⚽📈 Discover the Magic of Poisson Distribution in Football Predictions

Howdy!

Ever wondered how we can use math to predict the outcome of football matches? Before you click away at the sound of math, please hear us out!

Let us introduce you to the Poisson Distribution, a cool concept that helps us understand goal-scoring patterns in our favorite sport. This is not limited to just football, you can apply the technique to any sport! Very very nice!

The Poisson Distribution is a math concept that tells us the probability of a certain number of events happening within a fixed period. When it comes to football for example, we can use this to figure out the likelihood of a team scoring a specific number of goals in a match.

Think of each team as having a constant goal-scoring rate, kind of like a scoring "speed limit" (λ). The Poisson Distribution allows us to calculate the chances of different goal outcomes in a match based on this rate.

Imagine we know the average number of goals a home team scores (let's call it λ1) and the average for an away team (let's call it λ2). Using the Poisson Distribution, we create a matrix of probabilities for different goal combinations. This matrix gives us a sneak peek into the likely scorelines in a match.

  | Home \ Away | 0     | 1     | 2     | 3     |
  |-------------|-------|-------|-------|-------|
  | 0           | 0.028 | 0.051 | 0.036 | 0.015 |
  | 1           | 0.071 | 0.129 | 0.091 | 0.038 |
  | 2           | 0.107 | 0.195 | 0.137 | 0.058 |
  | 3           | 0.134 | 0.244 | 0.172 | 0.072 |

An example will make this clearer! Let's consider an example where the average number of goals for the home team (λ1) is 1.5, and for the away team (λ2) is 1.0. We'll create a sample Poisson matrix for goal combinations of up to 3 goals for each team.

This matrix represents the joint probabilities of different goal combinations. For example, the value in the row where the home team scores 1 goal and the column where the away team scores 2 goals (cell [1,2]) is approximately 0.091, indicating the probability of this specific scoreline occurring in the match. Adjusting the λ values and the range of goals will result in different matrices reflecting the scoring patterns of the teams.

How did we get the values you ask? We applied the Poisson distribution formula. You can read more about the inner workings of the algorithm online.

By finding the highest probability in the matrix, we can identify the most probable scoreline. This gives us a statistical way to predict who might win a match.

While the Poisson Distribution is a great starting point, it's important to remember that football matches are affected by lots of things. More advanced models consider additional factors like team strength and player form for even better predictions. However, this is just the first of many models we will be exploring going forward. We have to start somewhere, right?

Keep enjoying the magic of football, and may your predictions be as spot-on as your favorite player's goal kicks!