Poisson Calculator

Written by: Alex Windsor
Fact checked by Brian Webb  
Updated: June 19, 2024

Siméon Denis Poisson is a French mathematician and physicist whose contributions are of incredible value and they’re widely used in many real-world applications, including sports betting.

Poisson distribution is a probability theory that can show the likelihood of a given number of events happening within a particular time interval. While it can be used to predict the number of disease cases, the number of patrons walking into your local pub at a given time of the day, or the possibility of a Boeing 747 engine failure on your trip to Benidorm, it can also calculate goal probabilities and betting odds in football matches.

Bookies use this mathematical model to come up with their odds. However, you can use it too to calculate the most likely score-line and give yourself a pat on the back during your never-ending search for better value.

How Our Free Poisson Calculator Works

The Poisson calculator is based on the Poisson Distribution formula and is easier to use than the appearance of the formula suggests. To obtain the odds for a particular game using it, enter the expected average number of goals for each team, and as Siméon Denis Poisson himself would say, Voilà.

Let’s take a football match as an example. For the Poisson calculator to work, you first need to find out both teams’ attack strength and defence strength and their average goal expectancy.

Here is a step-by-step guide on how to do so based on statistics from the 2022/2023 English Premier League season and a hypothetical matchup between Manchester City and Manchester United.

Step 1: Calculate the Attack Strength of Each Team

To calculate the Attack Strength of the hosts, Manchester City in this case, you must divide their average number of goals scored at home by the league’s average number of home goals.

To get Man City’s average number of goals scored at home, divide the number of goals they scored at the Etihad by the number of games they played at home.

Premier League Table 1

To get the league’s average number of home goals, add up the total number of goals all teams scored at home during the season and divide it by the total number of games played at home, which in our case is 380 games, given the English Premier League has 20 teams, each playing 19 games in front of their crowd.

To obtain the Attack Strength of the visitors, Manchester United, you should divide their average number of goals scored away by the league’s average number of away goals.

To get United’s average number of goals scored away, divide the total number of goals they scored in their away games by the number of games played away.

Premier League Table 2

To get the league’s average number of away goals, add up the total number of goals all teams scored in their away games and divide it by 380 – the total number of away games.

According to our data from the 2022/2023 season:

#Goals scored at home (All EPL teams)Goals scored away (All EPL teams)Goals scored at home (Manchester City)Goals conceded at home (Manchester City)Goals scored away (Manchester United)Goals conceded away (Manchester United)
Goals68446360172233
Matches38038019191919
Goals Per Match1,81,2183,1570,8941,1571,736

Manchester City Attack Strength: 3,157 / 1,8 = 1,753

Manchester United Attack Strength: 1,157 / 1,218 = 0,949

Step 2: Calculate the Defence Strength of Each Team

The process for obtaining the defence strength values is nearly identical.

To get the defence strength of Man City, divide the average number of goals they conceded at home by the league’s average.

To get Man City’s average number of goals conceded at home, divide the total number of goals conceded at The Etihad by the number of games played there.

Premier League Table 3

Figuring out the league’s average number of goals conceded is a tad easier, as all you have to do is switch the numbers since the average number of goals conceded at home will always equal the average number of goals scored away and vice versa.

To obtain the defence strength of Man United, divide the average number of goals they conceded on their away games by the league’s average number of away goals conceded.

Premier League Table 4

According to our data from the 2022/2023 season:

#Goals scored at home (All EPL teams)Goals scored away (All EPL teams)Goals scored at home (Manchester City)Goals conceded at home (Manchester City)Goals scored away (Manchester United)Goals conceded away (Manchester United)
Goals68446360172233
Matches38038019191919
Goals Per Match1,81,2183,1570,8941,1571,736

Manchester City Defence Strength: 0,894 / 1,218 = 0,733

Manchester United Defence Strength: 1,736 / 1,8 = 0,963

Step 3: Calculate the Goal Expectancy of Manchester City

Now that we know the values for the Attack Strength and Defence strength of Manchester City and Manchester United, calculating their likely score is easy.

To calculate the goal expectancy of Man City, multiply their Attack Strength value by Man United’s Defence value and the league’s average number of scored goals at home.

Manchester City Attack Strength: 1,753

Manchester United Defence Strength: 0,963

League’s average number of scored goals at home: 1,8

Goal Expectancy of Manchester City: 1,753 x 0,963 x 1,8 = 3,038

Step 4: Calculate the Goal Expectancy of Manchester United

To figure out the goal expectancy of Manchester United in this particular game, multiply their Attack Strength value by the Defence Strength value of Man City and the league’s average number of goals scored away from home.

Manchester United Attack Strength: 0,949

Manchester City Defense Strength: 0,733

League’s average number of away goals: 1,218

Goal Expectancy of Manchester United: 0,949 x 0,733 x 1,218 = 0,847

Step 5: Use Our Poisson Calculator

The Poisson Distribution formula might seem challenging to understand at first sight. However, now that you have figured out the goal expectancy values for both teams, you can go ahead and input them into our Poisson calculator and get the odds for the full-time result and the likely number of goals each team will score.

Poisson Calculator Example

Poisson Calculator Correct Scores

Does This Poisson Calculator Guarantee Success?

Although learning the Poisson Distribution formula and implementing it in your sports betting endeavours can be beneficial, remember that it is not a cheat code for guaranteed success at the bookies.

Yes, the formula might seem complex at first. However, at the end of the day, it is only a simple predictive model that generates results without considering any situational factors that could influence the outcome of the football match.

Poisson Calculator Formula

While the Poisson calculator, when provided with enough data and utilised accurately, can reveal the bigger picture, it certainly cannot account for factors such as fatigue, injuries, and dressing room atmosphere. Or, in our hypothetical case, the additional motivation of the players during the fiercest inter-city rivalries and Erik ten Hag’s determination to avoid getting sacked in the following morning.

Found our Poisson calculator useful? Why not check out our range of other free bet calculators and see how they can help you with your wagering this season.

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Alex, a ten-year iGaming industry veteran and Managing Editor at BettingTools specializes in sports betting and betting tools. He also provides insightful reviews, ensures the accuracy of all offers, and maintains content quality helping you make informed choices. Combining professional expertise with a passion for football and soccer, Alex ensures we offer you a reliable resource, focusing on betting tools to assist with odds, accas, and other betting strategies.