# Nylon Calculus: Finding and quantifying similar shooters in the NBA

A couple of months back, we ran a series of posts at Nylon Calcculus that challenged our ability to blindly guess a player’s shot chart, presenting an unnamed chart with a brief, but more colorful description of the shooter’s background. While a fun game to play, it was indirectly testing our ability to translate our visual understanding to a more numerical, on paper understanding of a shooter. In general, when we watch a game, we can classify shooters based on what we see. For example, we can visually determine that J.J. Redick and LeBron James are very different shooters, but J.J. Redick and Kyle Korver are similar.

In a visual sense, we can separate shooters, but if we were to separate between a group of similar shooters, for instance three-point specialists, we would often turn to a more numerical approach, which requires us to look up their volume statistics, general locations based on player-tracking data and efficiency numbers. So, if two players look and statistically appear the same, they must be similar shooters, right?

As Lee Corso would say, “Not so fast, my friend!” The problem? Neither of these steps truly account for the specific spatial information of a player’s shots. While two players might visually and statistically look the same, in actuality, they could be very different based on where and how often they are taking their shots, which is often a reflection of how the player is used within their team’s offensive scheme. That leaves us with the question: How can we better quantify and identify similar shooters?

Measuring shot similarity

Fundamentally, shots should always be considered within the context of their spatial information. For example, it’s not just a James Harden two-point mid-range jump-shot, but it’s a James Harden two-point jump-shot, from the left wing, 14 feet from the basket. The former description more accurately describes Harden’s shot than what we process while watching a game or specifically find from his player-tracking statistics. More importantly, shots taken within close proximity of each other should also be considered when we compare shooting tendencies because Harden taking a jumper, one foot to the left of his 14-foot attempt, is near identical.

As a result, what we really should be considering when we compare shooters is the relative distribution and density of their shots. Now, shot charts can be found quite readily online, such as two excellent ones put together by Austin and Todd, but few, such as Peter Beshai’s application, allow for simultaneous comparison. In terms of finding similarities between shooters, some work related to this issue has been done previously by Kirk Goldsberry, Luke Borne, Andrew Miller and Alexander Franks who collectively developed a similar process to classify similar shooters, but their methodology was applied to characterize the defensive skill of NBA players.

So, embarking on somewhat of a new adventure, my Reader’s Digest approach is twofold:

Estimate the spatial distribution of a player’s shot chart two-dimensionally: For each shot, a small imaginative, uniform 2D bell curve or “bump” is placed on a 2D surface of a court at the location of the shot. The size of the “bump” is large enough where nearby shot locations also get a smaller “bump” too. Carry this over all shots taken and you are left with a 2D spatial density distribution that reflects the locations, but also the density (size of the bump) of shots that take into account the similarity of nearby shots.

Measure the divergence between players’ distributions: The divergence measures, for example, if you were to use Doug McDermott’s shot chart to predict Kyle Korver’s shot locations, how wrong would you be? The smaller the divergence, the more similar McDermott is to Korver.

## A tool to find similar shooters

Building off of this methodology, I created an interactive R-Shiny tool that allows you to numerically and visually find the shooters most similar by shot chart for a given targeted player. The application allows you to compare the targeted player’s shot chart side-by-side while browsing through a list of his most comparable shot charts. A couple quick notes:

The shot charts show attempts by location using a point, with the size of the point corresponding to the frequency of that shot location.

Divergence values are not cross comparable, so a divergence value of 1.17 for example, is not the same when looking at Steph Curry as it is for Brook Lopez.

## Finding similarity beyond spatial information

Typically, the process of identifying and measuring similar shooters in basketball requires us to mesh our visual and numerical interpretations of a player and conclude with a generalization. The advantage of this model is that it indirectly does both of those things for us simultaneously, but on a much finer level of detail because it’s based on the spatial information of the shot. However, it’s important to recognize what we are actually comparing with respect to shot charts, which is the combination of influences from individual player preferences as well as influences from a player’s offensive system.

From season-to-season, general habits from a player will show up. For example, James Harden will most likely always prefer shooting from the left side of the court and Steph Curry will proliferate from behind the three-point arc. However, their shot charts from season-to-season will never be the same and much of this is a result of how the Rockets and Warriors will vary their use of these players, let alone their individual development. As a result, the similarity between shooters that the model is capturing is also indirectly accounting for how a player is deployed on the court, which brings an additional dimension to the model.

To illustrate this point, let’s take a closer look at James Harden whose most similar shot chart is Kemba Walker. While watching these two players on the offensive end there are two apparent tendencies that they exhibit. First, both are not shy about pulling up from behind the arc, but second, and arguably the most notable trait they share is their natural inclination to drive and settle for mid- to deep- range jump shots. Conceptually, Walker might not be the first shooter that most would compare to Harden, but when you take into consideration their individual playing styles, their similarity becomes more apparent.

While the model is able to help find a shooter most comparable to Harden, it is also picking up on underlying reasons why we might additionally be seeing Walker associated to Harden and it may have to do with how the Hornets and Rockets use each of these players respectively. For each team, both Harden and Walker are often the beginning and end for offensive creation and production for their team. With the ball most often in their hands, the Hornets and Rockets rely upon these players to establish offense through nifty dribble-drives to create that results with them either finishing or distributing near the basket or pulling up for a mid-range jump shot. While they both might excel in these areas naturally, much of the reason their shot charts end up so similar is because of the position they are consistently put in on offense that leaves them taking shots from these areas.

The Harden-Walker scenario highlights an important concept to consider when we think about shot charts, let alone compare them between players. Certain similarity matchings may seem strange at first, but the beauty of shots charts are that they often tell us a secondary narrative about a shooter. For example, taking a closer look at Andre Iguodala tells us that Derrick Williams has the most similar shot chart to him. Give me ten guesses before I enter Iguodala into my application and none of those ten will be Williams. Not only do they come from offenses that are actually light-years apart, but on the surface they don’t seem like offensive players we associate together.

This is a scenario when potentially our visual understanding of a shooter can mislead how we would categorize him. Upon closer look, there are two immediate aspects of their games that stand out: Their ability to play close to and above the rim on lob passes and their ability to drift behind the three-point arc for open three-point attempts.

More importantly, many of these opportunities are a result of successful playmaking abilities by their teammates as they both fill a hybrid forward position where Iguodala is much longer than your typical small-forward and Williams is much rangier than your typical power-forward. Shooters that benefit from lob passes or drive-and-kicks are going to end up with shots near the basket and from behind the arc, so it’s not all too surprising to see these two players associated together. Do their shot charts reflect their personal preferences on shots? Maybe, but there is no doubt that what we see is a reflection of how they are used within their offensive system.

At the end of the day, regardless of offensive system, no two shooters will ever be exactly the same and that is part of the beauty of basketball. While this application can help us more accurately compare shooters, it’s still important to understand what is contributing to the similarity measurement. Knowing that Harden and Walker or Iguodala and Williams are similar shooters is revealing, but understanding why that is the case tells a more interesting story and is something we can now do a little bit better.