Using K-Means Clustering to Identify NBA Player Similarity | by Allen Chun | Oct, 2023

With the NBA heading into its 77th marketing campaign within the 2023–2024 season, groups and followers are anticipating a 12 months of acquainted faces on new groups, rookies with excessive expectations, and the introduction of a brand new trophy.

Final season was historic for town of Denver, who clinched their first championship by defeating the Miami Warmth in 5 video games. In a league closely wager on in Vegas and producing billions of {dollars} yearly from followers, it’s no shock that stats dominate basketball conversations and negotiations at this time.

I assumed it will be fascinating to make the most of participant statistics from the 2022–2023 season and apply an unsupervised machine studying algorithm often known as k-means clustering to categorize gamers into particular clusters primarily based on their on courtroom performances.

The k-means clustering technique is a widely known unsupervised machine studying algorithm that teams a set of observations into okay clusters such that the intra-cluster variance is minimized. The aim is to make it in order that observations inside a cluster are as comparable as doable and people in several teams aren’t.

The usual Hartigan-Wong algorithm defines the overall within-cluster variation because the sum of squared distances between gadgets and the corresponding centroid:

• xᵢ is the information statement belonging to cluster Cₖ
• μₖ is the imply worth of all observations assigned to cluster Cₖ

Initially introduced by MacQueen in 1967, the algorithm is described as having okay variety of clusters, every represented by its centroid (which, on this case, could be the imply of the gamers’ stats). The observations within the knowledge might be assigned to a centroid primarily based on an applicable measure of distance.

On this evaluation, we might be utilizing the usual Euclidean distance to assign gamers into clusters. The algorithm will then create okay clusters by associating every participant to its closest imply after which updating the step by recalculating the centroid. This course of might be regularly repeated till convergence may be achieved.

As basketball continues to realize recognition world wide, it’s essential for followers who make investments money and time to look at the very best gamers play, for gamers to realize recognition for his or her work on the courtroom, and for groups to speculate cash properly into constructing a championship-caliber squad.

On this evaluation, we might be making an attempt to make use of unsupervised machine studying to determine:

• gamers with comparable play types
• essentially the most worthy gamers for end-of-season awards
• area of interest gamers that may very well be of assist to particular groups

As I used to be researching and conducting the evaluation, I discovered a useful article by Nadir that went extra into depth about not solely utilizing k-means clustering but in addition different strategies akin to principal element evaluation (PCA) and agglomerative hierarchical clustering to evaluate NBA participant similarity. I’ll hyperlink his article here if you want to learn additional.

This challenge was carried out completely with R, with all knowledge being from the 2022–2023 NBA season. This knowledge was supplied by https://www.basketball-reference.com and comprises details about gamers’ normal stats on the courtroom in addition to their superior stats. If you want to take a more in-depth take a look at the information or code, be at liberty to check with the GitHub repository here.

Eradicating Duplicates

All through the course of the season, gamers transfer or are traded to completely different groups. The information is introduced in a manner that shows a number of rows for these gamers, one for the gathered totals of his stats and the opposite rows for every crew he was part of throughout the season. As a result of we would like one row to solely characterize one participant, we are going to take away the opposite rows that solely show stats for a selected crew and length.

As soon as this has been accomplished for each datasets (normal and superior stats), we are going to now mix and merge the 2.

Irrelevant Options

On this examine, we need to cluster gamers primarily based on their stats on their courtroom, irrelevant of their age or what crew they play on. Due to this, we are going to take away these columns and as a substitute solely concentrate on what they contributed to their crew.

Dealing with Lacking Values & Subsetting Information

For a number of gamers, there are numerous NA values in instances the place they didn’t try or make a three-point shot for instance. We are going to substitute these lacking values with 0 and in addition subset knowledge to solely embrace gamers who’ve performed at the least half the season and common at the least 24 minutes per sport. We are going to do that with the intention to take away gamers who haven’t performed a lot and solely showcase gamers who had a decently important function on their crew.

Finalizing the Information

After cleansing and subsetting the information, we’re left with 172 gamers and 42 options. All stats are recorded on a per-game foundation and embrace discipline aim and free throw percentages, effectivity numbers, and normal stats.

Normalizing the Information

Lastly, we are going to normalize the information with the z-score normalization technique. Z-score standardization transforms knowledge with the intention to have a imply of 0 and a regular deviation of 1. We are going to obtain this by subtracting the imply from the statement and dividing it by the usual deviation of the sphere.

We full this course of with the intention to be sure that particular fields like factors or rebounds wouldn’t have a larger affect on the information than fields with decrease numbers akin to three-point and free throw percentages.

Now that we’ve got our knowledge, we are going to apply the k-means algorithm. Earlier than working the algorithm, nonetheless, we should decide an optimum quantity of clusters (okay) to make use of.

Figuring out “okay”

Whereas there isn’t a clear-cut technique to decide on a selected worth for okay, there are a selection of choices obtainable that may assist us decide an optimum variety of clusters to make use of.

1. Elbow Methodology

For doable values of okay ranging from 1, we calculate the within-cluster sum of squares (WSS), and decide okay when there may be an “elbow” or a definite drop-off in WSS. The WSS quantifies the sum of squared variations between every knowledge level and its respective cluster centroid. Sadly, this elbow could not at all times be very clear, as proven under. Utilizing 7 or 8 clusters right here appears to be essentially the most optimum.

2. Silhouette Methodology

The silhouette technique compares factors inside a cluster by the standard of the opposite clusters. Starting from -1 to 1, a better silhouette worth signifies a better high quality within the clustering of observations.

Not like the elbow technique, the typical silhouette width is highest at okay = 3. Nonetheless, as a result of we are attempting to cluster 172 completely different gamers and wish our teams to be extra differentiated, we are going to transfer on to the following technique and see what we will discover.

3. Hole Statistic

The hole statistic standardizes the graph of log(Wₖ), the place Wₖ represents the pooled WSS across the cluster centroids. It compares this with “an appropriate null model” distribution of the information (distribution with no clear clustering). Ok is then decided by selecting the worth that maximizes the hole statistic. We will see under that selecting okay = 8 maximizes this.

Briefly,

1. Elbow Methodology: the decrease the higher
2. Silhouette Methodology: the upper the higher
3. Hole Statistic: the upper the higher

It’s essential to grasp that these strategies should not strictly options to one another however somewhat can work in conjunction to find out the optimum okay. Now let’s apply the algorithm to the information with okay = 8 clusters and see what we discover.

1. Darkish Inexperienced Cluster: All-Round Superstars

Fashionable Quintessential Participant: Giannis Antetokounmpo

These are the very best gamers all-around. It’s necessary to grasp that rebounding, effectivity, and profitable stats are additionally included within the knowledge, therefore why Sabonis is included on this cluster. These are the gamers which might be wanted to ensure that their crew to win, and so they do every thing on each offense and protection to make sure their crew’s success.

2. Crimson Cluster: Non-Taking pictures Facilities

Fashionable Quintessential Participant: Clint Capela

This cluster contains gamers who haven’t tailored to at this time’s sport. Comprised completely of massive males, these gamers can’t shoot the three ball and as a substitute play to their strengths contained in the paint.

3. Gold Cluster: Stretch Forwards

Fashionable Quintessential Participant: Brook Lopez

Now, this cluster contains gamers who have tailored to at this time’s sport. Additionally comprised primarily of massive males, these gamers play the sport in a way that offers their crew extra spacing on the ground and one other capturing menace to look out for.

4. Turquoise Cluster: Shot-Creating First Choices

Fashionable Quintessential Participant: Stephen Curry

These are gamers who’re creating pictures each for themselves and for his or her teammates. Widespread in Curry, LeBron, and KD, they’ll rating the ball at will, however they may even create open seems for his or her teammates. Oftentimes, they’re the primary possibility when it’s time to shut out a sport.

5. Purple Cluster: Defensive Anchors

Fashionable Quintessential Participant: Herb Jones

When the opposing crew’s greatest participant is on a warmth verify, it’s time to place one in every of these gamers in to protect them. They aren’t precisely essentially the most environment friendly on offense, however that’s okay as a result of their function is on the opposite facet of the ground.

6. Olive Inexperienced Cluster: Shot Creators

Fashionable Quintessential Participant: Jordan Poole

When the ball will get in these gamers’ arms, the ball is getting shot. Simply seeing Kyle Kuzma and Jordan Poole right here ought to let you know all you must learn about their dominating stats: factors. They’re right here to attain for his or her crew.

7. Pink Cluster: Dependable 3-Degree Scorers

Fashionable Quintessential Participant: Michael Porter Jr.

Michael Porter Jr. in all probability may have (and perhaps ought to have) been part of the cluster with Kuzma and Poole, however he isn’t as a result of these group of gamers can do a little bit of every thing at a barely decrease price than the first stars on their crew. They’ll shoot the three and the mid-range, however they’ll additionally rebound, help, and play first rate protection occasionally.

8. Blue Cluster: Strong Function Gamers

Fashionable Quintessential Participant: Dorian Finney-Smith

Offensively not essentially the most environment friendly however on the roster for a cause. Gamers on this cluster make performs that aren’t typically proven on the stat sheet and sometimes hit a 3.

Rookie of the 12 months

With a view to carry out the evaluation for rookies, I expanded the information to additionally embrace gamers who’ve performed at the least 24 video games somewhat than half the season (41) with the intention to get a wider perspective of the varied taking part in types of final season’s rookies. I additionally eliminated profitable stats from the information as a result of awards just like the Rookie of the 12 months are sometimes given out to the rookie who carried out the very best, no matter how his crew carried out. After cleansing the information, I calculated the within-cluster sum of squares and located a big drop-off at okay = 6 clusters.

The finalists for the Rookie of the 12 months (Banchero, Kessler, Jalen Williams) are notably in three completely different clusters. It goes to indicate that these gamers all have very completely different taking part in types and contribute to their groups in several methods. Finally, Banchero was chosen as Rookie of the 12 months with 98 of 100 doable first-place votes, and it isn’t shocking to see why. He’s an influence ahead who’s in the identical cluster as two high-usage guards, averaging 20 factors, 7 rebounds, and 4 assists on an Orlando crew that appears to be trending upwards.

Deserved Rookie of the 12 months: Paolo Banchero

Precise Rookie of the 12 months: Paolo Banchero

Defensive Participant of the 12 months

For the Defensive Participant of the 12 months (DPOY) and Most Worthwhile Participant (MVP) awards, I filtered to account for the brand new guidelines going down this season: a minimal of 65 video games performed and 20 minutes per sport. Because of this, the DPOY winner Jaren Jackson Jr. is just not included right here as a result of he solely performed in 63 video games. I additionally filtered the information to solely use defensive stats and embrace gamers whose sum of steals and blocks per sport was at the least 2. For context, the final time a participant received the DPOY award with out matching that standards was in 1991, when Dennis Rodman averaged 0.8 steals and 0.7 blocks per sport.

Whereas it’s no shock to see gamers like Herb Jones and Bam Adebayo, it is perhaps odd to see gamers like Anthony Edwards and Shai Gilgeous-Alexander on this visualization. However each of those gamers have made important strides in guarding the perimeter and affecting the opponent’s capacity to shoot effectively.

The purple cluster contains two of the three finalists for the Defensive Participant of the 12 months Award. Based mostly solely on crew stats, it would appear like Evan Mobley could be a front-runner for the award. Final 12 months, the Cleveland Cavaliers had the very best defensive score within the league, gave up the third least factors within the paint, and gave up the fourth least second-chance factors. However the DPOY is a person award, and it’s exhausting to disregard what Brook Lopez achieved final season: a league-high 193 blocks. Contemplating Milwaukee already has former DPOY winner Giannis and solely ranked thirteenth in opponent factors within the paint, it’s simple to see why Brook Lopez could have deserved to have received the award.

Deserved Defensive Participant of the 12 months: Brook Lopez

Precise Defensive Participant of the 12 months: Jaren Jackson Jr.

Most Worthwhile Participant

With a view to choose what standards to make use of for the MVP award, I filtered the information to solely embrace gamers who averaged at the least 20 factors per sport and had at the least 5 win shares.

The cluster evaluation reveals two compelling clusters that solely embrace one participant in every of them: Nikola Jokić and Joel Embiid. Embiid, though averaging 33 factors per sport, shot worse than Jokić with a a lot greater utilization price and had worse stats in PER, BPM, VORP, and principally every thing efficiency-wise. It additionally doesn’t damage to have a look at the playoffs, the place Embiid’s 76ers misplaced to the Celtics in seven video games. He shot 5 for 18 and had 15 factors in a sport the place Jason Tatum had a historic 51 factors. In the meantime, Jokić led his crew to a first-ever championship, simply beating the Suns, Lakers, and Warmth on the way in which. In hindsight, it’s simple to see why Jokić ought to have received the award.

Deserved Most Worthwhile Participant: Nikola Jokić

Precise Most Worthwhile Participant: Joel Embiid

Now, how can an evaluation like this be of use from a enterprise perspective? Coaches and common managers are at all times on the lookout for particular gamers to assist strengthen their roster. This doesn’t at all times imply “go and get the very best participant” obtainable. We noticed what pairing Kyrie, Harden, and KD did, and we might even see one thing comparable with Beal, Booker, and KD in Phoenix this season.

As an alternative, it’s higher and extra strategic for groups to focus on gamers who specialise in a selected class, whether or not that be in three-point capturing or on protection. That manner, they’ll construct a roster round their star(s) somewhat than with. This technique will also be used throughout the NBA Draft with the intention to choose the very best participant to assist their roster.

Ok-means clustering will also be utilized when making an attempt to sport plan for an opposing crew or matchup. Information may be segmented to account for the way effectively a selected participant or lineup performs in opposition to an opposing matchup or at a selected location. Gamers or lineups can then be clustered to show how efficient they are often in opposition to one other participant or lineup. From there, coaches can resolve their greatest beginning lineup, matchup gamers, and distribute minutes accordingly to what the information reveals.

Ok-means clustering is only one of many algorithms that may be utilized at this time. As groups proceed to evolve in the way in which they give thought to basketball, knowledge will solely more and more change into extra necessary in a sport the place the smallest modifications may be the distinction between profitable and dropping.