Cesromon

In this project we have a database of statistics collected from the 21-22 season of the Premier League. There are variables that cover all aspects of the game, from the number of goals and assists, to more specific statistics in each phase of the game. The intention of this project is to find interesting relationships that are not so obvious in soccer, also testing if unsupervised methods manage to classify players with the positions they play. We will see how t-SNE and UMAP methods far outperform the analysis done in a traditional method such as Component Analysis or k-means.

The database was obtained from the site https://fbref.com/en/ additionally and comes with the guide to understand each variable in detail.

The Data

You can see the full base details below:

Now to find relationships, working with all the variables it’s complicated as we mentioned since all the phases of the game are summarized and many variables can be grouped. So we select 34 variables that summarize the data well. In the future to find the clusters we will use all the variables.

Exploratory Data Analysis

First let’s see if the correlation matrix we find some kind of relationship between variables, the closer to 1 or in this case the bluer the ball in the box is, it will indicate how much the variables are related.

Correlation matrix

Now interesting things are those who shoot, because variables such as assists, dribbles, goal creations, have a stronger relationship with those shot was a goal, this may be due to the nature of the goal, since are much more complex actions than only shot on target. So we see those “creative” players, who are more effective in these phase of the game, than those who are effective in scoring. Also, we see how the long pass variable is very little related to shooting and goals, since they are usually players who are close to the rival area and the number of passes is mostly considered short.

Another detail to consider is the minutes, we see how in some way it has a relationship with practically all the variables, the more minutes you play the rest of the variables will grow in one way or another, this in soccer may be obvious, but the important thing here is that statistics reinforces those preconceived ideas that we often have.

This graph allows us to make certain simple inferences to practically all the variables, even eventually reducing the base size, because for example if I only take a pass, since it is closely related to the other types of passes, we will not lose as much information and we will gain interpretability by reducing the dimensionality.

From this graph applying Principal Components Analysis, we see an interesting behavior with certain variables. Remember that the interpretation of this graph, the closer the lines of variables are, the greater relationship between them. In the case of the variables are with an angle close to 90, this indicates that the variables have little or no relationship, while those variables that generate angles greater than 90 reaching up to 180 degrees, is that the relationship becomes negative. It is clear to us how the group of offensive and defensive variables exists. Something of interest is that the pressure variable is more associated with offensive tasks, since it is usually the forwards or advanced midfielders who carry out these tasks.

Clustering

Now, we have already seen the behavior of the variables at a general level, let’s see if the different unsupervised methods in a certain way generate the 4 expected clusters: goalkeepers, defenders, midfielders and forwards. We will see which method is more effective to realize these analyzes. Just for interpretive reasons, we are going to color each position with different colors and see if they can effectively be separated.

K-means

It is not possible to see the 4 groups formed so clearly. We try to force generating the 4 expected clusters, but it is not possible to see a clear separation from cluster to cluster. Although we could continue looking for more clusters until we find the optimal one, let’s continue with other methods and see if we manage to find all 4 clusters, or if we should consider fewer or more clusters in future analyses.

PCA

Again, like k-means, it is not possible to see clear differences between the groups.

Now, let’s try 2 more modern methods, both the t-SNE and the UMAP,methods that for clustering could give us better results.

t-SNE

The results improve compare to the others methods. Our intuition that 4 clusters should actually be formed is better appreciated here. Although in t-SNE the distance is not interpretable, it does give us a notion that each group is separated and grouped.

UMAP

Using UMAP the results are even better than we obtained in t-SNE, not only separate each position much more clearly, but also gain interpretability in distances. Here it is clearly the goalkeepers are in terms of statistics very separated from the rest of the positions. Additionally, we see how there are defenders who due to their performance could be considered as midfielders, in the same way for the group of forwards with some midfielders.

Conclusions

In this article, using the Premier League 21-22 database, there are interesting relationships between different variables, some of which are quite obvious such as the relationship of total passes with the rest of passes according to type, or those who shoot the most are related more with goals. Also we found more interesting like those players dedicated to making shots and goals, they have a relationship with passes, but only with those that are considered short.

Now, perhaps the most important results of this article is to show how useful are unsupervised methods to classify clusters of groups that we previously known and if the methods actually work or not. Here the superiority of methods such as t-SNE and UMAP against to more traditional methods such as k-means and PCA is clear. Although the final preliminary results are very obvious, because anyone with knowledge of football knows that the 4 positions are very different and therefore should be analyzed separately. In this case, 2 methods gave us expected results: 4 very well marked clusters with just a few exceptions that are players whose skills are out of the ordinary and the machine itself considers that they should be in another position. More specifically, defenders like Trent-Alexander Arnold and Joao Cancelo just fall into these exceptions, they are players with such high offensive contributions that the system practically considers them midfielders.