# Predict Football Matches by Using the Poisson Distribution (Part 1) [Excel-Guide]

The Poisson distribution is a well-known and simple theory that can be used for predicting correct scores and match odds in football. Knowing how to apply the Poisson distribution helps making better informed betting decisions, which is one of the essentials of making money with betting. In this two part series we will learn how to predict football matches correctly by applying the theory of the Poisson distribution.

## ► How to predict football matches with Poisson?

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 definition is very simple, 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, 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 will focus on step (1). In part 2 of this series we will find out how to calculate step (2) and step (3). After completing this series you have learned how to accurately predict the outcome of football matches. The theory of this series gives you a wide range of betting markets to predict. This includes the Correct Score, Over/Under and Match Odds markets.

## ► Step 1 – Gather enough historical football data

Let’s say that we want to predict the match Man Utd versus Man City (the Manchester Derby). Now if we want to predict football matches correctly, it is very important to use enough historical football data. I cannot emphasize this enough.

Think of this: Crystal Palace scored a spectacular amount of 8 goals in their last two games of the 2018-2019 season. Although this is pretty impressive, do you expect this performance to correctly reflect their future performance? Generally, a mid-league team like Crystal Palace won’t be able to maintain an average of 4 goals per game throughout the season. If we opt for a longer data range (at least 10 matches per team), our predictions will be more balanced and should better reflect the true strength of Crystal Palace.

The data range used for this guide consists of all games played in the 2018-2019 Premier League season. That is a sufficient sample size for predicting football matches. I have gathered the data from WhoScored, but there are many other good recources for football statistics as well.

## ► Research – How strong is Man Utd at home?

Before we can calculate the expected goals for both Manchester United and Manchester City we first want to estimate their offensive and defensive strength ratings. At first we calculate the strength ratings for Manchester United. We know that the Mancunians finished sixth in last season’s campaign, but how will our Poisson model rate Manchester United?

The first step is to calculate the average number of goals that Manchester United scored and conceded during their home games in the 18-19 season. This is a very straightforward calculation.

##### Man Utd | Basic home match performance statistics from WhoScored $textrm{MP}_{textrm{ManU}}=textrm{Num. matches played at home}=19$ $textrm{GS}_{textrm{ManU}}=textrm{Num. goals scored at home}=33$ $textrm{GA}_{textrm{ManU}}=textrm{Num. goals against at home}=25$

Based on the above statistics we can easily calculate the strength ratings for Manchester United. Note that the below formulas make use of the three variables that we have defined above.

##### Man Utd | Calculate average number of goals scored and conceded $textrm{AvgGS}_{textrm{ManU}}=textrm{Avg. goals scored at home}=frac{textrm{GS}_{textrm{ManU}}}{textrm{MP}_{textrm{ManU}}}=frac{33}{19}=1.74$ $textrm{AvgGA}_{textrm{ManU}}=textrm{Avg. goals against at home}=frac{textrm{GA}_{textrm{ManU}}}{textrm{MP}_{textrm{ManU}}}=frac{25}{19}=1.32$

As you can see average number of goals scored and conceded by the Mancunians is 1.74 and 1.32 respectively. Interesting, but … these numbers are meaningless without the context of other teams. Therefore, we quickly move on to the next step: calculating the attacking and defensive strength ratings for Manchester United. In order to do this we should compare the home match performance of Man Utd with the other Premier League teams.

### ► How to calculate strength ratings of football teams?

Calculating the attacking and defensive strength ratings for Man Utd is very straightforward as well. We can simply do this by dividing Man United’s average goals scored/against (above formulas) by the Premier League averages. The corresponding formulas are shown below, and are similar to the ones that we have seen above.

##### Premier League | Basic home match performance statistics $textrm{MPH}_{textrm{EPL}}=textrm{Num. matched played at home}=19times20=380$ $textrm{GSH}_{textrm{EPL}}=textrm{Num. goals scored at home}=596$ $textrm{GAH}_{textrm{EPL}}=textrm{Num. goals against at home}=476$

##### Premier League | Calculate average number of goals scored and conceded $textrm{AvgGSH}_{textrm{EPL}}=textrm{Avg. goals scored at home}=frac{textrm{GSH}_{textrm{EPL}}}{textrm{MPH}_{textrm{EPL}}}=frac{596}{380}=1.57$ $textrm{AvgGAH}_{textrm{EPL}}=textrm{Avg. goals against at home}=frac{textrm{GAH}_{textrm{EPL}}}{textrm{MPH}_{textrm{EPL}}}=frac{476}{380}=1.25$

As you can see the average number of goals scored and conceded at home by all Premier League teams is 1.57 and 1.25 respectively. Remembering the Man Utd statistics, we can conclude that Man Utd both scores and concedes more goals at home than the average Premier League team.

We can use the above numbers to calculate the strength ratings of Manchester United:

##### Man Utd | Calculate home match strength ratings for 2018-2019 $textrm{Att}_{textrm{ManU}}=textrm{Attack rating}=frac{textrm{AvgGS}_{textrm{ManU}}}{ textrm{AvgGSH}_{textrm{EPL}}}=frac{1.74}{1.57}=1.11$ $textrm{Def}_{textrm{ManU}}=textrm{Defense rating}=frac{textrm{AvgGA}_{textrm{ManU}}}{ textrm{AvgGAH}_{textrm{EPL}}}=frac{1.32}{1.25}=1.05$

The strength ratings of Man Utd indicate that the club has scored (+ 11%) and conceded (+ 5%) more goals at home than the average Premier League team. This indicates that their offensive strength is above average. On the contrary, their defense performs relatively poor for a club like Manchester United.

Below I have added a printscreen from the Excel spreadsheet that I have created for this series (download link in part 2). What you can see from the printscreen is an overview of the home team strength ratings for all 2018-2019 Premier League teams. The corresponding strength ratings are shown in the below image as well. By subtracting the defensive strength rating from the offensive strength rating we can calculate an overall home strength ranking for all teams. We can clearly see that Liverpool and Man City are the strongest home teams. Further, we can observe that Huddersfield is the worst performing home team with a very low attacking strength rating of 0.34. Now if we take a look at Man Utd: they are the 7th best home team according to this model. ## ► Next – How strong is City away from home?

We now know the strength ratings for the home team Man Utd. However, if we want to predict football matches, we need to calculate the strength ratings for both teams. The calculations are very similar, so I will only show the results in the below image. Nevertheless, if you need more guidance on how to calculate the away team strength ratings: download the corresponding Excel spreadsheet in part 2 of this series.

As you can see from the below image, Manchester City scored 60% more goals away from home than the average Premier League team. Their defensive strength rating is even better (- 63%). Man City is the strongest away team in the Premier League, although Liverpool shows spectacular numbers as well. Again we can observe that Huddersfield is ranked among the worst teams. It is no surprise that they have been relegated last season. ## ► Predict number of goals in Manchester Derby

After calculating the strength ratings for both teams we can predict the expected number of goals scored by both teams in the Manchester Derby. However, how can we do this? Let’s use Man Utd as an example. At first, we multiply their attacking strength rating with the defensive strength rating of Man City. After that, multiply the previous calculation with the average number of goals scored by home teams in the Premier League. We can predict the expected number of Man City goals in a similar way. Below you can see the exact formulas for both calculations.

##### Predict the expected number of goals in the Manchester Derby $textrm{xG}_{textrm{ManU}}=textrm{Att}_{textrm{ManU}}timestextrm{Def}_{textrm{ManC}}times textrm{AvgGSH}_{textrm{EPL}}=1.11times0.37times1.57=0.64$ $textrm{xG}_{textrm{ManC}}=textrm{Att}_{textrm{ManC}}timestextrm{Def}_{textrm{ManU}}times textrm{AvgGSA}_{textrm{EPL}}=1.60times1.05times1.25=2.10$

As you can see from the above, Manchester United is expected to score 0.64 goals in this match. Manchester City, on the other hand, is expected to score 2.10 goals. In other words: Man City are very likely to score more goals than Manchester United. They are obviously the favorites to win this match. This is interesting, but how can this be used to predict football matches? Thus, based on the above, what is the actual winning probability of Man City?

In this first guide we have learned how to predict the expected goals for the Manchester Derby. In part 2 of this series we will also find out how to correctly predict football matches by using the Poisson distribution. We will use the results from this guide for predicting the Match Odds market (i.e. home win, draw, away win) for the Manchester Derby.

Moreover, the next guide includes an Excel spreadsheet that covers everything we have learned in this two part series. By downloading this Excel spreadsheet you can immediately apply everything you have learned and accurately predict football matches right away!

## ► 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: [email protected]. Feedback is always welcome! 