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Distribution Controlled TS%: A New Way Of Looking At The NBA’s Best Shooters

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USA Today Sports

Off the top of your head, who’s the best shooter in the NBA?

I’m guessing you said Kyle Korver or Stephen Curry, maybe even Ray Allen or Dirk Nowizki. But whatever your answer was, you’re right. That’s the problem with answering a question like “best shooter,” there is no generally agreed-upon definition of what makes someone a “shooter” and thus everyone ways all the myriad variables in their own subjective ways.

We have plenty of statistics to measure a player’s shooting ability — field goal percentage, effective field goal percentage, true shooting percentage (TS%) — but they are all entirely dependent on context. LeBron James led the league in TS% (which accounts for both free throws and the added value of three pointers) this season, at 64.9%. But he would probably fall pretty far down anyone’s list of best shooters in the NBA. That’s because LeBron’s astronomical TS% is buoyed by his ability to get to the rim and the free throw line, an ability that isn’t shared by players like Ray Allen or Kyle Korver.

TS%, and all shooting percentages really, provide a somewhat flawed basis for comparison of shooting ability because they are reflections of both a player’s shooting accuracy and their shot selection. This combination is not always intuitively understood, but it’s there nonetheless. For instance, imagine if LeBron made a point of not taking any shot from outside of the paint. It might collapse the entire Heat offense, but it would undoubtedly cause his TS% to skyrocket. Tyson Chandler would be a less hypothetical example of this phenomenon. Research I did last season showed that nearly a quarter of a player’s TS% can be explained by their shot selection, separated from their individual shooting accuracy.

However, there is a way to disentangle shot selection and shooting accuracy, creating a version of TS% that highlights just how good a shooter each player is and leveling the playing field for comparison. The technique is essentially an answer to this question:

What would each player’s TS% be if we had them take the same shots as everyone else?

First of all, because we are talking about TS% when I say shots I’m talking about true shot attempts, essentially shots from the field and trips to the free throw line. The process is simply to identify a league average distribution of shots and then use each player’s own shooting percentages from those locations to calculate what their TS% would be if that was their shot distribution pattern.

However, there is one kink that needs to be worked out before plowing ahead – it’s a little unfair to judge the accuracy of players based on a shot distribution that doesn’t match their actual skill set. For example, if we use the league average shot distribution as the constant for all players, we’ll be including three-pointers. Judging someone like Andre Drummond and his 0.0 three-point percentage on a shot we wouldn’t ever expect him to take in an actual game seems self-defeating. Making this distinction is less important for a player like Drummond who’s offensive skill set essentially rules him out of any discussion of shooters, but it becomes very important around the three-point line. There are several players like David West and LaMarcus Aldridge who merit inclusion in this discussion but don’t take enough three-pointers to make that a fair variable on which to judge them.

The solution was to take all players in the NBA this season who attempted at least 500 shots (remember, true shot attempts) and separate them into three bins based in their shot distributions patterns. I used 90% of shot attempts as the cut-off for each bin, but in layman’s terms they break down like this:

  • In the Paint – Players who rarely shoot outside the paint
  • Mid-Range – Players who shoot mid-range jumpers but rarely shoot three-pointers
  • Three-Point Shooters – Players who shoot from all over the floor, including from beyond the three-point line

Drummond falls into the first group, West and Aldridge are in the second. The third group is the largest and includes players from Chris Paul to Dirk Nowitzki. With these groups defined, I then calculated an average shot distribution from the players in each group. The graphs below show that that average distribution looks like for each.

Screen Shot 2014-04-29 at 7.38.16 AM

With these distribution patterns I calculated something I’m calling Distribution Controlled TS% for each player. The name needs a lot to be desired but this is the metric we’re after — what would each player’s TS% be if they took the same shots as everyone else in their group.

The results for each group are laid out in tables below. For each player you’ll see their Distribution Controlled TS%, their actual TS% and the difference between the two, a very revealing number. Players who have a positive differential are those whose TS% would improve if they used this average shot distribution. Essentially these are players who are hurting themselves with shot selection, players who would be more efficient if they moved closer to an average distribution pattern. Players with a negative differential are the opposite. These are players whose TS% is largely a function of a limited and focused pattern of shot selection. They would be less efficient, sometimes drastically so, if they had to expand their games and take the same shots as everyone else.

Here are the results for the first group, players who take at least 90% of their shots from the free throw line or in the paint.

This is an extremely small group, by virtue of the very limited shot distribution pattern. This is a striking reminder of how important spacing is in today’s NBA and how few players fill a significant offensive role without having a mid-range jumpshot. Of the five, Nikola Pekovic has the highest Distribution Controlled TS%, which would give him claim to being the best shooter in this group. Obviously FT% has a lot to do with those results as free throws make up 17.6% of the shot distribution here and Dwight Howard, DeAndre Jordan and Drummond are all among the league’s worst free throw shooters.

But no one’s definition of best shooter in the league really includes players who don’t leave the paint so let’s move on to the more revealing groups. Here are the results for the second group, players who take less than 10% of their shots from beyond the three-point line.

Surprised? Me too.

Dwyane Wade has the reputation as being a horrifically inconsistent shooter but he’s good enough in the mid-range that his big edge in accuracy at the rim and at the free throw line put him on top. With the caveat that shots in the paint still make up a considerable portion of this groups shot distribution everything else makes sense. Serge Ibaka, Tony Parker, David West and Marc Gasol are all in the top-10. Players who are considerably better in the mid-range than they are at the rim, like Brandon Bass, Dante Cunningham and Luis Scola rank a little bit lower. And of course Tyreke Evans ranks dead last so there is a certain fit with conventional wisdom from the top to the bottom.

What’s interesting here is that with a more versatile average shot distribution than the first group we can start to see how players differentiate themselves with the shots they take. Jordan Hill, Anthony Davis, Blake Griffin and Amir Johnson all rank in the top-15 for Distribution Controlled TS%, but with marks much lower than their actual TS%. This shows them to be capable shooters but ones who recognize the limitations of their own skills and leverage them into more effective patterns. The shot distributions each of those players use is a better fit for their skills than the league average one. We see the same thing at the bottom for players like Evans, Joakim Noah and Greg Monroe.

We also see a few players in this group whose real-life shot patterns make their actual TS% lower than the Distribution Controlled TS% we get with the league average shot distribution. Gasol is one such player although sharing the floor with Zach Randolph and his effectiveness as a passer from the elbows make up for some of the losses in shooting efficiency that come from keeping farther from the basket. But LaMarcus Aldridge is a curious case. The difference between his Distribution Controlled TS% and his actual TS% is 3.2 percentage points, making him stand out as an excellent shooter who could probably benefit from being a little more selective.

Here are the results for the third group, players who take at least 10% of their shots from beyond the three-point line.

This is the group I think most people would consider shooters and there, right at the top, we have our answer. If every player who is active behind the three-point line were given the same distribution of shots, Kyle Korver would be our best shooter. His Distribution Controlled TS% is lower than his actual TS% by virtue of working a few more shots at the rim and mid-range jumpers into his pattern, but Korver still has a has a healthy margin over the rest of the field. Rounding out the top five we have Kevin Durant, Marco Belinelli, Dirk Nowitzki and LeBron James. Even here LeBron’s numbers are inflated by his absurd abilities at the rim, but the fact that he falls in the top five is also a testament to just how much his jump shot has improved.

At the bottom we have Tony Wroten, Giannis Antetokounmpo, Tayshaun Prince, Ricky Rubio and Derrick Williams who would also likely find themselves included on any subjective list of the worst shooters in the league, so again we haven’t moved that far from the conventional wisdom. One surprise is to Stephen Curry ranked eighth in Distribution Controlled TS%. This is probably because his actual shot distribution pattern is so heavily tilted towards three-pointers that pulling him to a league average pattern gives him more shots at the rim and reduces the margin of effectiveness from his jumper.

While Distribution Controlled TS% brings us closer to an empirical answer to who the best shooter in the league is, it still leaves a lot to be desired. Although I referred several times throughout the piece to giving every player the “same shots” that’s not really possible outside the closed virtual reality of a video game. Distribution Controlled TS% removes a player’s shot selection from the equation but the shots a player decides to take are still reflected in their actual percentages from each zone. LeBron’s mid-range jump shots are different in context and defensive pressure than Korver’s and thus their shooting percentages on each don’t reflect their abilities in the same way. I’ve teased shot selection out as much as possible, but it’s still lurking in their somewhere.

However, I think this does give us a more detailed look at a player’s shooting ability than a straight TS% and offers some interesting insights about which players are using an effective shot distribution pattern for their own skills and abilities. We’ve gotten closer to an answer, but numbers can only take us so far. In the hypothetical doomsday scenario of one shot to save my life, I’m still taking Stephen Curry, no matter what my numbers say.

  • nick restifo


    • Ian Levy

      Thanks Nick! I’m hoping to play around with these numbers some more over the next week or two and dive into looking at some individual players.

  • donte

    I think you should make it more clear that by “the same shots” you just mean from the same positions on the floor. If Chris Bosh had to take the same crazy pullup/stepback/highly contested/whatever threes Curry takes he’d shoot in the low teens.

  • Andrew Sutton

    Shot to save my life…I choose Dirk.

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