Here at ThePuntersPage (TPP) we’re dedicated to building a trustworthy brand and strive to provide the very best content and 5️⃣ offers for our readers. Please note that some of the links included on TPP may be affiliate links, which means 5️⃣ we may earn a commission (at no additional cost to you) if you click on a link and subsequently open 5️⃣ an account. We only recommend products and companies we use and trust. To learn more, visit our About Us Page 5️⃣ .
Poisson distribution in betting is used to calculate the frequency of any occurrence in a game. In this article, you 5️⃣ will learn how to calculate the probability of any score in football, and how to use it to calculate who 5️⃣ is likely to win.
What is Poisson Distribution in Betting?
Poisson distribution was developed by 19th century French mathematician Siméon Denis Poisson. 5️⃣ It is a probability theory that uses historical sports data to predict the outcome of a sports event. It measures 5️⃣ the likelihood of how many times an event will occur during a specific period.
This may seem complicated to someone who 5️⃣ has no background in maths, but it is actually a fairly simple method. To put it simply in terms of 5️⃣ football betting, Poisson distribution can help you predict how likely each number of goals scored is.
Why is Poisson Distribution Important?
When 5️⃣ bookies set their odds, it is important to know how likely any event is, based on past performance. Bookies do 5️⃣ not simply come up with odds out of the blue. They use mathematical models. If you want to take a 5️⃣ scientific, mathematical approach to betting, you should calculate for yourself how likely you think a specific game event, or set 5️⃣ of events will be. That is the first step to finding value. If you have found something that is more 5️⃣ likely to happen than what the bookies predict, that is what value is.
Poisson distribution in betting is particularly relevant for 5️⃣ games like football, where scoring happens on an incremental scale. It helps you determine the likelihood of each possible score.
The 5️⃣ Poisson distribution is commonly used to calculate the likelihood of a specific score in football, as well as a win, 5️⃣ lose or draw. You need to first calculate your league’s average goal expectancy, along with the attack strength and defence 5️⃣ strength for both sides.
How to calculate goal expectancy
Your team's goal expectancy depends on your team’s attack strength and defence strength, 5️⃣ and as well as that of the opposite team.
In our example, we will use the data from the 2024-2024 English 5️⃣ Premier League to calculate a hypothetical match between Manchester City and Liverpool. Manchester is the home team, while Liverpool is 5️⃣ the away team.
Before calculating these, we need to know:
The total home goals scored by all EPL teams
The total away goals 5️⃣ scored by all EPL teams
The average number of home goals and away goals per match for the whole league
We need 5️⃣ to calculate Manchester City’s:
Home goal average
Average goals allowed per home match
We need to calculate Liverpool’s:
Away goal average
Average goals allowed per 5️⃣ away match
These stats are easy to find at the Premier League’s official site.
Calculating Attack Strength
With these results, we can easily 5️⃣ calculate attack strength for the home and away team. Attack Strength is the team’s average number of goals, divided by 5️⃣ the league’s Average number of goals.
Home
Manchester City’s Attack Strength: 3.00 ÷ 1.53 = 1.96
Away
Liverpool’s Attack Strength: 1.78 ÷ 1.147 = 5️⃣ 1.55
Calculating Defence Strength
Calculating Defence Strength is just as easy. Simply divide the team’s average number of goals allowed by the 5️⃣ league’s average number of goals allowed.
Manchester City’s Defence Strength: 0.63 ÷ 1.147 = 0.55
Away
Liverpool’s Defence Strength: 0.63 ÷ 1.532 = 5️⃣ 0.41
Goal expectancy
Now that we have determined each team’s Attack Strength and Defence Strength, we can calculate each team’s likely score.
Manchester 5️⃣ City goal expectancy
To determine how many goals Manchester City will likely score, we need to multiply Manchester City’s Attack Strength 5️⃣ by Liverpool’s Defence Strength and the league’s average number of home goals.
That gives us:
1.96 × 0.41 × 1.532 = 1.23
Liverpool 5️⃣ goal expectancy
To determine how many goals Liverpool will likely score, we need to multiply Liverpool’s Attack Strength by Manchester City’s 5️⃣ Defence Strength and the league’s average number of away goals.
That gives us:
1.55 × 0.55 × 1.147 = 0.997
Average goals scored 5️⃣ 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 5️⃣ each team’s home and away defence and attack strengths, we can easily use them with the Poisson formula to calculate 5️⃣ the probability of any possible outcome.
The Poisson Formula
The Poisson Formula is:
P (k events in interval) = (λk e –λ) / 5️⃣ k!
In this formula:
P is the probability
is the probability k is the number of occurrences in the interval (number of goals)
is 5️⃣ the number of occurrences in the interval (number of goals) λ is the expected number of goals
is the expected number 5️⃣ of goals e is Euler's number (e = 2.71828…)
is Euler's number (e = 2.71828…) k! is the factorial of k
Poisson 5️⃣ Calculator
Using this formula, you can calculate the probability for any number of goals. However, there are plenty of online calculators 5️⃣ which will make the job simpler. To use the calculator, fill in each possible score (limit yourself from 1 to 5️⃣ 5) separately in the top in “Event occurrences”, and the expected average goals score per match in the bottom, in 5️⃣ “Expected event occurrences”.
That gives us the following probability for Manchester City Goals:
That gives us the following probability for Liverpool City 5️⃣ Goals:
Predicting the match outcome based on these probabilities
To get each possible score, simply multiply the probability of each possible score 5️⃣ by each team by the probability of each possible score by the other team. This gives you the following distribution:
As 5️⃣ you can see, the most likely score is 1 – 1, or 1 – 0 followed by 0 – 0 5️⃣ or 0 – 1. Given the defence averages of both teams, it is easy to see how these would be 5️⃣ very likely scores.
How Bookies Convert Estimated Chance Into Betting Odds
Bookies use Poisson distribution to calculate betting odds for outcomes in 5️⃣ various markets. You can do the same by converting your calculated probabilities into odds. The calculations are quite simple.
To calculate 5️⃣ the chance of a Manchester City win , we add all the red squares from the table above: that gives 5️⃣ us an estimated chance of 0.4142, or 41.42%
, we from the table above: that gives us an estimated chance of 5️⃣ 0.4142, or 41.42% To calculate the chance of a Liverpool win , we add all the green squares from the 5️⃣ table above: that gives us an estimated chance of 0.29867, or 29.87%
, we from the table above: that gives us 5️⃣ an estimated chance of 0.29867, or 29.87% To calculate the chance of a draw, we add all the yellow squares 5️⃣ from the table above: that gives us an estimated chance of 0.286118, or 28.61%
To convert each of these chances into 5️⃣ odds, we use the following formula:
Odds = 1/ (probability)
That gives us the following odds:
Manchester City win: 1/ (0.4142) = 2.4390
1/ 5️⃣ (0.4142) = 2.4390 Liverpool win: 1/ (0.29867) = 3.3333
1/ (0.29867) = 3.3333 Draw: 1/ (0.286118) = 3.4483
You can convert these 5️⃣ to American or fractional odds, but decimals are easier to work with. The calculator on our page about implied probability 5️⃣ should help you do the maths faster.
Advantages of Poisson Distribution in Betting
Using Poisson distribution in betting has many advantages. First 5️⃣ of all, it helps you understand how odds are set in the first place. By adding up the likelihood of 5️⃣ various possibilities, bookies are able to set up relatively accurate odds. You can do the same and compare your result 5️⃣ to what the bookies are presenting. Betting lines are not only set by using these equations. Popular matches in particular 5️⃣ often see the odds offered (betting lines) change, as more money comes in on a particular outcome.
That is one example 5️⃣ of how you can use Poisson distribution to beat the bookies. Comparing your own odds to the ones offered by 5️⃣ the bookies is part of a sound betting strategy.
Limitations of Poisson Distribution in Betting
Poisson distribution is a mathematical formula that 5️⃣ offers estimated probabilities, not certainties. The more data it has to rely on, the more accurate it can get. On 5️⃣ the other hand, no squad is the same for each match of the year.
A player’s injury or absence can make 5️⃣ a huge difference in how the entire squad will perform. At the beginning of the season, most teams also have 5️⃣ a different line-up than the year before. This makes setting odds using data from a previous season problematic. Still, that 5️⃣ does not necessarily put you at a disadvantage, since the bookies also have fewer data to rely on.
As the season 5️⃣ goes longer, it becomes easier to predict, since there is more current data available.
It is not so hard to create 5️⃣ your own Poisson distribution calculator with Excel; in fact, you do not need to download one from an external site. 5️⃣ This step-by-step guide will show you how to make your own.
1. Calculate your team’s expected goals
First, calculate your team’s expected 5️⃣ goals. That is the team's average attack strength × the other team’s defence strength × average goals per match. Below, 5️⃣ we calculated Manchester City’s expected goals at 1.23.
Check out: Expected Goals Explained.
2. Create the following table in Excel:
3. Go to 5️⃣ the square next to 0, and right click.
4. Click on formulas> Insert Function > Poisson.Dist
5. Fill in:
X = B5 (or 5️⃣ click on the number next to 0)
Mean = 1.23 (Your team’s expected goals)
Cumulative = FALSE
6. Move the cursor to the 5️⃣ bottom right of C5 and use the plus cursor to drag the formula down.
This gives you the Poisson distribution for 5️⃣ 0 to 5 goals of the expected goal average which is 1.23. You can combine the results of your team’s 5️⃣ probabilities to get a distribution that looks like this (the same as the above).
Here at ThePuntersPage we have a full 5️⃣ range of football statistics that you may also like to check out ranging across all the major countries and leagues:
Player 5️⃣ Stats
Team Stats
Profit & Loss Stats
Streaks & Trends
Poisson Distribution FAQs How do you use Poisson Distribution in football? Poisson distribution uses 5️⃣ probability to determine the odds of any score, based on both team’s past performance and league averages. First, you need 5️⃣ to calculate each team’s attack and defence strength and multiply them by the league average. Next, you use the Poisson 5️⃣ formula to determine the likelihood of any individual score. How do you predict football scores? One way to predict football 5️⃣ scores is with Poisson distribution. This is a mathematical way to estimate the probability of any score. It is based 5️⃣ on both team’s past performance and league averages. Use it to calculate each teams the likelihood of each possible number 5️⃣ of goals for a team, and multiply that by the likelihood of each possible number of goals for the other 5️⃣ team. How is goal expectancy calculated in football? Goal expectancy in football uses the following formula: Attack Strength of the 5️⃣ team × Defence Strength of the other team × the league’s Average Number of Goals. How do you calculate the 5️⃣ attack strength of a football team? Attack Strength is the team’s average number of goals divided by the league’s Average 5️⃣ number of goals for that season. How do you calculate the probability of winning a football match? Using Poisson distribution, 5️⃣ the probability of winning a football match is the sum of the probabilities of each individual possible winning score. How 5️⃣ do you make your own odds? To make your own odds, first calculate or estimate the likelihood of an event, 5️⃣ then use the following formula: Odds = 1/ (probability). Compare your odds to your bookie's odds to see if they 5️⃣ offer any value.
ThePuntersPage Final Say
It can be a bit of work understanding how to calculate odds for various game outcomes. 5️⃣ Once you understand Poisson distribution, it becomes much simpler. Luckily, our calculators, as well as the Excel method explained in 5️⃣ this article, can help you. Knowing estimated odds and comparing them to the bookies odds is a sure path to 5️⃣ finding value in betting.
