The Poisson distribution is a well-known and simple theory that can be used for predicting football matches. Knowing how to apply the Poisson distribution in football helps making better informed betting decisions. This is one of the essentials of making money with betting. In this guide we will learn how to accurately predict football matches by applying the theory of the Poisson distribution.
*Note – This series includes a handy Excel spreadsheet that covers all the theory and corresponding Excel formulas (download link at the bottom of this page). By downloading this Excel spreadsheet you can immediately apply everything you have learned and start predicting football matches by using the Poisson distribution right away!
Recap – What is the Poisson distribution again? ◄
Let me start with a definition: the Poisson distribution is a probability distribution that can be used to measure the likelihood of different events to occur within a certain interval of time (e.g. the number of goals scored in a game of football).
Now the above sounds reasonable, but how does this relate to predicting football matches? Well, suppose that we expect Manchester City to score 2 goals in their next game. By using the Poisson distribution we can easily calculate the probability that Man City will score 1 goal (27%), 2 goals (27%) or 3 goals (18%). Further, if we would also know that their opponent (let’s say Man Utd) is expected to score 1 goal in this game, we can derive the probability for a Man City win, a draw and a Man Utd win as well.
As you can see we can break the above down into three parts:
- Calculate the expected number of goals (xG) that Man City and Man Utd will score.
- Based on (1), calculate the probability that both teams will score 1, 2, 3 or even more goals.
- Knowing the expected number of goals that both teams will score, calculate the probability for a Man City win, a draw and a Man Utd win.
In the first article of this two part series we have focused on step (1). After completing the first article we can start transforming our expected goals predictions into Match Odds predictions (i.e. home win, draw, away win) by using the Poisson distribution. In order to do this we should first complete step (2). After that, we can easily predict the Match Odds, Over/Under and Correct Score markets for the complete English Premier League ( Step 3).
Note: if you need more guidance, you might first want to download the Excel spreadsheet from the bottom of this page. You can use this spreadsheet as a reference, since this enables you to find out exactly what I have done and what Excel formulas I have used to create this guide.
► How to apply the Poisson distribution in Excel?
Let’s say we want to calculate the probability that the Manchester Derby will end in a 2-0 win for Man Utd. However, how can we do this? This is where the advanced maths (the Poisson distribution) come into play. Luckily, Excel does all the hard work for us. All we have to know is how to apply the Excel function POISSON.DIST ( x, mean, cumulative ), with the following parameters:
- x = The number of goals scored.
- mean = The expected goals (xG) value.
- cumulative = FALSE, since we want to calculate the probability that the number of goals scored is exactly x instead of greater than or equal to x.
Fore more information about the POISSON.DIST function check the official guide written by the Microsoft Office Support Team.
Note: in this betting guide you don’t need to know the mathematical formulas behind the Poisson distribution. However, check this excellent guide if you want to dive deeper into the Poisson distribution and its formulas. This guide covers everything you need to know about the Poisson distribution.
► How to predict the chance of a 2-0 win for Man Utd?
By using the Excel function POISSON.DIST we can easily calculate the probability of all theoretically possible match scores in the Manchester Derby. Previously we have already calculated that the expected number of goals scored in this match by Man Utd and Man City is equal 0.64 and 2.1 respectively. For calculating the probability of a 2-0 home win, we multiply the chance that Man Utd scores 2 goals by the chance that Man City scores 0 goals. Below you can see how:
Man Utd | Calculate probability of scoring 2 goals
Man City | Calculate probability of scoring 0 goals
Calculate chance of a 2-0 win for Manchester United
As you can see the likelihood of a 2-0 win for Manchester United is equal to 1.3%. This result appears to be very unlikely. Now what if we want to calculate the probability of Man Utd winning the match, regardless of the exact score? We simply repeat the above calculation for every possible Man Utd win (e.g. 1-0, 2-0, 2-1, 3-1, 3-0, …). Therefore, our next step is to calculate the likelihood of all other possible match outcomes.
► Use Poisson distribution to predict all scores
We have already learned how to calculate the probability that the match will end in a 2-0 win for Manchester United. Now the next step is to calculate every other match outcome as well. Below I have visualized the distribution of all possible outcomes within a range of 10 goals per team. I have opted for a range of 10 goals, since this includes more or less every practically possible outcome.
As you can see the most probable outcome is a 0-2 victory for Man City, which happens with a 14.2% chance. Moreover, it is clear that Man City is the favourite to win this match, since they also have a relatively good chance of winning with the match with either 0-1 (13.5%) or 0-3 (10%).
The above results can already be applied to betting in the Correct Score market. However, if we put in a tiny amount of extra work we can easily predict other betting markets as well. For example, we could predict the Over/Under 1.5, 2.5 or 3.5 goals markets or the Match Odds market. Since I think predicting the Match Odds market is most fun, we will take our predictions one step further and start predicting the 1X2 Match Odds of this match as well.
► Use Poisson to predict football matches
At first we will calculate the probability for a draw. Since we know the probability that the match will end in either 0-0, 1-1, 2-2, …, 10-10 we can easily calculate the likelihood of the matching ending in a draw. This can be done by summing over all possible draw outcomes from the above table. Thus, the likelihood of a draw is equal to the sum of the chances of the match ending in 0-0, 1-1, 2-2, 3-3, …, 10-10, which is equal to 18.5%.
Calculate the probability for a draw to occur
In the same way we can calculate the chance that Manchester United will win, and the chance that Manchester City will win the Manchester Derby. For example, calculating the probability for a home win can be done by summing over all possible home wins (i.e. 1-0, 2-0, 2-1, 3-0, 3-1, 3-2…, 10-9).
Calculate the probability of a Manchester United win
Calculate the probability of a Manchester City win
From the above match probabilities we can immediately calculate the Match Odds as well. The corresponding formula is as follows: we divide 1 by the probability P that an event occurs (i.e. 1/P). For example, the odds for a draw are equal to 5.4 (=1/18.5%). The below image shows all the Match Odds predictions for the Manchester United – Manchester City game. Thus, according to our Poisson model, Man City are the clear favorites with a 71.4% chance of winning the match.
► What to conclude about our Poisson model?
In this two part series we have learned how to accurately predict the Correct Score and the Match Odds markets in football by using the Poisson distribution. Further, the corresponding Excel spreadsheet can be downloaded from the download link on the bottom of this page. In this guide we have built a framework for predicting football matches in the English Premier League based on the results of the 2018-2019 season. Moreover, this framework can easily be extended to other leagues as well. For example, if you want to predict the Serie A you can simply replace the Premier League data by Serie A data. It should be mentioned that this model is particularly suited for predicting regular competitions.
Predicting international competitions (e.g. Champions League, Europa League) is going to be a lot more difficult. In general, predicting matches between teams from different competitions is very difficult, even for the bookmakers. For example, how can we accurately predict a match between Liverpool and Real Madrid? This would require us to compare the league strengths of both the Premier League and the Primera División, which is a very difficult task. It is possible, but it would require a lot of extra work.
Limitations of this Poisson distribution model
The Poisson distribution model that we have implemented can form a basis for multiple profitable betting strategies, but it has a couple of limitations as well. At first, factors like managerial changes or important players injured/suspended are not included in the model. Moreover, at the start of the season we base our predictions solely on the results from the previous season. Summer period transfers are not included in the model. That makes it particularly difficult to predict the first matches of the season. Further, the model only takes into account the final score. Since goals are rare, it sometimes happens that the dominant team loses the match by conceding a goal on the counter attack. Factors like shots (on target) or created chances are not included in the model.
Download Excel spreadsheet
► Final words
Hopefully you have enjoyed this betting guide. As always: if you have any questions you can either reply below, or send me an e-mail: firstname.lastname@example.org. Feedback is always welcome!