Football

Note: please keep in mind that I did this project long ago (about 6 years).

This program creates a ranking of the best* football players basing on the analysis of the matches/fixtures downloaded from Sportmonks API.

What is understood by a "good player"? Football is a team sport. Therefore how good the player is is defined as how much he increases the probability of a win of a team in which he plays.

* This program finds out which players increase the chances of team winning the most. This is not completely the same as "best players" because if player A is average and his substitute is player B who is very bad, then player A will be very high in the ranking despite being average because his presense in the lineup increases the probability of his team winning a lot (because if he wasn't in the lineup, then the very bad player would play instead of him). In other words, this algorithm is not perfect for finding out who is the best player but still provides useful information.

Results

You can find the results in the folder "results".

Installation

1. Install required packages from requirements.txt file using pip3.
2. Create an account on Sportmonks.com and put your api token into api_token.txt file.

Usage

Before you run the program, you need to have a subscription on Sportmonks.com and API token so that the program can connect to Sportmonks API. You need to have Python3 installed as well.

To run the program, execute (from the project root folder):

python3 football/main.py

How does the algorithm work

General idea

It uses a linear regression for accomplishing the task.

If you're not familiar with linear regression, you need to read about it first. Here you have a simple explanation of linear regression (choose one of these links that better fits you):

https://medium.com/simple-ai/linear-regression-intro-to-machine-learning-6-6e320dbdaf06

https://www.spss-tutorials.com/multiple-linear-regression/

Note: I did this project some time and if I was doing it now, I'd do some things differently (e.g. I'd use OLS instead of SGD as an optimization algorithm).

The algorithm is trained to predict the results of matches (y) taking the players playing in the match as an input (x)

Let's suppose that:

1. y - a real number representing how much the local team won over the visitor team in the given match. So y > 0 if the local team is the winner, y = 0 in case of draw, y < 0 if the visitor team is the winner.

2. x[i] = 1, if the player with id = i (all players have some id assigned) played in the local team, x[i] = -1, if the player with id = i played in the visitor team, x[i] = 0 if the player with id = i didn't play in the match.

If we have a model like this:

y = x[1] * w[1] + x[2] * w[2] + ... + x[n] * w[n]

and we train w (weights) to give correct predictions of y (the result of the match converted to a single real number) basing on x (who played in the match and in which team), then after training w[i] will be as high as good the player with id = i is (basing on the given input).

Why?

We want to learn how the presence of a player in the team affects the result of the match. So if the player with id = i plays in the first team, then x[i] = 1 because he has positive impact on the result (y) - the better he is, the more positive impact he will have on the value of this variable. If he doesn't play, then he doesn't have any impact on the result (y) so x[i] = 0. If he plays in the second team, then he has negative impact on the result (y) so x[i] = -1 - the better he is, the more negative impact he will have on the value of this variable. This way, w[i] will be high if he's good and it will be low if he's weak.

Notice that:

y = x[1] * w[1] + x[2] * w[2] + ... + x[n] * w[n] = f[1] + f[2] + ... f[11] + s[1] + s[2] + ... + s[11]

where: f - the skills of players in the first team s - the skills of players in the second team

In fact, in the program:

y = f(f[1] + f[2] + ... f[11] + s[1] + s[2] + ... + s[11]), where f(x) = x^a, where a was chosen basing on what worked best on the validation data (this is how it should be done, in practice I didn't have time for that so I chose the value of 'a' that I thought will be ok :) ).

Notice that if the algorithm analyzes data from Belgian league and Spanish league, then if the best teams from those league compete with each other in the Champions League or European league, then the algorithm will learn that Spanish league is better than the Belgian league (and it will affect also the teams in those leagues which doesn't play in Champions League).

Some people can notice that the predictors of this linear regression are collinear. That's true, but if you analyze how they are collinear, then you can realize that this fact doesn't make the algorithm useless. It still gives quite accurate results (although if they weren't collinear, then the results would be even more accurate), especially if you take substitutions (and in which minute the goal was scored) and national teams matches into account.

The fact that the predictors are colinear to some extent has three consequences on the results:

1. The algorithm doesn't actually measure how good the player is when he plays with random players but with the players that he usually plays with <- which is desirable because you don't want to know how good Lewandowski is when you put him to a team of totally random, average players but how good when he plays in Bayern Munich where he usually plays.
2. If the players X and Y play for the same team and the real skill of X is 5 but the real skill of Y is 3 and there are not many matches/minutes when they don't play toghether, then the algorithm will give them both a skill close to 4, instead of 5 and 3. <- this is in fact disadvantage, but a small disatvantage, because the results indicate that for every player there are enough matches/minutes in the analyzed data when they don't play in the team and the algorithm is still able to learn which player is good and which player is bad basing on those moments when the player didn't play.
3. The estimated skill of a players depends to some extent on the skill of his substitute. So when a player is high in the ranking it might be caused by the fact that the substitute on his position is weak. <- this is in fact disatvantage, but there's no way to avoid that disadvantage basing only on the information that the algorithm is given.

If you analyze the algorithm, you can notice that in practice the players at the top of the ranking will be mostly the players which meet the below criteria the most:

1. They play in the good teams (those teams that win a lot, taking into account with whom they play).
2. When they play in their team, their team achieves better results than when they are not present on the pitch.
3. If national teams are included, they increase the level of their national team (meaning that their team play surprisingly well with them when taking into account the level of other players in the team).

Data set

The algorithm analyzes football matches. The algorithm is given the following information about each match:

1. Players playing from the first minute in the local team.
2. Players playing from the first minute in the visitor team.
3. Result of the match.
4. Match length (it's sometimes longer than 90 minutes due to extra time).
5. Substitutions made (who came in, who came out, in which minute).
6. Goals (which team scored, in which minute).
7. The date of the match.
8. Position on which every player plays. <-- to do

Substitutions and goals

In "General idea" section, I explained how the algorithm uses the first three information (players playing in the first team, the second team and the result of the match). But we have also the following data about every match:

...

4. Match length (it's sometimes longer than 90 minutes due to extra time).

5. Substitutions made (who came in, who came out, in which minute).

6. Goals (which team scored, in which minute).

To make use of this information, every match is divided into smaller matches (smaller data samples) with the minutes when substitutions were made as a delimiter.

x[i] in each sample represents if player with ID = i played at the time represented by given sample.

y variable is set to the result of the match only taking into account that period of time which the data sample represent. 'y' is multiplied by (match_length / sample_time) because it represents how much the local team beaten the visitor team and if they scored more goals in the short time then they beaten them more than if they scored it in a long time. The sample weight of the data sample representing this period equals how long was the period divided by match length.

The above explanation is probably not clear, so I'll give an example:

Let's suppose that the data is like this:

1. Local team players: 2, 3, 4.

2. Visitor team playes: 7, 8, 9.

3. The result of the match: 2:1 (local team won).

4. Substitutions:

a) The player 4 was replaced with the player 5 in the 30 minute.

b) The player 7 was replaced with the player 6 in the 60 minute.

5. Goals:

a) The first goal was scored in 20 minute by the visitor team.

b) The second goal was scored in 70 minute by the local team.

c) The third goal was scored in 80 minute by the local team.

We divide this match into three data sample:

1. One represents the period of time from 0 minute to 30 minute (time of the first substitution).

2. The second one represents the period of time from 30 minute to 60 minute (time of the second substitution).

3. The third one represents the period of time from 60 minute to 90 minute.

The first data sample will be like this:

x = [0, 1, 1, 1, 0, 0, -1, -1, -1, 0] (indexed from 1) (because those players played from 0 to 30 minute)

y = (-1) * (90 / 30) = -3 (the result was -1, but it was in only 30 minutes, so we multiply it by 3)

sample_weight = 30 / 90 = 1/3 (it is only 1/3 of the match so importance of this sample is 1/3)

The second data sample will be like this:

x = [0, 1, 1, 0, 1, 0, -1, -1, -1, 0] (indexed from 1) (the player 4 was substituted by player 5 in the local team)

y = 0 * (90 / 30) = 0 (the result is 0 because there were no goals in this part of match)

sample_weight = 30 / 90 = 1/3 (it is only 1/3 of the match so importance of this sample is 1/3)

The third data sample will be like this:

x = [0, 1, 1, 0, 1, -1, 0, -1, -1, 0] (indexed from 1) (the player 7 was substituted by player 6 in the visitor team)

y = -2 * (90 / 30) = -6 (visitor team won 2:0 in this part, so the result is -2 multiplied by 3 because it's only 1/3 of the match)

sample_weight = 30 / 90 = 1/3 (it is only 1/3 of the match so importance of this sample is 1/3)

Date of the match

The date of the match only affects the sample weight because if we want to know who is the best player at this moment, then the match that was yesterday is more important than the match that was 10 years ago. Cristiano Ronaldo wasn't 10 years ago as good as he is now, so if we want to know how good he is now, then we should take the match from yesterday into account more than the match from 10 years ago.