# Nylon Calculus: Introducing defense-adjusted 3-point percentage

## 3-point percentage is the most commonly used statistic to measure shooting in the NBA. By adjusting for defensive attention, we can create a more accurate figure.

If you asked any 100 NBA fans who is a better shooter, Damian Lillard or Pascal Siakam, all 100 would say Lillard. However, if you asked those same fans the best way to judge 3-point shooting, most would likely respond with 3-point percentage. Last season, Pascal Siakam shot 36.9 percent from 3-point range; Damian Lillard also shot 36.9 percent.

NBA defenses are designed to take away opponents’ best options, and as a result, teams’ most prolific shooters are typically given the toughest diet of looks. Not all shots are created equal, and as a result, neither are all shooting percentages.

It’s much more difficult for players such as Damian Lillard, Stephen Curry and James Harden to maintain a certain efficiency from 3 than it is for Meyers Leonard, Draymond Green or P.J. Tucker. The bottom line is that 3-point percentage has blind spots as a metric to accurately judge 3-point shooting ability.

## Points above expected

Rather than looking at raw 3-point percentage, we can more accurately judge a player’s shooting ability by judging how well they shot against differing levels of defensive pressure. Using NBA tracking data, we can see how often and how well a player shot when closely contested, lightly contested and when they were open. We can then look at how well they performed against the expected outcome for a league-average shooter.

I took data from NBA.com’s tracking stats, which records a player’s 3-point attempts, makes and percentages with defenders at varying distances. I then calculated the league average percentage at each level, multiplied it by the number of attempts, and created an “expected points” basis for each player’s difficulty of attempts.

Tracking data breaks down when the nearest defender is 0-2 feet away, 2-4 feet, 4-6 feet, and 6+ feet away. Comparing a player’s actual 3-point scoring against their expected points generates a figure we’ll call “3-point value added.” 3-point value added is an estimate of how many points a player’s shooting ability creates above the average shooter — how many points they scored, relative to what an average shooter would have scored on the same difficulty of looks.

The names at the top of the list are the ones you would expect:

Bryn Forbes and Danilo Gallinari being in the top 10 is perhaps a bit of a surprise, but the rest of the names are exactly who we consider the league’s top shooters. Stephen Curry’s place at No. 1 isn’t surprising in the slightest, but it’s jarring to see the country mile by which he’s beating the rest of the competition.

The list of the league’s most harmful shooters is a bit more eye-opening. Good players who have poor 3-point percentages and attempt a high volume of looks, typically generate a ton of negative value:

These aren’t necessarily the worst shooters in the NBA. Instead, they’re the players who would have benefited the most from league-average 3-point shooting, given their shot selection and volume. A bad shooter with a high volume of shots will have a more negative impact than a horrible shooter with a low volume of looks.

Plotting the league average 3-point value added gives us pretty close to a bell curve distribution:

Our sample is skewed pretty heavily below to the left, with 320 players posting a negative figure and just 169 posting a positive one. Better shooters are more likely to have more attempts, so it shouldn’t be surprising that they’re able to skew the average above the median.

## Points added per 100 shots

A large part of 3-point value added is the number of shots a player puts up. If we wanted to look at just how efficiently a player shoots relative to league average, the better number would be “points added per 100 3-point shots.”

Eliminating players with fewer than 82 attempts last season, we’re able to find which players added the most volume per shot. Of course, the volume of shots a player can generate at above-average efficiency is extremely important. However, if we’re trying to find which shooters were the most efficient last season, we should be basing it off their value-added per attempt.

The list of least efficient shooters in the league (min. 82 attempts)  still features many familiar names:

The biggest name that jumps out on this list is Giannis Antetokounmpo. Looking deeper, it’s easy to see why he ranks so low. Giannis shot 25.6 percent on 3-pointers, the third-lowest among all players with at least 82 attempts, and because of his unbelievable skill-set, defenses are willing to sag off him and give him open looks. A poor percentage on an easy set of shots, it’s no wonder he was only better than Dragan Bender as a shooter last season.

For a statistic to be effective, people want to compare it against numbers they’re already using. Saying that Curry added 25.35 points per 100 3-point attempts is nice, but without a subset to base it off of, we don’t have much to judge it against. Instead, we can look at how much value a player created per shot attempt, translate that to their “expected percentage above/below average,” and factor the league average back in for a “Defense-adjusted 3-point percentage.”

Hopefully, this shouldn’t come as a shock, but the correlation between raw percentage and defense-adjusted percentage is extremely high. Defense impacts shooters, but in general, good shooters are still going to shoot a high percentage, and bad shooters are going to shoot poorly.

However, there are many players whose 3-point percentage is deceivingly high or low based on opposing defenses (min. 82 attempts).

Players whose defense-adjusted 3-point percentage exceeds their normal percentage are players who demand the defense’s attention. It makes sense that James Harden has the largest gap between his 3-point and defense-adjusted 3-point percentage, given his notably difficult shot selection. Perhaps no one in the NBA has a higher difficulty of attempts than the almost-MVP. Other names like Kevin Durant, Kemba Walker and Kyle Korver all check out as well. In general, better shooters are going to outshoot their 3-point percentage.

There is also a clear trend in players who receive an easier set of looks than their percentages would suggest. Every player in the bottom 10 — with the exception of Royce O’Neale — is a power forward or center. Why might big men receive more open looks than their percentages suggest? That’s an interesting question on its own. The primary reason likely relates to their defensive matchups and their opponent’s inability to effectively guard the perimeter.

Finding the difference between a player’s 3-point percentage and their defense-adjusted 3-Point Percentage can help us determine how much a player’s 3-point percentage is aided by their teammates, how much a defense respects the opposing shooters, and how well a player/team is able to generate open looks from behind the arc.

Comparing the differences between raw and defense-adjusted 3-point percentage may be more insightful than using the statistic on its own. Defense-adjusted 3-point percentage doesn’t account for shots off the dribble or shots from varying distances behind the arc. However, it does give us a metric that is more representative of a player’s true shooting ability than raw 3-point percentage; it gives an idea of how defenses cover opposing shooters and it tells us which players provide the most value relative to league-average shooting.

If you’d like to view a full leaderboard of Defense-adjusted 3-point percentage, 3-point value added or points added per 100 shots, I’ve made the entire database publicly available.