Poisson distribution in betting is used to calculate the frequency of any occurrence in a game. In this article, you will learn how to calculate the probability of any score in football, and how to use it to calculate who is likely to win.

- What is Poisson Distribution in Betting?
- Why is Poisson Distribution Important?
- Calculating Football Results
- How Bookies Convert Estimated Chance Into Betting Odds
- Advantages of Poisson Distribution in Betting
- Limitations of Poisson Distribution in Betting
- How to Create Your Own Poisson Football Spreadsheet
- TPP Football Stats Centre
- Player Stats
- Market Stats
- Profit & Loss Stats
- Streaks & Trends
- Poisson Distribution FAQs
- ThePuntersPage Final Say

## What is Poisson Distribution in Betting?

**Poisson distribution** was developed by 19^{th }century French mathematician **SimĂ©on Denis Poisson**. It is a **probability theory** that uses **historical sports data** to predict the outcome of a sports event. It measures the likelihood of how many times an event will occur during a specific period.

This may seem complicated to someone who has no background in maths, but it is actually a fairly simple method. To put it simply in terms of football betting, Poisson distribution can help you predict how likely each number of goals scored is.

## Why is Poisson Distribution Important?

When bookies set their odds, it is important to know how likely any event is, based on past performance. **Bookies do not simply come up with odds out of the blue.** They use mathematical models. If you want to take a scientific, mathematical **approach to betting**, you should calculate for yourself how likely you think a specific game event, or set of events will be. That is the first step to **finding value**. If you have found something that is more likely to happen than what the bookies predict, that is what value is.

Poisson distribution in betting is particularly relevant for games like football, where scoring happens on an incremental scale. It helps you determine the likelihood of each possible score.

## Calculating Football Results

The Poisson distribution is commonly used to calculate the likelihood of a specific score in football, as well as a win, lose or draw. You need to first calculate your **leagueâs average goal expectancy**, along with the **attack strength** and **defence strength** for **both sides**.

### How to calculate goal expectancy

Your **team's goal expectancy** depends on your teamâs **attack strength** and **defence strength**, and as well as that of the **opposite team.**

In our example, we will use the data from the 2018-2019 English Premier League to calculate a hypothetical match between Manchester City and Liverpool. Manchester is the home team, while Liverpool is the away team.

**Before calculating these, we need to know:**

- The total home goals scored by all EPL teams
- The total away goals scored by all EPL teams
- The average number of home goals and away goals per match for the whole league

**We need to calculate Manchester Cityâs:**

- Home goal average
- Average goals allowed per home match

**We need to calculate Liverpoolâs:**

- Away goal average
- Average goals allowed per away match

These stats are easy to find at **the Premier Leagueâs official site.**

### Calculating Attack Strength

With these results, we can easily calculate attack strength for the home and away team. **Attack Strength** is the **teamâs average number of goals, divided by the leagueâs Average number of goals.**

#### Home

**Manchester Cityâs Attack Strength:** 3.00 Ă· 1.53 = 1.96

#### Away

**Liverpoolâs Attack Strength: **1.78 Ă· 1.147 = 1.55

### Calculating Defence Strength

Calculating **Defence Strength** is just as easy. Simply **divide the teamâs average number of goals allowed by the leagueâs average number of goals allowed.**

**Manchester Cityâs Defence Strength: **0.63 Ă· 1.147 = 0.55

#### Away

**Liverpoolâs Defence Strength: **0.63 Ă· 1.532 = 0.41

### Goal expectancy

Now that we have determined each teamâs Attack Strength and Defence Strength, we can **calculate each teamâs likely score. **

#### Manchester City goal expectancy

To determine how many goals Manchester City will likely score, we need to **multiply** Manchester Cityâs **Attack Strength by **Liverpoolâs **Defence Strength** and the **leagueâs average number of home goals. **

**That gives us: **

1.96 Ă 0.41 Ă 1.532 = 1.23

#### Liverpool goal expectancy

To determine how many goals Liverpool will likely score, we need to **multiply** Liverpoolâs **Attack Strength** by Manchester Cityâs **Defence Strength** and the leagueâs average number of away goals.

**That gives us: **

1.55 Ă 0.55 Ă 1.147 = 0.997

#### Average goals scored in the match

**Manchester City:** 1.23

**Liverpool:** 0.997

### Using the Poisson Formula to calculate the likelihood of each possible score

Now that we have each teamâs home and away defence and attack strengths, we can easily use them with the **Poisson formula** to **calculate the probability of any possible outcome**.

#### The Poisson Formula

The Poisson Formula is:

**P (k events in interval) = ****(Î» ^{k }e ^{âÎ»}) / k!**

**In this formula:**

**P**is the probability**k**is the number of occurrences in the interval (number of goals)**Î»**is the expected number of goals**e**is Euler's number (e = 2.71828…)**k!**is the factorial of k

#### Poisson Calculator

Using this formula, you can calculate the **probability for any number of goals**. However, there are plenty of **online calculators** which will make the job **simpler.** To use the calculator, fill in **each possible score** (limit yourself from 1 to 5) separately in the top in **âEvent occurrencesâ**, and the **expected average goals score per match** in the bottom, in **âExpected event occurrencesâ.**

That gives us the following probability for Manchester City Goals:

That gives us the following probability for Liverpool City Goals:

### Predicting the match outcome based on these probabilities

To get each possible score, simply multiply the probability of each possible score by each team by the probability of each possible score by the other team. This gives you the following distribution:

As you can see, the most likely score is 1 â 1, or 1 â 0 followed by 0 â 0 or 0 – 1. Given the defence averages of both teams, it is easy to see how these would be very likely scores.

## How Bookies Convert Estimated Chance Into Betting Odds

Bookies use Poisson distribution to calculate betting odds for outcomes in various markets. You can do the same by converting your calculated probabilities into odds. **The calculations are quite simple**.

- To calculate the chance of a
**Manchester City win**, we**add all the red squares**from the table above: that gives us an estimated chance of 0.4142, or 41.42% - To calculate the chance of a
**Liverpool win**, we**add all the green squares**from the table above: that gives us an estimated chance of 0.29867, or 29.87% - To calculate the chance of a
**draw**, we add**all the yellow squares**from the table above: that gives us an estimated chance of 0.286118, or 28.61%

To convert each of these chances into odds, we use the following formula:

*Odds = 1/ (probability)*

#### That gives us the following odds:

**Manchester City win:**1/ (0.4142) = 2.4390**Liverpool win:**1/ (0.29867) = 3.3333**Draw:**1/ (0.286118) = 3.4483

You can convert these to American or fractional odds, but **decimals are easier to work with**. The **calculator on our page about implied probability** should help you do the maths faster.

## Advantages of Poisson Distribution in Betting

Using **Poisson distribution** in betting has **many advantages**. First of all, it helps you understand how **odds are set **in the first place. By adding up the likelihood of various possibilities, bookies are able to set up relatively accurate odds. You can do the same and compare your result to what the bookies are presenting. **Betting lines are not only set by using these equations**. Popular matches in particular often see the odds offered (betting lines) change, as more money comes in on a particular outcome.

That is one example of how you can use Poisson distribution to **beat the bookies**. **Comparing your own odds to the ones offered** by the bookies is part of a sound betting strategy.

## Limitations of Poisson Distribution in Betting

Poisson distribution is a mathematical formula that offers **estimated probabilities, not certainties**. The **more data** it has to rely on, the **more accurate** it can get. On the other hand, no squad is the same for each match of the year.

A playerâs injury or absence can make a huge difference in how the entire squad will perform. At the beginning of the season, most teams also have a different line-up than the year before. This makes setting odds using data from a previous season problematic. Still, that does not necessarily put you at a disadvantage, since the bookies also have fewer data to rely on.

**As the season goes longer, it becomes easier to predict, since there is more current data available**.

## How to Create Your Own Poisson Football Spreadsheet

It is not so hard to **create your own Poisson distribution calculator with Excel**; in fact, **you do not need to download one** from an external site. This step-by-step guide will show you how to make your own.

#### 1. Calculate your teamâs expected goals

First, calculate your teamâs expected goals. That is the team's average **attack strength Ă the other teamâs defence strength Ă average goals per match**. Below, we calculated Manchester Cityâs expected goals at 1.23.

Check out: Expected Goals Explained.

#### 2. Create the following table in Excel:

#### 3. Go to the square next to 0, and right click.

#### 4. Click on formulas> Insert Function > Poisson.Dist

#### 5. Fill in:

- X = B5 (or click on the number next to 0)
- Mean = 1.23 (Your teamâs expected goals)
- Cumulative = FALSE

#### 6. Move the cursor to the bottom right of C5 and use the plus cursor to drag the formula down.

This gives you the Poisson distribution for 0 to 5 goals of the expected goal average which is 1.23. You can combine the results of your teamâs probabilities to get a distribution that looks like this (the same as the above).

## TPP Football Stats Centre

Here at ThePuntersPage we have a full range of football statistics that you may also like to check out ranging across all the major countries and leagues:

## Player Stats

## Team Stats

## Profit & Loss Stats

## Streaks & Trends

## Poisson Distribution FAQs

Poisson distribution uses probability to determine the odds of any score, based on both teamâs past performance and league averages. First, you need to calculate each teamâs attack and defence strength and multiply them by the league average. Next, you use the Poisson formula to determine the likelihood of any individual score.

One way to predict football scores is with Poisson distribution. This is a mathematical way to estimate the probability of any score. It is based on both teamâs past performance and league averages. Use it to calculate each teams the likelihood of each possible number of goals for a team, and multiply that by the likelihood of each possible number of goals for the other team.

Goal expectancy in football uses the following formula: *Attack Strength of the team Ă Defence Strength of the other team Ă the leagueâs Average Number of Goals.*

Attack Strength is the teamâs average number of goals **divided by** the leagueâs Average number of goals for that season.

Using Poisson distribution, the probability of winning a football match is **the sum of the probabilities** of each individual possible winning score.

To make your own odds, first calculate or estimate the likelihood of an event, then use the following formula: *Odds = 1/ (probability). * Compare your odds to your bookie's odds to see if they offer any value.

## ThePuntersPage Final Say

It can be a bit of work understanding how to calculate odds for various game outcomes. Once you understand Poisson distribution, it becomes much simpler. Luckily, our calculators, as well as the Excel method explained in this article, can help you. Knowing estimated odds and comparing them to the bookies odds is a sure path to finding value in betting.