The Diff: Estimating NBA ShotScores through shooting zones

The Diff

The Diff is your weekly WFNY look into the amazing world of sports statistics. For a complete log of articles, click this link. Last week, I wrote about three intriguing stat-lines to watch for the 2013-14 Cavaliers. This week, I’m getting into NBA shooting charts.

The Diff

One of my favorite sportswriters is Grantland’s Kirk Goldsberry. Like many of my favorites, he’s a non-traditional writer. A geography professor at Michigan State, he emerged onto the NBA scene via the 2012 Sloan Sports Analytics Conference. His project, titled CourtVision, applied his signature specialty of spatial analysis to the game of basketball. It went viral – or at least basketball Twitter viral. Since then, Goldsberry has taken off, and the visiting scholar at Harvard also contributes regularly to Grantland and ESPN properties. His latest column from last week, about a new statistic called ShotScore, is what I’ll be writing about today.

With his article last week, Goldsberry uses the example of LeBron James. Not only the best all-around basketball player in the world, he’s also by far its most effective interior scorer. He shot 72 percent inside the paint last season, a staggering number compared to the NBA average of 56 percent, per the reported data. This difference leads to the overall formula he uses for ShotScores:

For example, last season LeBron James attempted 1,354 shots. Using that league-wide baseline as our guide, if an average NBA shooter attempted this exact same set of 1,354 shots, he would produce a yield of 1,397 total points.

James actually yielded 1,628 points from that constellation, 231 more than expected. No player accumulated more points than expected than James. By accounting for the fundamental relationship between court space and NBA shooting averages, we can see which players scored the most and least points above expected levels in the NBA. And we can figure out which players are actually the most effective scorers in their native shooting habitats.

(Emphasis added my myself for future clarity.)

As you can see in Goldsberry’s description, that makes James’ 2012-13 ShotScore a total of 231 — that’s what he scored more than expected. Then, Kevin Durant ranked second at 204, followed by Steph Curry at 164. In order to compute these ShotScores, Goldsberry was able to track the exact space of every single shot in the NBA last season. That’s a fascinating data set of about 200,000 total shots. That’s insane and incredibly time-consuming.

Thus, whereas Goldsberry’s introductory post to ShotScores was more scientific and proprietary (using exact spots on the court) my follow-up data today will be more basic and transparent (shot zones). Instead of using a team of co-researchers, I’m just using the friendly tools over at By looking at shooting zones, not specific exact shooting positions, I can create an estimated version of ShotScores that’s good enough for basic arguments and easier to parse through en masse.

NBA averages by shot zone

Let’s start with this chart of NBA averages for various field goal zones over the past five years.

nba shot zones 2008-2013

Note the similarities between that chart and the more aesthetic one that the spatial analyst Goldsberry created for Grantland. Based on efficiency field goal percentages – which assign an extra point to threes, of course – the most efficient shooting zones are in the restricted area or all around the three-point line. The least efficient shots are the other type of two-pointers, which still account for nearly half of all field goal attempts.

Now, the formula I’ll be using for my estimated ShotScore algorithm is just based on the expected average from these various zones. Instead of actually tracking the exact difficulty of every single spot on the court, I’m just doing a more simplistic interpretation. The end product is somewhat similar: Finding the most effective shooters and shooting teams, given their choices of shots.

So again, this is where my results and Goldsberry’s will differ. For example, my analysis has James leading the NBA with a 271 (not 231) ShotScore, followed by Durant at 243 (not 204) and Curry at 204 (not 164). Perhaps my data magnifies both positive and negative extremes by grouping all shooting zones together. I’m not certain just yet; this is merely an estimate to be used in larger practice. I’d love to continue the comparison analysis another time. More caveats to this data analysis are listed at the bottom.

Looking at the ’12-’13 Cavs

Next up, here’s a list of the top seven and bottom seven ShotScore teams overall during the 2012-13 season, comparing their shooting efficiency to league average expectations:

 nba teams shot zones 2013

The Cavs as a team ranked No. 25 in ShotScore last season. That’s not great. And this fits into an underrated offseason Cavaliers narrative: the team ranked No. 27 overall in the league with a 47.3% efg last year. So for as much as the defense needs help – as’s John Schuhmann wrote in detail recently – the offense, and the team’s shooting in particular, still needed a significant amount of work.

The reason why the team likely jumped from the efg% rankings to ShotScore: More bad shots. Just 37.1% of the team’s field goal attempts came from the restricted area or from corner threes, the two most efficient zones on the court. This was the third-lowest such proportion in the league, trailing only Dallas and Golden State.

Cleveland’s offensive shooting strengths last season: They were an above average mid-range shooting team with an odd propensity for making non-corner three pointers. They were one of just three NBA teams to shoot better from non-corner long-distance opportunities than the usually more effective choice (Miami and Dallas were the other two). From mid-range, the team did well thanks to Kyrie Irving and C.J. Miles, and projects to get even better this season with thanks to Jarrett Jack, Anthony Bennett and internal improvements.

But, the Cavs were among the worst inside the paint. Overall, they shot just 49.5% inside the paint, second-worst to only the Charlotte Bobcats. By contrast, the NBA’s best ShotScore team, the Miami Heat, shot a tad over 60% inside the paint. That’s a gigantic difference over the course of an entire NBA season where teams averaged nearly 3,000 field goal attempts inside the paint. This lack of efficient inside scoring was a huge issue for Chris Grant’s roster.

Individual Cavs Notes

A final chart for today: Looking at the 2012-13 Cavs by individual player ShotScores in each shooting zone.

cavs shot zones 2013

The team’s leader in field goal attempts, unsurprisingly, was Kyrie Irving. While he ranked among the top 60 in the NBA in ShotScore despite missing one-quarter of the season, he still has one major weakness: finishing inside the restricted area. This was something that Jalen Rose and Bill Simmons mentioned in passing during their now-controversial Grantland Cavs preview. The average NBA guard had a 57.3% efg% inside the restricted area. Irving has to improve here, especially in the middle quarters.

Also on the negative side, Dion Waiters (eighth) and Alonzo Gee (fourth) ranked among the worst players in the NBA last season in this estimated ShotScore. Waiters struggled immensely in the restricted area, although not as much as he did at the start of the season. As mentioned last week, Gee was absolutely miserable from the corner three, despite taking over 120 shots from that zone.

C.J. Miles was quite good last year. But he hasn’t always shot that well. In his previous three seasons, he had just a 33.2% efg% from mid-range and 48.6% efg% from threes. Those are dreadful, way below average numbers compared to his surprisingly efficient production with the Cavs. Will it continue? Perhaps not, but it would be a huge boost to the offense.

As mentioned last week, Wayne Ellington and Shaun Livingston were large catalysts for the Cavs having the seventh-most efficient offense in the NBA for a 38-game stretch last season. They were the other two positive ShotScore performers for the Cavs, after Irving and Miles. Their departure could be an underrated storyline as well.

And finally, to touch on Fear The Sword’s David Zavac’s great follow-up post about Anderson Varejao’s mid-range tendencies, I’ll share a few more stats. Out of Varejao’s limited field goal attempts last season, 29.2% came from mid-range. That’s a comparable number to Ellington (29.5%) or Waiters (29.7%). The average NBA player had 28% of their attempts coming from mid-range. Again, I think Varejao shouldn’t be out there that much.

Caveats of this analysis

Again, this post today serves as a follow-up to Goldsberry’s introduction to the ShotScores statistic. I really enjoy how his formula puts a very hard-to-understand relationship in simple terms with one easy number. His formula obviously has its more scientific advantages than my zone-based approach. Alas, I did what I could with easily available data.

Some of the other items that I wanted to point out for the sake of future analysis: shot creation, floor spacing and defensive ShotScores. The first three are tricky topics as it relates to statistical analysis in basketball. Obviously, analysts want there to be easy efficiency metrics; but how can one truly enumerate the value of a volume scorer?

Guards like Kobe Bryant and Allen Iverson have been vilified for years for their inefficiencies, yet have transformed the game. Perhaps that’s where Dion Waiters will lie. Do I ever expect him to become a Steph Curry efficiency magnet? Absolutely not, but there is still practical value in what he can do and he’s sure to improve as his career continues.

Where my argument with David Zavac also began was from the concept of floor spacing. How much does it help that a player like Anderson Varejao even is a mediocre threat from mid-range? Maybe if he’s doing that throughout 82 games, it can open up the interior for other players to improve. That could increase other team shooting efficiencies. Who knows how domino effects really work in terms of team shooting metrics.

And finally, I’d love to look at estimated defensive ShotScores some time in the future. Everyone knows that Indiana’s Roy Hibbert was a great deterrent of inside shot attempts, but what does that really mean? How does it affect estimated points? And does the Cavs defense have similar problems to their offense inside the paint?

What other items are you curious about with this data for the future? Feel free to share in the comments and I’ll reply back as possible with some of the possible answers from my spreadsheets.

  • WayneEmbrysKids


  • WFNYJacob

    Gee had the second-worst ShotScore on corner threes in the NBA. Only player that was worse: Andre Iguodala (-40.1), who was just 26-for-101 from the corners.

  • Ezzie Goldish

    The Waiters and Gee issues make me wonder if those are a) why the Cavs have them (their ability to get those shots) and b) if those are reasonable to expect improvement on this year.

    I believe Grant said what they loved about Waiters was his ability to get to certain spots on the floor.

  • WFNYJacob

    The expected improvement caveat is far easier to see with the 21-year-old Waiters than the 26-year-old low-profile journeyman Gee.

    But it’s been oft-reported how inefficient Waiters was last season. Matt Moore wasn’t in the wrong for so widely criticizing him. The good news is that he improved his shot selection and efficiency throughout the year, as I shared on Twitter a few times.

  • Ezzie Goldish

    Yeah, meant to add I’m more confident re: Waiters in that regard. Good stuff.

  • mgbode

    somehow missed this Goldsberry article, thanks for bringing it to my attention and then going 10steps further and providing the Cavs element to it.

    the only thing I think I’d add to the score would be a per shot indicator. It’s useful to see the volume people are doing better, but to find the hidden gems it’d be nice to see who does the most per shot too and how they compare to the elite guys.

    great stuff.

  • WFNYJacob

    Well, mgbode, that’s why efg% and such exists. So I could share some folks, but that’s why shooting percentages and all those already are useful tools for comparisons. :)

  • WFNYJacob

    Another thing: The ShotScore / 100 FGA stat is something Goldsberry cited in his article.

    Here’s your top 6 NBA leaderboard in that stat (min. 200 FGA):
    Matt Bonner, 23.7
    Jose Calderon, 22.9
    Brandan Wright, 22.7
    Kyle Korver, 22.4
    Serge Ibaka, 20.5
    LeBron James, 19.9

    And your bottom 6 NBA leaderboard (min. 200 FGA):
    Gerald Wallace, -19.9
    Ricky Rubio, -20.3
    Dahntay Jones, -21.0
    Will Barton, -23.2
    Kevin Love, -24.5
    Draymond Green, -27.4

    A few quick notes: Serge Ibaka is spectacular from mid-range. Jose Calderon had a great offensive season. LeBron is a monster. And man, yuck, Kevin Love had a really bad year.

  • mgbode

    thanks. this is exactly what I was asking. eFG% doesn’t demonstrate where they shot on the floor, which was my point. this simple additional metric adds the two together great.

  • WFNYJacob

    Well, it’s in my Cavs chart up above. Enjoy. :)

  • Vindictive_Pat

    I seem to recall that Earl Clark excelled in that spot (at least on one side of the court), and I think it was a Goldsberry graphic, but can’t remember where I saw it. It’d make sense if Chris Grant wanted a SF who could get more production from that spot than what Gee was giving since it’s such a valuable position to shoot from.

  • mgbode

    that’s what I get for commenting after reading, but not pulling up the charts to go through :)

    hopefully, replacing Gee shot attempts with other people (Jack, etc.) and getting improvements from Waiters is a big shot in the arm to make up for the losses of Ellington/Livingston. also, maybe the bolstering of the reserve units overall is enough to help the final line as well.

  • Ben Frambaugh

    I had seen that too…and I believe the spot is the right corner (when looking at the basket.)

  • Ben Frambaugh

    I’m quite amazed that Kyrie does significantly better from “Other Threes” than he does from “Corner Threes” (where he was sligthly below average there.)

  • WFNYJacob

    Clark was just 10-for-26 (38.5%) from corner threes last year. Just about average. He attempted just 10 total threes in his first three NBA seasons; that jumped to 104 last year, but most weren’t from the corners.

    Overall, he had a -12.5 ShotScore in 386 FGA. Clark is not really here for offense, although he’s slightly better than Gee.

    Wrote much, much more here about Clark right after he signed:

  • WFNYJacob

    Among the 170 players with 100+ three-pointers last season, Kyrie had the fourth-lowest ratio of Corner Threes / Total Threes at just 5.6%. The top eight players with lowest ratios: Dirk, Harden, Lillard, Irving, Durant, Bargnani, Kemba, Nash. Kyrie’s Corner Three and Other Threes shooting percentages weren’t far off, considering the sample size.

    Schuhman at wrote about Jeff Green having the best difference (17.9%) between corner three makes (45%) and non-corner three makes (27.1%) over the last three seasons:

    Looking at last season alone, Nick Young (16.5%) and Ty Lawson (14%) had the two other largest differences at being better from above the break threes. Kyrie only was at 2%.

  • Ben Frambaugh

    All of this data still changes nothing about my amazement. LOL

  • Vindictive_Pat

    Correct, I think he was better from the right corner than the left corner, but I wouldn’t say he’s always that way… probably too small of a sample.