024 Premier League season we have the following data;

  • Average number of goals scored at home: 1.8
  • Average number of goals scored away: 1.48

The ratio of a team’s average and the league average is what constitutes “attacking strength.”

This gives us a measurement of comparison between teams. Now that we know the average we have a metric which shows which teams are above average and which are below.

Calculating Defensive Strength

We can now look at the average number of goals a team concedes. This gives us a defensive metric to use.

To do this we simply have to invert 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: 1.48
  • Average number of goals conceded away from home: 1.8

Now we have a metric to use for defensive strength.

Poisson Distribution Example

Let’s use Man City and Man Utd as an example to use. Man City topped the Premier League in the 2023/2024 season and had incredibly impressive numbers.

We will start with their attacking strength!

  1.  Step 1 – Number of goals scored at home by Man City (51) divided by number of home games (19). (Sum – 51/19 = 2.68).
  2.  Step 2 – Divide this value by the seasons average for goals scored at home. Sum – 2.68/1.8 = 1.48.

This gives us a value of 1.48 for Man City’s attacking strength. Now we need to look the defensive strength of Man Utd.

  1. Step 1 – Take the number of goals conceded away from home last season by Man Utd away (30) divide by the number of away games (19). (Sum – 30/19 = 1.57)
  2. Step 2 – Divide this by the season’s average goals conceded by an away team per game (1.57/1.8)

We now have a defensive value for Man Utd of 0.87.

Poisson Calculation For Man City Number Of Goals

We can now use the following formula to calculate the likely number of goals Man City might score against Man Utd. This is done by multiplying Man City’s attack strength by Man Utd defensive strength. Alongside the average number of home goals in the Premier League.

1.48 x 0.87 x 1.8 = 2.31

Using the Poisson distribution we now have an expected number of 2.31 goals to be scored for Man City.

We still however need to predict the number of goals that Man Utd may score.

Poisson Calculation For Man Utd Number Of Goals

To calculate the likely number of goals for Man Utd we use the same formula’s as above. However we replace them with the average number of away goals.

Man Utd attacking strength numbers:

Goals scored away (26/19) = 1.36/1.48 (average away goals scored) = 0.91

Man City defensive strength numbers:

Goals conceded at home (16/19) = 0.84/1.48 (average away goals scored) = 0.56

In the same way we predicted the number of goals Man City will score. We can calculate the likely number of goals Man Utd might score away from home. This is done by multiplying Man Utd’s attacking strength by Man City’s defensive strength and the average number of away goals in the Premier League.

0.91 x 0.56 x 1.48 = 0.75

This gives Man Utd an expectancy of 0.75 goals away from home against Man City.

Poisson Distribution in football – Predicting Multiple Scores

We now  have the average for the expected number of  goals from both teams.

  • Man City expected goals = 2.32
  • Man Utd expected goals = 0.75

A football match cannot finish 2.3 – 0.75 as a final score. However what this does is give us the data that we need to use for the poisson distribution formula. This is a mathematical formula created by Simeon Denis Poisson (hence the name).

It allows us to use these figures to distribute 100% of probability across a range of goal outcomes for each side.

Poisson Distribution formula:

P(x; μ) = (e-μ) (μx) / x!

Poisson Distribution Online Calculators

If you are not great with algebra do not worry!

There are some excellent free Poisson calculators available online which do all of the hard work for you.

Since a win is great website to use if you are looking at Poisson distribution for predicting football scores in betting. The website does all work for you. It will take the goal expectancy averages and calculate a number of different probabilities for:

  • Match Odds
  • Goals Over/Under
  • Clean Sheet
  • Both teams to score
  • Correct score

Poisson Distribution For Football Betting – Drawbacks

Poisson distribution is great way to get an outline of the most likely scenarios of a football match, alongside probabilities for each possible scenario. However, it is a method that definitely has its drawback and should probably be the sole reason you place a bet.

This strategy does not take into account the more human factors of a football match, such as:

  • Player Injuries
  • Form
  • Managerial Changes
  • Weather Conditions
  • Time Between Games (Are players tired or well rested?)
  • League Conditions
  • Predicted Line Ups

As such you should always consider what other factors are possibly affecting an upcoming game. Using Poisson distribution could indicate there is strong value in a bet. It is wise to look at whether there are other factors which may be at play.

Related: Corners Betting in Football: A Market Full of Hidden Value?

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