How to Use Poisson Distribution for Predicting Football Matches (Part 2) [Excel-Guide]

How to use the Poisson distribution for predicting football matches in the English Premier League

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:

  1. Calculate the expected number of goals (xG) that Man City and Man Utd will score.
  2. Based on (1), calculate the probability that both teams will score 1, 2, 3 or even more goals.
  3. 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:

Expected goals for Manchester United versus Manchester City
Man Utd | Calculate probability of scoring 2 goals

\textrm{P[Man Utd 2 goals]}= \textrm{POISSON.DIST ( } 2, 0.64, \textrm{FALSE )}=0.108=10.8\%

Man City | Calculate probability of scoring 0 goals

\textrm{P[Man City 0 goals]}=\textrm{POISSON.DIST ( } 0, 2.10, \textrm{FALSE )}=0.122=12.2\%

Calculate chance of a 2-0 win for Manchester United

\textrm{P[Man Utd 2-0 Man City]}= \textrm{P[Man Utd 2 goals]} \times \textrm{P[Man City 0 goals]}=

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.

Correct score market prediction in football

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

\textrm{P[Draw]}= \textrm{P[0-0]} + \textrm{P[1-1]} +...+ \textrm{P[10-10]} =6.4\%+8.7\%+...+0\%=18.5\%

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

\textrm{P[Home]}= \textrm{P[1-0]} + \textrm{P[2-0]} +...+ \textrm{P[10-9]} =4.1\%+1.3\%+...+0\%=10.1\%

Calculate the probability of a Manchester City win

\textrm{P[Away]}= \textrm{P[0-1]} + \textrm{P[0-2]} +...+ \textrm{P[9-10]} =13.5\%+14.2\%+...+0\%=71.4\%

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.

Match odds market prediction in football

► 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: Feedback is always welcome!

21 Comments on “How to Use Poisson Distribution for Predicting Football Matches (Part 2) [Excel-Guide]”

  1. Really enjoyed working through this. Thanks .The download was a great addition . i look forward to your new stuff. somthing to keep me busy in these terrible days.

  2. Great work with examples. I look forward to continuing your work. In the future, it is good to take into account the absence of the team’s leading players in the game, the importance of the home field, the threat to leave the league standings.

  3. Very difficult to understand the calculation on home win, draw and away win please can you explain it for me please in a plain form.thanks

    1. Hi Wellington, happy to help! I would first advise you to analyze the formulas that I have used in the included Excel spreadsheet. If this does not work out for you, send me an e-mail or contact me on Twitter and I will take my time to help you out.

  4. Hi George I’ve downloaded app for under Dog to score first goal and it lwont let me enter anything , any help please ,

    1. Hi Ben, I guess you have not clicked on ‘Enable editing’ in your Excel sheet. This will let you enter new data. Another option would be to save the Excel file under a different name. Hope this helps!

  5. Thank you for your free excel file on poison distribution. Excel seems to be a boring and less followed app on the internet. Though there are tens of thousands of excel tutorials, there are actually little or no downloadable soccer collation/prediction excel programs on the internet. This is the first sensible excel file I have ever downloaded; Anytime I download an excel file, it’s always a half-done work uploaded by one motherfucker somewhere. It would have been nice if you can create more excel files for 18 team leagues (bundesliga), 16 team leagues (ekstraklasa), 14 team leagues (ethniki katigora)

    1. Hi, thanks for your kind reply. Always aim to write guides and building Excel files that are actually useful and (if you apply the theory correctly) can make you a profitable bettor. It is not that difficult to adjust the Excel file to 18-14 teams. You only need to change a couple of formulas. I’m happy to help though. Just send me an e-mail or reach out to me on Twitter.

  6. Interesting article, well explained and simple to follow.

    Other than using an Expected Goals model, have you considered other variables such as points difference?

    1. Hi Paul, thanks for your reply. The reason for using a goal model is the fact that goals are assumed to follow the Poisson distribution. This assumption enables us to easily build a reliable model like this in Excel. This would not be possible in case of a points difference model. Nevertheless, I have built other types of models (including points difference models) as well in the past, but not in Excel.

  7. I have a strong feeling that using over and under probabilities in bivariate poisson may be a better resuly estimator

  8. What do you do about newely promoted and relegated Teams? How do you factor in their previous season form? I have been using Poisson since the 2016-2017 season but each season I have to start again so I can’t use my excel sheet until I am happy that the data has settled down. I would be intrested to hear your thoughts?

    1. Hi Dandy, very good question. It is certainly possible to take competition strength into account, but this is challenging. Unless you have years of betting experience, I usually recommend not to bet on newly promoted/relegated teams until 4-6 months into the season. I mean, there are enough other teams to bet on in this world, right?

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