Poisson Distribution can be used to calculate the score of a soccer match.

By the time you’ve read this guide, you’ll be able to use Poisson Distribution to predict the scores and apply them to your betting strategy.

Here’s how to use Poisson Distribution for soccer betting.

## What Is Poisson Distribution?

Poisson distribution is a statistical distribution that shows how many times an event is likely to occur within a specified period of time. It is used for independent events which occur at a constant rate within a given interval of time.

In sports betting, Poisson Distribution can be used to translate averages into probabilities.

As such, in order to predict the score of a soccer match, we first need to calculate how many goals a team is likely to score on average.

This is done by calculating the Attack Strength and Defence Strength of both teams.

From here, the results can be compared to the sportsbooks’ odds to find value.

Now, it’s very important to select the right range of data; using too much and the data will not be relevant, while using too little can skew the results.

A good range would be to use league every game a team plays throughout a season.

For this article, we will use the 2018/19 EPL season.

Here are the EPL home and away tables:

Home EPL Table

Away EPL Table

## Calculating Attack Strength

We need to determine the average number of goals scored per team at home and away from home.

Here’s how to calculate:

- Total number of goals scored at home / total number of games in the season
- Total number of goals scored away from home / total number of games in the season

The above tables show there were 596 goals scored across 380 games at home, while there were 476 goals scored across 380 games away from home.

This shows:

- Average number of goals scored at home: 1.568
- Average number of goals scored away from home: 1.253

A team’s** Attack Strength **is the ratio between their average and the league’s average.

## Calculating Defence Strength

Similarly, we need to determine the average number of goals conceded per team at home and away from home.

This is simply the inverse of the Attack Strength numbers:

- Average number of goals conceded at home: 1.253
- Average number of goals conceded away from home: 1.568

A team’s** Defence Strength **is the ratio between their average and the league’s average.

## Predicting Goals In Soccer Matches

Here’s the match we are going to predict the goals for:

### Predicting Chelsea Goals Scored

Step 1: Calculate Chelsea’s Attack Strength:

- Average goals scored at home by Chelsea = 39/19 = 2.053
- League average goals scored at home = 1.568

Chelsea’s Attack Strength = 2.053/1.568 = 1.309

Step 2: Calculate Man Utd’s Defence Strength:

- Average goals conceded away from home by Man Utd = 29/19 = 1.526
- League average goals conceded away from home = 1.568

Man Utd Defence Strength = 1.526/1.568 = 0.973

We can now use the following formula to calculate the likely number of goals Chelsea will score:

Predicted Goals = Attack Strength * Opposition Defence Strength * League Average Home Goals

So, for Chelsea:

Predicted Goals = 1.309 * 0.973 * 1.568 = 1.997

### Predicting Man Utd Goals Scored

Step 1: Calculate Man Utd’s Attack Strength:

- Average goals scored away from home by Man Utd = 32/19 = 1.684
- League average goals scored away from home = 1.253

Chelsea’s Attack Strength = 1.684/1.253 = 1.369

Step 2: Calculate Chelsea’s Defence Strength:

- Average goals conceded at home by Chelsea = 12/19 = 0.631
- League average goals conceded at home = 1.253

Man Utd Defence Strength = 0.631/1.253 = 0.504

This uses the same formula as above but replaces the average home goals with the average away goals.

So, for Man Utd:

Predicted Goals = 1.369 * 0.504 * 1.253 = 0.865

## Poisson Distribution For Predicting Soccer Matches

Now, it’s obvious that the match between Chelsea and Man Utd is not going to finish 1.997 vs 0.865 – this is just the average.

This is where Poisson Distribution comes in handy.

It allows us to use these average scored to distribute 100% of probability across a range out outcomes.

The Poisson Distribution formula is as follows:

P(x; μ) = (e-μ) (μx) / x!

While this may look confusing, we can use a Poisson Distribution Calculator to do most of the work.

Simply enter:

- The number of different events that could occur, ie the number of goals a team could score
- The average number of goals they are likely to score.

In this example, we would choose:

- Between 0 and 5 goals
- Our previously calculated average Predicted Goals for Chelsea (1.997) and Man Utd (0.865).

The calculator then shows the probability of the score for this match.

## Poisson Distribution For Chelsea vs Man Utd

This example shows that Chelsea has a 13.57% chance of not scoring, but a 27.11% chance of scoring one goal and a 27.07% chance of scoring two goals.

On the other hand, Man Utd have a 42.11% chance of not scoring, a 36.42% chance of scoring one goal and a 15.75% chance of scoring two goals.

Both scores are independent in terms of mathematics.

As a result, the expected score from this game is 1-0, since these are the most probable outcomes for both teams.

Note that the probability of this outcome can be calculated by multiplying the two most probable outcomes together ie

0.2711 * 0.4211 = 0.1141 or 11.41%

## Converting Probabilities Into Odds

Using the above example, we can see that there is a 9.87% chance of the match ending 1-1 after applying Poisson Distribution.

But how can you calculate the odds on draw?

To do this, calculate the probability of all possible draw combinations.

Then add them together.

Now, there are an infinite number of possible scorelines (for example, technically both teams could score 10 each) but the chances of the score ending 5-5 and above are tiny, so it’s safe to disregard them from this distribution.

Using the Chelsea vs Man Utd example:

Adding these up gives a probability of 21.04% that the match ends as a draw.

This gives true odds of 4.75 (1/0.2104).

## The Limits Of Poisson Distribution

While this is a simple model, Poisson Distribution fails to consider situational factors, such as game status, and the subjective evaluation of a change in team during a transfer window.

In this case, for example, the above Poisson formula does not take into account any effects that new manager Frank Lampard could have had on the team.

Poisson also ignores correlations. For example, games that take place during wet weather tend to have few goals scored.

These areas become important in lower league games, creating an edge opportunity.

Considering how big the English Premier League is and the wealth of resources at a sportsbook’s disposal, it’s tough to get an edge

Finally, Poisson does not consider the sportsbook’s margin built into the odds, which is crucial for finding value bets.

## Conclusion

Poisson Distribution can help you predict the score of a soccer game.

While it has its flaws, it can still give you a decent estimate.

Now we’d like to hear from you.

Have you ever used Poisson Distribution in soccer?

Or in any other sport?

Let us know in the comments below or over on Twitter.