# Football predictions and betting with the Poisson distribution

In the 19th century the french mathematician Simeon Denis Poisson came up with the Poisson distribution which can be used to determine "the probability of a given number of events occurring in a fixed interval of time". Like, I don't know, the number of goals scored during 90 minutes? :)

Some people believe that the bookmakers are using this model, or a model based on this distribution, to determine the probabilities for sport events. If you think about it this model can be used to predict all kinds of things that can happend during a footbal match: number of yellow cards, number of penalty kick, number of corner kicks. Another advantage of this model is that it is very "cheap", in the sense that it doesn't require a lot of computing power to make predictions.

In our days, artificial intelligence is all the rage but many of the models are computationally intensive. Sure, the bookmakers have powerfull computers but they also have to worry about risk management so anything that would give them predictions fast is very usefull for them. This distribution can be used to make predictions during a football match. For example it can answer questions like: "How many goals will Real Madrid score in the second half given the fact that, at half time, they lead 2-0?" or "What are the chances of Liverpool scoring 1 goals in the last 10 minutes of a game when the score is 1-2 for the guest team?"

The Poisson distribution is a simple math formula that requires only one input: the average numbers of events that can occur in an interval. So you may ask yourself how accurate is it to predict specific outcomes.

The image above shows how the Poisson distribution compared to real life for the Premier League 2017-2018 season. It shows the number of games (on the vertical axis) where a specific number of goals scored by the home team (the horizontal axis). The blue color shows the actual number of games and the orange color shows the Poisson predictions. There were 124 games where only one goal was scored by the home team and 127 games predicted by the Poisson model. Pretty accurate or not? Since the graph includes teams with different skill levels we think these differences are natural.

The image above shows the same comparison between reality and the Poisson predictions but limited to Manchester City playing at home between 2012 and 2017. More accurate, don't you think?

We concluded that the Poisson distribution is good enough to create a tool that will help you improve your betting skills. Below you will find a video explaining how to use the tool for... profit.

The Poission distribution requires only one parameter and that is the number of average goals scored during a match. This is where you, as a professional bettor, have to use your skills to determine the how to calculate the average numbers of goals scored by a team. If you use any other statistics service on the market you are really limited to the number of 5, 8, or 10 previous games and this is not good for various reasons. The team you are looking at may have recently played strong/weak teams. The team may be out of shape or in excelent shape.

So, in order to come up with a valid number of average goals scored by a team you need to look at similar games. Here are some tips:

- For the numbers of goals scored you can use games that are similar based on the "
**attack force**" or "**shape**" - For the number of goals conceided you can use games that are similar based on the "
**defense strength**" or "**shape**" - Try to use games based on their type ("home games" are different than "away games")
- The more games you use, the better.

If are computer-savvy and you have subscribed to the "**Legend**" package you will have access to a lot more games. You can search for matches that are similar based on shape and not take into account the team (eg: "What was the average numbers of goals scored by the home team when the shape of the home team was close to 75 and the shape of the away team was close to 50?") or you can make your own formula to determine how "similar" the matches are (eg: "Find matches that are close to 80 on the attack force, 60 on the defense strength and 70 on the shape and make the shape 3 times as important as defense and attach 2 times as important as the defense?"). Once you have found the matches to use for computing the "average number of goals scored" you can plug the data into our excel file and start using the Poisson model for betting. Remember, the goals is to find value bets that bring consistent profit.

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