Defining NBA players by role with k-means clustering

With the rise of small ball and 3-point shooting, the old power forward position has been phased out of the NBA. Strong or athletic power forwards became small ball centers, while shooting power forwards became more and more like small forwards. Following this revolution, Brad Stevens claims that the NBA no longer has five positions – it has three (ball handlers, wings, and bigs).

Even within a position, players serve significantly different roles. While Clint Capela will spend almost all of his time on offense setting screens then rolling to the rim, Brook Lopez will spend most of it on the perimeter. Given this difference and the general direction of the NBA, it’s not informative anymore to just classify a player by the typical five positions.

By clustering, or grouping players by their stats, we can determine the different roles of an NBA player.

What is k-means clustering

k-means clustering is a method of grouping a data set in a certain number of ways by their stats. Though the concept seems mathematically daunting, it is not hard to visualize. As an example of k-means clustering, let’s look at the top five players in steals and blocks.

If we take the top five players in steals per game and the top five players in blocks per game, and compare their steals and blocks, we’ll see a very pronounced difference.

The large space between the groups makes it clear to us that the bottom right corner shows the steals leaders, while the top left shows the blocks leaders. So, just by looking at the graph, we can separate the data intp two groups like this.

k-means clustering just makes this separation mathematical. First, the algorithm creates k random “cluster centroids.” k represents the number of clusters we want to create. The algorithm groups the data into the closest cluster, then moves the centroid to the average coordinates of the data for that cluster. It repeats this process until the centroids are at the “best” position, where they can’t move any closer to the average of the cluster. Note that in this example, the clusters will end up being equally sized. However, they don’t always have to have the same number of data points.

Let’s see what happens when we create two clusters for the steals and blocks leaders.

The algorithm successfully grouped together the steals leaders and the blocks leaders. Each point was assigned to the cluster based on its distance from the cluster centroid (or center), represented by the large grey dot.

We can cluster with more than just two predictors. If we add points, rebounds, and assists as features to our clustering algorithm of the steals and blocks leaders, it separates Paul George, James Harden, and Russell Westbrook (one cluster) from Chris Paul, Jimmy Butler, Myles Turner, Mitchell Robinson, Rudy Gobert, Brook Lopez, and JaVale McGee (another cluster). So, when we added these other factors, it separated the true superstars from the rest.

We can also create more than two clusters. If we look at the top 50 players in PPG, we can clearly distinguish some roles with a few clusters. For example, let’s look at PPG and usage (USG%).

All the secondary scorers like Klay Thompson, CJ McCollum, and Tobias Harris were placed in a cluster at the bottom left, separate from the primary scorers. James Harden’s stats were so extraordinary that he earned his own cluster (just goes to show how amazing he is; if you create three groups from the top 50 players in PPG, his stats are so unique that he earns his own group).

Now, let’s create four clusters for assists and usage.

The four clusters separated the data into scorers, passers, stars, and James Harden. The scorers group contains shooters like Thompson, McCollum, and Buddy Hield who are often not going to handle the ball. A mix of point guards like Trae Young, De’Aaron Fox, and Mike Conley compose the passers group along with a few bigmen like Nikola Jokic, Nikola Vucevic, and Julius Randle. The superstar group combines team-leading players like D’Angelo Russell and Lou Williams with the true superstars. Yet again, Harden earns his own group (hard to see in this graph, but it’s in the top right, behind where it says “Cluster 1” in the legend).

Methods

Now that we’ve looked at a few examples of k-means clustering, we can dive into the analysis. First, I restricted the data set to players who played at least 1,000 minutes and 50 games in the regular season. For these players, I recorded all of Basketball Reference’s stats (not all of them were used in the analysis – more on this a bit later). These included:

* POS = position as a number; 1 = guard, 2 = wing, 3 = big

Dimensionality reduction

The above table has 44 different stats, many of which are related. For example, each counting stat except for points also has a rate stat (i.e. there’s both STL and STL%). This creates a problem, as players with more steals will also have a higher steal percentage. Therefore, we don’t gain much information – if any – by having both steals and steal percentage as parameters in the clusterer.

To solve this dimensionality issue, we’ll use something called principal component analysis (PCA). PCA essentially does a fancy mathematical transformation to all our features into different “principal components.” These components have no actual meaning (i.e. they’re just numbers, not data like steals or steal percentage). With this transformation, we can ignore some variables, as our principal components capture most of the differences – or variance – in the data set.

Now that we’ve established how PCA works, we need to decide how many principal components we want. To measure the “effectiveness” of each number of principal components, we’ll look at the explained variance ratio, meaning “how much of the variance in our initial data set do these n principal components capture.” The graph below shows the explained variance ratio for each n_components between two and ten.

As the number of components increases, the difference in explained variance between the nth component and the (n-1)th component decreases. From what I’ve seen, there’s no commonly accepted way to determine how many components to use. Intuitively, I think looking at the derivative makes sense.

The derivative, which in this case represents the change in explained variance, can help us determine the optimal number of components by looking at where there are the sharpest changes in the derivative. This seems to occur at n_components = 6.

Visually, this means that after n_components = 6, the explained variance ratio increases at a very slow, decreasing rate. Before n_components = 6, the explained variance ratio is still increasing significantly. Therefore, I chose to use 6 components in the PCA. These 6 components explain 85.85% of the data set’s variance.

Determining n_clusters

Along with determining the number of principal components, it’s important to find the “correct” number of clusters for our k-means clusterer to create. To find the right number of clusters, we’ll use silhouette scores. 

The silhouette score measures how similar a data point in a cluster is similar to its own cluster compared to other clusters by comparing the point’s distance from its own cluster to its distance from other clusters. If a point is “perfectly” matched to its cluster, it will have a silhouette score of 1, while the worst possible score is -1. The graph below shows the silhouette score for each n_cluster no greater than 20.

Though the silhouette score generally decreases as n_clusters increases, this doesn’t mean we’re going to use n_clusters = 2. With n_clusters = 2, the data will be separated in a way that gives us no information about player roles. Furthermore, the difference between n_clusters = 2 and n_clusters = 3 is negative, meaning that the clusters get worse if we use 3 clusters instead of 2.

To pick a number of clusters, we’ll look at this difference. However, we won’t look at the difference through subtraction; we’ll look at it in a standardized fashion. The percent improvement in silhouette score for the n_clusters = x over n_clusters = x – 1 will equal 1 – (1 – silhouette score at x) / (1 – silhouette score at x – 1). This standardizes the percent improvement relative to the best possible silhouette score of 1. The graph below shows this improvement for each n_cluster value.  

We want to pick pick an n_cluster value where there’s a positive improvement in silhouette score. This leaves us with possible values of n_clusters = 10, 12, 13, 17 and 19 (n_clusters = 3, 7, and 8 also have positive improvements, but wouldn’t give us much information. Out of these values, n_clusters = 10, 12, and 13 had the best silhouette scores. Because n_clusters = 12 had the biggest improvement, we’ll use that.

Results

Now that we’ve gone over k-means clustering, principal component analysis, and silhouette scores, we can finally group together NBA players. As we can see from the relatively low silhouette score, the clusters will not be extremely well defined. This combined with the fact that many players fit multiple archetypes makes the analysis imperfect. However, the trends in the clusters are still noticeable and interesting.

By looking at the types of players in each cluster, we can define the cluster as a “role,” such as a 3&D player. We’ll look at some of the players in the cluster who embody this role, and then examine the average stats of the cluster.

Note that the average stats of the cluster are not the cluster centers because we’re giving the clustering algorithm the principal components and not player stats. So, the average stats for each cluster is just the average of each stat for all players in the given cluster.

Several players fit multiple of these roles, as evidenced by the fact the silhouette score is not very high. The table below shows the cluster, description, example players, and average stats.

The “???” cluster consists mostly of young, inefficient players on bad teams and role players on bad teams. This isn’t necessarily a “role,” but all these players weren’t good enough to make it into the other roles for one reason or another.

The table below includes the role and stats of every player who met the qualifications (min. 50 games and 1,000 minutes). To find a player, use the search bar. You can also sort by different stats; the ten rows showed are just a preview.

Conclusion

Many additional subsets can be made from these 12 clusters and many players fit multiple of these roles. For example, Giannis fits into the star big category because of his high rebound total, but he is also a star ball-handler. A versatile player like Draymond Green or Marcus Smart will fit many of the roles.

Though the roles aren’t perfect, they embody the general 12 roles an NBA player will serve. These roles give much more information on a player’s purpose to a team than naming them by the typical five positions.