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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?
Poisson distribution was developed by 19th century French mathematician Siméon 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.
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 league’s 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 team’s attack strength and defence strength, ❤️ and as well as that of the opposite team.
In our example, we will use the data from the 2024-2024 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 City’s:
Home goal average
Average goals allowed per home match
We need to calculate Liverpool’s:
Away goal average
Average goals allowed per ❤️ away match
These stats are easy to find at the Premier League’s official site.
Calculating Attack Strength
With these results, we can easily ❤️ calculate attack strength for the home and away team. Attack Strength is the team’s average number of goals, divided by ❤️ 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 = ❤️ 1.55
Calculating Defence Strength
Calculating Defence Strength is just as easy. Simply divide the team’s average number of goals allowed by the ❤️ 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 = ❤️ 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 ❤️ City goal expectancy
To determine how many goals Manchester City will likely score, we need to multiply Manchester City’s Attack Strength ❤️ 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 ❤️ goal expectancy
To determine how many goals Liverpool will likely score, we need to multiply Liverpool’s Attack Strength by Manchester City’s ❤️ 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 ❤️ 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 team’s 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) = (λk e –λ) / ❤️ k!
In this formula:
P is the probability
is the probability k is the number of occurrences in the interval (number of goals)
is ❤️ the number of occurrences in the interval (number of goals) λ is the expected number of goals
is the expected number ❤️ of goals e is Euler's number (e = 2.71828…)
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 “Event occurrences”, and the expected average goals score per match in the bottom, in ❤️ “Expected event occurrences”.
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 – 1, or 1 – 0 followed by 0 – 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%
, we 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%
, we 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
1/ ❤️ (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 ❤️ 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 player’s 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.
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 team’s expected goals
First, calculate your team’s expected ❤️ goals. That is the team's average attack strength × the other team’s defence strength × average goals per match. Below, ❤️ 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 ❤️ 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 team’s 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 team’s ❤️ probabilities to get a distribution that looks like this (the same as the above).
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 How do you use Poisson Distribution in football? Poisson distribution uses ❤️ probability to determine the odds of any score, based on both team’s past performance and league averages. First, you need ❤️ to calculate each team’s 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. How do you predict football scores? 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 team’s 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. How is goal expectancy calculated in football? Goal expectancy in football uses the following formula: Attack Strength of the ❤️ team × Defence Strength of the other team × the league’s Average Number of Goals. How do you calculate the ❤️ attack strength of a football team? Attack Strength is the team’s average number of goals divided by the league’s Average ❤️ number of goals for that season. How do you calculate the probability of winning a football match? Using Poisson distribution, ❤️ the probability of winning a football match is the sum of the probabilities of each individual possible winning score. How ❤️ do you make your own odds? 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.
