Redefining Premier League Forwards using k-means
By: Senan Mc Grath
Tags: K Means, Machine Learning, Data Science, Premier League, Soccer

With more teams using fullbacks to provide width, the role of forwards has significantly changed in world football. The modern forward can no longer be defined by the traditional labels of winger and striker. Traditionally teams operating with a front three will have an “out-and-out” striker whose main purpose is to score goals and two wingers who provide width, creating chances for the striker as well being a secondary source of goals. This is epitomized by José Mourinho’s 2005/06 Chelsea team where Damien Duff and Arjen Robben provided the width for Didier Drogba on the inside. The front three has evolved in recent years, however, with the central player dropping deeper in many systems. The “false 9” role became highly popular after Lionel Messi’s success in the position for Barcelona under Pep Guardiola. In this role, the central player comes deep and becomes much more involved in the build-up play with the wingers drifting further infield and supplying more goals. Jurgen Klopp has taken this a step further and developed a system where the striker’s main role is not seen as goal scorer. Instead the striker, Roberto Firmino, is much more involved in build-up play and creating chances for the two wingers, Sadio Mane and Mo Salah.

“A football team is like an orchestra, you have different people for different instruments. Some of them are louder than others but they are all important for the rhythm. Bobby plays something like 12 instruments in our orchestra.” - Jurgen Klopp on Roberto Firmino’s role in the team

Despite being a key part to a successful system, some are critical of the striker’s lack of goals:

Another example of how the front three has evolved is Arsenal where Pierre-Emerick Aubameyang will be named at left-wing but be expected to provide most of the attacking threat while Alexandre Lacazette, as striker, is deployed to hold up play and Nicolas Pepe at right-wing will provide width and crosses into the area. Here, the two players named as wingers have completely different roles within the same system.

The same can be said for the two man strike partnership which traditionally involves a striker/center-forward who plays near the goal with a second striker/number 10 playing behind them. This is still a popular system with teams like Burnley, where Jay Rodriguez gets involved in play slightly deeper behind Chris Wood whose purpose is to hold the ball up and score goals. Other teams have gone for a more direct approach to a two man forward line, like Everton where Richarlison and Dominic Calvert-Lewin both look to play in advanced positions and attack the goal. Sheffield United, then, are at the opposite end of the spectrum where both forwards, David McGoldrick and Ollie McBurnie, look to hold play up in advanced areas in order to allow their wingbacks to create space.

The aim of this article is to redefine the roles of Premier League forwards by grouping players based on their stats using a technique called k-means clustering.

Understanding k-means clustering

K-means clustering is a popular unsupervised machine learning algorithm. “Unsupervised learning” algorithms take data with no pre-existing labels and attempt to find structure in the input. The goal of k-means clustering is to group similar data points into a set number of clusters based off their input variables. In this case each player is a data point and the input variables are their statistics. This sounds complex but it’s actually quite easy to visualize with an example. Lets look at the tackles per game and shots per game of several Premier League players last season:

Clearly we can see that there are two groups of players here, forwards and defenders. This is confirmed by seeing the player names and knowing that Pereira, Wan-Bissaka, Aurier and Tarkowski are all defenders and that Firmino, Jimenez, Jesus and Salah are all forwards.

In order to make this grouping mathematical we use k-means. This algorithm creates k random cluster centroids and then iteratively adjusts the centroids until they are best placed. This is when the centroids can’t move any closer to the average (mean) of the cluster. We can try this out using the example above. There seems to be two clusters so we’ll try k=2:

The algorithm has correctly grouped together the players based on these stats with the grey dots representing the cluster centers. We can now label these groups as “Forwards” and “Defenders” based on our own knowledge of the players in each group. Now that we have a basic understanding as to how k-means works, we can move on to applying it to our main problem.

Criteria & Stats

First, I separated the forwards into central players and wide players. This was done fairly subjectively as many players could be classified as both. Anthony Martial was put into the central category as he played most of his games for Manchester United in the center of a front three last season. This meant both Marcus Rashford and Mason Greenwood were put in the wide category. Aubameyang started an equal number of games in both wide and central positions so he was included in both. Only players with over 1000 minutes played and to have made most of their appearances as a starter were included. I then selected the top 25 players in each category based off of average player ratings. Several statistics were recorded trying to incorporate the players’ overall game. Some of these statistics were then adjusted into a “per 90 minutes” metric. The following statistics from the 2019/20 season were used in analysis:

Attack: Goals/90min, Shots/90min, Shots on Target/90min, xG/90min, Successful Dribbles/90min, Total Dribbles/90min, Hit Woodwork/90min, Big Chances Missed/90min, Offsides/90min,Open Play Goals, Headed Goals, Surplus xG, Shot Accuracy, Conversion Rate Defense: Tackles/90min, Fouls/90min, Interceptions/90min, Headed Clearances/90min Team Play: Passes/90min, Assists/90min, xA/90min, Touches/90min, Crosses/90min, Big Chances Created/90min, Surplus xA Physical: Height, Distance Covered/90min

The stats were collected from the Premier League’s official website so any ambiguous statistic such as Big Chances Created is down to their interpretation. Most of the statistics are self-explanatory but some may not be familiar with xG and xA. Expected Goals (or xG) is a relatively new metric that attempts to measure the quality of a goal scoring chance and the likelihood that it is scored. It is measured by analyzing the chance in terms of the angle of the shot, the distance, type of shot etc. and giving a rating from 0 to 1. If a chance has an xG of 0.4 that means you would expect a player to score that chance 40% of the time. Summing up a players xG over the course of the season gives an approximation as to how many goals they should have scored. Similarly xA calculates the likelihood a pass will become a goal assist.

Principal Component Analysis

The above list has 27 different stats and many of them are related, for example, players with a high amount of goals scored will also have a high xG. Having a high number of variables (or dimensions) is not desirable for k-means as it relies on a distance measure, i.e. data points near each other are clustered together. When you have a high number of dimensions distance metrics become increasingly less reliable so reducing the number of metrics will allow k-means to work better. Principal Component Analysis (PCA) solves this issue for us by creating a set of principal components from the existing variables. Each of these principal components is a linear combination of the variables such that they are not correlated and most of the variance is accounted for by the first few components. This allows us to reduce the number of dimensions by using the main principal components.

With that established, we now must determine how many principal components we want. There is no exact way to determine this but we want each component to add a significant amount of variance and we want most of the variance in the dataset to be explained by these components. The graph below shows the % of total variance explained by each component for the set of central players.

Here we can see that the first two components account for most of the variance and that very little variance is explained by the ninth component onwards.

Looking at the cumulative variance explained with each we find that 79% of the variance is explained by the first 6 components and 90% by the first 9 components.

Based off this I decided to choose 6 components as the total variance explained by these components was nearly 80% and each component after that didn’t add much.

With the set of wide players I also ended up using 6 components with 81% of the variance explained.

Clustering

Now that we have determined the number of principal components, we now need to determine k, the optimal number of clusters. To do this I used Silhouette Coefficients. The Silhouette Coefficient measures how well a data point is defined in its cluster by measuring the average distance between it and all the other points in the same cluster (cohesion) and the average distance between it and all of the points in the nearest cluster (separation). Silhouette Coefficients range from -1 to 1: a score near 1 indicates a point is well matched to its cluster, a score near 0 means it is on the boundary of its cluster and a score negative score indicates it may be assigned to the wrong cluster. By finding the mean Silhouette Coefficient across all data points for different values of k we can determine the optimal number of clusters.

In our example from above the Silhouette Coefficient was 0.72 for k =2 as the clusters were well separated. But now look as we add more players the Silhouette Coefficient is now 0.36 as the clusters are closer together with more points on the boundary.

However when we choose k=3, the silhouette coefficient is now 0.42 as the clusters are better defined. The clusters are still close but the points seem better grouped.

Clearly k=3 is the optimal number of clusters here, however in some instances we may want to separate the data into more clusters causing us to choose a value for k that doesn’t necessarily have the highest silhouette coefficient.

Below is a plot of the silhouette coefficient for both sets of players across several values of k:

From the graphs it’s clear that the optimal number of clusters is 5 for the set of central players and 3 for the set of wide players. We could also look at 7 or 10 clusters for the central players but, considering there’s only about 25 players in each set, that would probably be too many groups to have.

Results

Now we can group the players together and attempt to label the groups. As we can see from the relatively low silhouette scores, the clusters will not be perfectly defined. This is to be expected as many players can fit into several types of role and some players will have different roles week in week out depending on several factors such as their opposition, injuries on the team, etc. With that being said, let’s have a look at what the analysis produced.

Central Players

The optimal number of clusters was 5 and were grouped as follows:

(*indicates highest scoring cluster, ^indicates lowest scoring cluster)

Cluster 1 (Target Man):

Calvert-Lewin| Giroud | Wood | Abraham | Kane

Key stats:

Goals/90min — 0.58, Shots/90min — 3.04, Shot Acc. — 46.6%*, Conversion Rate — 19.3%, Offsides/90min — 0.83*, Headed Goals/90min — 0.13*, Total Dribbles/90min — 1.03^

Headed Clearances/90min — 0.95*, Tackles/90min — 0.43^, Interceptions/90min — 0.21^

Assists/90min — 0.05^, Passes/90min — 19.70, Touches/90min — 34.06, Crosses/90min — 0.45^, Big Chances Created/90min — 0.08^

Height — 189.6cm*, Distance Covered/90min — 7.2km

These players are finishers that look to play close to the goal. This is illustrated by the fact that they have the highest number of offsides and least number of dribbles showing they stay in advanced positions. They also have the highest shot accuracy indicating their opportunities arise near the goal. They look to use their physical presence to their advantage - on average they are the tallest players and score the most headed goals.

They are not very creative players — they have the lowest number of assists and big chances created. They also have the least number of crosses per 90 minutes further proof that they like to stay central and look to finish rather than create.

Their defensive game is again based on their physicality. They have the highest number of headed clearances indicating their main defensive duties involve defending set pieces. They have the lowest number of tackles and interceptions per 90 minutes showing they do not like to get involved in pressing defenders.

The first 4 players definitely fit this archetype however as the statistics recorded were from the 2019/20 season, when Spurs were going through a transition after sacking Pochettino and hiring Mourinho, Kane’s role varied across the season. Since the 2020/21 season started he has assumed a different role and I believe he would be classified in another group if we were to repeat this analysis at the end of this season.

Cluster 2 (Advanced Playmaker):

Firmino | Jiménez

Key Stats:

Goals/90min — 0.37, Shots/90min — 3.12, Shot Acc. — 38.0%, Conversion Rate — 11.7%^, Offsides/90min — 0.34^, Total Dribbles/90min — 2.72, xG Surplus- 3.6*

Assists/90min — 0.20, xA/90min — 0.21*, Passes/90min — 31.15*, Touches/90min — 47.98*, Crosses/90min — 0.52, Big Chances Created/90min — 0.33*

Headed Clearances/90min — 0.47, Tackles/90min- 0.83, Interceptions/90min — 0.33

Height - 185.5cm, Distance Covered/90min — 8.13km

These players drop deeper, looking to get involved in build up play and create chances for other players. They have the lowest number of offsides and highest number of passes and touches showing they tend to be in less advanced positions and have a desire to be involved in play. Despite having the lowest conversion rate, they have the highest xG Surplus which is a sign that the goals they score come from further out and more difficult areas. Having a high number of assists and the most big chances created shows their creativity but their low number of crosses indicate this mainly comes from central positions.

A high number of tackles, interceptions and headed clearances show they get involved in both pressing and defending set pieces. They also cover a high distance each game showing their high work rate on both ends.

Cluster 3 (False 9):

Aguero | Jesus | Antonio | Martial

Key Stats:

Goals/90min — 0.67*, Shots/90min — 3.84*, Shot Acc. — 45.25%, Conversion Rate — 17.7%, Offsides/90min — 0.54, Total Dribbles/90min — 3.42*, xG/90min — 0.76*

Assists/90min — 0.21*, xA/90min — 0.17, Passes/90min — 23.97, Touches/90min — 42.68, Crosses/90min — 0.91, Big Chances Created/90min — 0.26, xA Surplus - -0.98

Headed Clearances/90min — 0.22^, Tackles/90min- 0.59, Interceptions/90min — 0.62*

Height — 177.3cm^, Distance Covered/90min — 6.53km^

These players are given free role in attack. They get involved in every area of attack having the highest number of goals and assists as well as a high number of touches, passes and crosses. This type of forward is direct, they have the highest number of shots and dribbles showing they like to attack the goal. They are the only group with a negative xA surplus meaning they create a lot of opportunities that are not always converted.

On the defensive end, they have the highest number of interceptions indicating they get involved in high pressing. They score low in tackles and distance covered suggesting a generally low defensive work rate. They are the shortest on average and have the lowest number of headed clearances, a sign that they are not involved in defending set pieces.

Cluster 4 (Hold-up Striker):

A.Barnes | McBurnie | Haller | Maupay | Ayew | Joelinton | Lacazette | Wilson | Pukki | Deeney | King

Key Stats:

Goals/90min — 0.30^, Shots/90min — 2.10, Shot Acc. — 42.91%, Conversion Rate — 14.8%, Offsides/90min — 0.58, Total Dribbles/90min — 2.11, xG/90min — 0.35^

Assists/90min — 0.07, Passes/90min — 22.99, Touches/90min — 39.35, Crosses/90min — 0.50, Big Chances Created/90min — 0.15

Headed Clearances/90min — 0.50, Tackles/90min- 0.87, Interceptions/90min — 0.34

Height — 182.09cm, Distance Covered/90min — 8.14km*

This is a hardworking type of striker whose main role is to hold up play high up the pitch providing relief for the defense and opportunity for the more creative players. They have the lowest number of goals as well as low shot accuracies and conversion rates showing they are not clinical in nature. They have an average number of dribbles, passes and touches but the lowest number of shots which is a sign that they are either not the first scoring option or they are on a team that does not create a lot of opportunities.

They have a high number of tackles, interceptions and headed clearances and the highest distance covered showing they have a high work-rate on the defensive end.

Hold-up Strikers heights range from very tall (Haller 190cm) to very short (Maupay 173cm). Target Men all tend to be tall while False 9’s tend to be short.

This group had the widest range of heights showing the role is not height specific. For example, West Ham will look to play high long balls to Haller who uses his height and strength to ward off defenders whereas players like Maupay look for the ball to be played to their feet or into space.

Some of the players in this group have probably fallen victim to being on bad teams. Wilson, Pukki and King are all natural goal scorers but were on teams that got relegated. Had they been on better teams they might have been grouped into different clusters. This is an example of how statistics can often be deceiving in football.

Cluster 5 (Centre-Forward):

Ings| Aubameyang| Vardy

Key Stats:

Goals/90min —0.67*, Shots/90min — 2.76, Shot Acc. — 44.67%, Conversion Rate — 24.4%*, Offsides/90min — 0.60, Total Dribbles/90min — 1.86, xG Surplus — -5.36^, Headed Goals/90min — 0.06

Assists/90min — 0.10, Passes/90min — 19.04^, Touches/90min — 33.48^, Crosses/90min —1.47*, Big Chances Created/90min — 0.21, xA surplus — 1.24*

Headed Clearances/90min — 0.37, Tackles/90min- 0.89*, Interceptions/90min -0.25

Height — 181.33cm, Distance Covered/90min — 7.16km

These clinical forwards are the main goal threat on their teams. They have the highest conversion rate and joint highest number of goals showing their clinical nature. Like target men, they have a high number of offsides indicating they like to play on the shoulder of the defender however a higher number of crosses and a lower number of headed goals is probably a sign that they favor running into space rather than relying on aerial ability. They score a lot of goals like false 9’s, however, they have a lower number of touches, passes and dribbles indicating that they are finishers rather than creators.

They have a low number of interceptions and headed clearances as well as a low distance covered which might indicate a low defensive work rate. They do, however, have a high amount of tackles perhaps showing an eagerness to create opportunities by tackling high up the pitch.

Wide Players:

The optimal number of clusters was 3, producing the following:

Cluster 1 (Inside Forward):

Greenwood | Pulisic | Aubameyang | Rashford | Richarlison | Son | Sterling | Mane | Salah

Key Stats:

Goals/90min — 0.59*, Shots/90min — 2.93*, Conversion Rate — 17.9%*, Shot Accuracy — 45.0%*, Total Dribbles/90min — 3.60, Offsides/90min — 0.46*

Assists/90min — 0.21, Passes/90min — 31.92, Touches/90min — 49.76^, Crosses/90min — 1.62^, Big Chances Created/90min — 0.30

Tackles/90min — 0.91^, Interceptions/90min — 0.40^, Headed Clearances/90min — 0.14*

Height — 180cm*, Distance/90min — 7.21km^

This is the most attacking form of wide player. They have the highest number of goals, shots and offsides showing they play in the most advanced areas and are of the main goal threat on a team. They have the lowest number of crosses indicating they play more central compared to traditional wingers. They have a low number of touches and passes showing that they look to be involved at the end of the attack rather than the build up. Many of these players are converted strikers (Rashford, Greenwood) or would be strikers if not for their size (Richarlison, Salah).

Their low number of tackles, interceptions and distance covered is probably a sign that they have little defensive responsibility. The height differences between the clusters is negligible.

Cluster 2 (Wide Midfielder):

Redmond | Zaha | Perez | Saint-Maximin | Sarr | Trossard | Pepe | Traore | McNeil | Grealish | Jota

Key Stats:

Goals/90min — 0.22^, Shots/90min — 1.95^, Conversion Rate — 10.0%^, Shot Accuracy — 32.0%^, Total Dribbles/90min — 4.26*, Offsides/90min — 0.17

Assists/90min — 0.16^, Passes/90min — 31.53^, Touches/90min — 54.12, Crosses/90min — 3.35, Big Chances Created/90min — 0.27^

Tackles/90min — 1.14, Interceptions/90min — 0.49, Headed Clearances/90min — 0.11

Height — 178cm, Distance/90min — 7.53km

This cluster is probably the closest to the traditional idea of a wide player. They have the highest number of dribbles and a high number crosses showing a desire to get wide, create space and then cross the ball into the strikers. They have the lowest number of goals, shots and assists which is a sign that they do not play as advanced as the other clusters. They also have the lowest conversion rate and shot accuracies indicating they are not as clinical.

They have a slightly higher number of tackles, number of interceptions and distance covered compared to the inside forwards suggesting they play a similar defensive game but with slightly more responsibility.

Cluster 3 (Attacking Midfielders):

Bernardo Silva | Willian | Mahrez

Key Stats:

Goals/90min — 0.311, Shots/90min — 12.47, Conversion Rate — 12.7%, Shot Accuracy — 41%, Total Dribbles/90min — 3.18^, Offsides/90min — 0.14^

Assists/90min — 0.31*, Passes/90min — 50.89*, Touches/90min — 74.83*, Crosses/90min — 4.08*, Big Chances Created/90min — 0.42*

Tackles/90min — 1.55*, Interceptions/90min — 0.84*, Headed Clearances/90min — 0.10^

Height — 175cm^, Distance/90min — 8.23km*

These are the most creative form of wide player. They have the lowest number of offsides showing they like to play infront of defenses rather than looking to get in behind. They are in the middle in terms of goals and shots showing they are more involved in the latter parts of the attack than the wide midfielders but not as relied upon for goals as much as the inside forwards.

What really distinguishes this cluster from the others is their creativity. The lead the stats in assists, crosses and big chances created. They also score substantially higher in touches and passes than the other two, clearly they get involved in play much more than the other two clusters. The players placed in this cluster are known to be versatile: the play advanced and come deep as well as playing wide and coming inside.

They have more tackles and interceptions than the other groups showing more defensive involvement, presumably in high pressing. This coupled with their desire to attack in several areas mean they also cover the most ground.

The players in this cluster (Willian, Bernardo Silva and Mahrez) are probably as suited to playing number 10 as they are to playing wide.

Conclusion

Overall I feel k-means clustering worked quite well at grouping the different types of forward, particularly for the wide players. This is interesting as the clusters for wide players had a higher silhouette coefficient also. Obviously there are some major drawbacks. The statistics were gathered from the 2019/20 Premier League season only. This season had a break midway through due to the coronavirus outbreak which disrupted a lot of players form and the lack of fans in the second half of the season might have had an impact on how some players played. Also players have a different role season to season, for example Wilfried Zaha was playing in a much more defensive system that season and would probably be in a different cluster if based on previous seasons statistics. As mentioned above, weaker teams will usually have to defend more which could affect their forwards’ attacking stats. It should also be mentioned as well that statistics don’t always tell the full story which is particularly true for sports like soccer, however, more advanced stats such as xG are being introduced to help improve this.