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LeBron James vs. Kevin Durant: What matters when we assess the NBA's best scorers?

Thursday's Hook is a response to Kirk Goldsberry's ShotScore, a metric aimed at assessing scoring effectiveness in the NBA. The question, as usual, pits LeBron vs. Durant. Here are the problems with Goldsberry's result.


On Wednesday, Grantland's Kirk Goldsberry unleashed his newest creation: ShotScore. The metric aims to credit scorers based on where shots are taken. The impetus Goldsberry presents is that LeBron James scored more points at the rim than anyone in the NBA and at the league's highest conversion rate, yet led no conventional stat leaderboards, specifically field goal percentage. You really need to read the whole thing, but this is a critical explanation for what Goldsberry seeks.

Anybody who has ever played H-O-R-S-E can tell you that some shots are easier than others; a layup is easier than a free throw, which is easier than a corner 3. This basic tenet is almost entirely overlooked by our most popular shooting metrics. Similarly, NBA players are all special, and over the course of a season each player generates his own unique "constellation" of shot locations. [...] We can improve our shooting metrics by accounting for court space and the unique natures of players' shot constellations.

At the end of the season, James's average shot distance was 11 feet; [DeAndre] Jordan's was 2.8 feet. Essentially, through the hazy lens of FG percentage, James is penalized for having a jump shot, while Jordan is rewarded for not having one. Despite being a very good 3-point shooter, a good midrange shooter, and the most dominant interior scorer in the game, James trailed players like DeAndre Jordan and JaVale McGee in a crucial scoring metric. What the hell?

ShotScore aims to fix that by giving players credit for shooting more efficiently in any given spot on the floor than the league average. If the league shoots 50 percent at spot x inside the arc and LeBron shoots 75 percent there and takes 100 shots there over the course of a season, he scores 150 points whereas the average spot-x shooter would score 100. So at this spot, LeBron's unique spot-x shooting skill earns 50 extra points for the Heat. Do that for every spot on the floor -- it's not clear how many zones Goldsberry actually crunched, but it appears to be a lot -- and add it all up and you get a stat (ShotScore) that tells us the three most effective scorers in the league were, in order, LeBron, Kevin Durant and Stephen Curry. This is, of course, a more reasonable result than, say, the field goal percentage leaderboard led by Jordan and McGee.

But, as fascinating, lovely and valuable as ShotScore appears to be, there are three problems I see.


[Shotscore is] complex enough to potentially turn off the metric-curious fans out here

The average Excel jockey cannot do what Goldsberry did. The detailed shot data is not open source and the effort is, as with what most of Goldsberry publishes, both extremely complex and elegant (a powerful combination). But the mere fact of the statistic's complexity is not totally relevant. The question is whether the complexity adds anything of value. (Because boy do I know arty but extraneous complexity ...)

To answer that, I went about creating my own "effective scoring" stat using public data available at Basketball-Reference (and many other places) and a Google Spreadsheet. (Here's that spreadsheet. Do with it what you will.) I used straight theory and a common base stat one step up from field goal percentage, effective field goal percentage (eFG). My formula gets each player's number of expected points by multiplying the number of field goals they attempted, league average eFG (.496) and two (the number of points a made basic shot under eFG is worth). Then I subtracted their actual points from the field (points minus made free throws) from the expected points. I named it Extra Field Points.

Goldsberry's complex creation resulted in a ShotScore top three of, in order, LeBron (+231), Durant (+204) and Curry (+164). Here is the Extra Field Points leaderboard.


If the metric was primarily created because existing scoring effectiveness metrics were lackluster -- and they certainly were -- then I fear that ShotScore is the result of using the Large Hadron Collider where a bowling ball dropped from the roof would do. Scoring effectiveness is certainly a product of scoring production and scoring efficiency, with one big ol' asterisk we'll talk about in Question No. 3. To remind myself of it, I'll go ahead and put the asterisk right about here.*

The TL;DR for Point No. 1: there is no chance the average box score jockey can replicate ShotScore on a game or partial season basis, and it's complex enough to potentially turn off the metric-curious fans out here.


This isn't figure skating. You don't get extra points for degree of difficulty, so why should scoring metrics incorporate it?

What ShotScore does is give credit to players for being more efficient than the average league player in the various zones of the floor that Goldsberry has created. But is there any actual value in being a better shooter than the next guy on 16-23 footers on the right side if that shot is still one of the least efficient in your repertoire?

What ShotScore does beyond Extra Field Points is give credit to players who take and make shots from the less efficient spots on the floor, but there's no actual scoring value at the team to taking and making those shots. A two-pointer at the rim, which the average player will convert at a high rate, is worth the same number of points as a 20-footer, which the average player will convert at a low rate. But consider that DeAndre Jordan doesn't take those 20-footers, he takes shots at the rim. Chris Bosh does take those 20-footers, and converts them at a high-level. But a standard DAJ at-the-rim attempt is still more efficient than a standard Bosh 20-footer. So what's the advantage in the 20-footer? Why give Bosh credit for taking a less efficient shot?

You could argue that 20-footers are easier to get off than dunks and layups, and you'd be right. But ... so? Data repeatedly shows a direct inverse relationship at the team level between eFG (and/or offensive rating) and the percentage of shots taken in the long two-pointer range. History tells us that shooting long twos hurts a team's shooting numbers more than it might help by opening up the floor or limiting turnovers. So why would we credit players who take and make long twos at 50 percent at the expense of guys who take and make shots at the rim at 70 percent? All told, that 70-percent shot at the rim helps the team more, based on the numbers. Ten DAJ shots at the rim will earn 14 points. Ten Bosh long twos will earn 10 points.

Yet this is one of the major groups of players that ShotScore elevates: the guys who shoot long twos abnormally well (i.e. the Chris Boshes). Goldsberry's top 10 in ShotScore includes Serge Ibaka (a 15 ppg scorer who drains long, assisted, twos at a high rate), Al Horford, Bosh and Dirk Nowitzki. LeBron and Durant are the only guys who live at the rim and appear in Goldsberry's top 10 (though Ibaka, Horford and Chris Paul do damage there as well). It is otherwise a list of the best perimeter shooters in the league, including low-volume guys like Kyle Korver and Jose Calderon, who each averaged about 11 points per game. You're subbing in Korver and Calderon for Jordan and McGee on the basis that while Korver and Calderon are not more efficient, they are doing damage further from the rim.

The other piece of the pro-jumper argument is that, well, DAJ isn't getting off more than six or seven high-efficiency shots at the rim per game, whereas Bosh can get that 20-footer all night long. The capacity to expand the paint-only player's shot frequency is highly limited. Jordan, JaVale McGee and Tyson Chandler cannot take 20 shots per game and maintain their excellent efficiency. That's absolute true. But Extra Field Points addresses that by incorporating shot frequency just as ShotScore does.

In addition, that's a question on the value of assisted field goals and shot creation itself, which totally isn't addressed in either stat. We know that the unassisted shot is some degree less efficient than the assisted shot. A future iteration of ShotScore may very well account for and give credit to players (like Monta Ellis and Kobe Bryant) who create most of their own shots, much as it currently gives credit to players who take less efficient shots. But as is the case with valuing made long twos over made layups, there's no case to be made that the more difficult shot is worth more to the team unless you can prove that a frequency limit on easier shots exists. The 2012-13 Nuggets, for example, who lived at the rim and behind the arc taking the most efficient shots on the floor all season long, would be the initial counterexample to that theory that comes to mind.

The TL;DR for Point No. 2: this isn't figure skating. You don't get extra points for degree of difficulty, so why should scoring metrics incorporate it?


Free throws really, really matter in measuring scoring effectiveness, but are not incorporated into ShotScore.

* There's that asterisk. This is the big limit on ShotScore as it currently exists. It leaves out a crucial piece of the scoring effectiveness puzzle.

There are two issues at play. The first is that while ShotScore credits better perimeter shooters at the expense of the DeAndre Jordan All-Stars, most free throws are created down where the DAJ types live and not out at the elbows. So, by leaving out free throws, you're negating one of the crucial benefits in having an at-the-rim game, be it at the team level or as a personal choice. There is, of course, the caveat that you've got to be able to draw and hit free throws. Not all DAJ types, especially the namesake, can do those things.

The other issue is that when comparing the effectiveness of scorers, leaving out free throws (both the foul-drawing aspect and the free throw shooting aspect) you're ignoring a fat chunk of the actual scoring happening in the NBA. About 30 percent of Kevin Durant's points last season came at the free throw line. You can't ignore that if you're looking at overall scoring effectiveness.

ShotScore could easily be upgraded with free throws in some fashion, either just figuring in rates at which they are scored or by crediting the different zones on the floor for fouls drawn there. Going more simply, I upgraded Extra Field Points by tweaking the minimalist expected points formula: it's now a player's total shooting possessions (using the standard 0.44 as the adjuster to convert free throw attempts into shooting fouls drawn) multiplied by the league average True Shooting percentage (.539) multiplied by two (the value of a base shot). I subtracted that from total points scored to get Extra Total Points. Here's the leaderboard:


Durant eclipses LeBron, and Harden tops Curry. How? Well, for starters, Durant made 68 percent more free throws than LeBron. KD was No. 2 in the league in free throw attempts and hit them at a 91 percent clip. LeBron, though an effective foul-drawer, took far fewer FTAs than Durant (215 fewer) and hit them at a 75 percent clip. Part of what makes Durant just an incredibly effective scorer is his ability to draw fouls at a high rate and convert them at such a high rate. ShotScore, it seems, ignores that.

Harden over Curry is the same story: the Rocket finished No. 1 in the league in FTAs and attempts 2.7 times as many freebies as Curry. So while Curry did convert his free throws at a high rate (90 percent), he didn't take them nearly as frequently as Harden, James or Durant. In leaving out a crucial piece of scoring, ShotScore negates some of the effectiveness of guys like Harden and Durant, who get to the line really often, and often turn those trips into two points.

There are five players that the ShotScore and XTP top 10s do not have in common. ShotScore includes Calderon, Horford, Bosh, Nowitzki and CP3. In their places, XTP has Harden, Tyson Chandler, Kobe Bryant, Kevin Martin and Tony Parker. The common thread among the XTP exclusives: free throws. Chandler, for example, "only" took 258 free throws. But he did that while taking just 400 FGAs. That's a really high rate of foul-drawing given his shooting frequency. Curry, by comparison, took 291 FTAs and 1,388 FGAs.

The TL;DR for Point No. 3: free throws really, really matter in measuring scoring effectiveness, but are not incorporated into ShotScore.


Goldsberry's work is so exciting. I get giddy when I find out he has something cooking. And ShotScore is an engaging creation. The source of the inspiration -- our total lack of useful metrics to compare effective scorers -- is spot on.

But ShotScore has some pretty glaring problems, some easily fixed and some inherent in the metric itself. My larger concern goes back to something I wrote about SportVu in The Hook a couple weeks back:

It's clear that this is an information gamechanger: so many questions we've wanted answered for years will be able to be addressed by the data. So, a word of caution that also applies to the video indexing and data service Synergy, the current belle of the basketbloggers' ball: let's use this new trove of information for more than just ranking players.

I find Goldsberry's effort here somewhere in the middle: in the end it is a stat that makes its own case by ranking players, but it is trying to address a gap in understanding. But then I think of something TrueHoop's Henry Abbott put eloquently on Wednesday:

As new breed analytics have come to hoops, that's the stuff that excites me. The stuff where not only the best evidence, with the biggest samples, sifted through by the fairest-minded researchers tells similar stories again and again, but where it also lines up nicely (like vegetables and exercise) with things wise people have pretty much always known.

In other words, you can keep your petty little squabbles, the he-said she-said tug-of-war between spreadsheet-based and eye-test or tradition-based analysis. The far more fundamental and interesting question to me is: What is basketball common sense now? When you pan for gold in the muddy new soup of everything we know now from stats, video, coaches, players, GMs ... what glitters? What are the emerging "earth is round" things that, decades from now, we'll hardly fight about anymore, 'cause time will make those things look even smarter?

The end result of ShotScore and its simpler cousin Extra Field Points is that you get a list that matches up with common sense far better than standard shooting efficiency or scoring volume stats would. But a few bits of other basketball common sense -- the importance of free throws, the lack of benefit from taking long twos -- were omitted. When we're trying to advance the discussion and doing so in such high-profile ways, I feel like we as a basketball metric community need to ensure we're incorporating the relevant basketball common sense that Abbott discusses. Leading readers and fans down a crooked path doesn't help the cause, the cause being better understanding and through that more enjoyment of basketball for more people.

But there's one thing Goldsberry writes that I'm in absolutely full agreement with:

This is an exciting time for basketball analytics, but as is often the case, deep explorations into performance often provoke more questions than answers. It's still tempting to assert that NBA analytics are advanced now, but the truth is that we will look back at the current state of affairs the same way baseball nerds look back at the batting average and RBI era. These players give us so much; the least we can do in return is come up with an accurate way of appreciating them.


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