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October 23, 2013

Advanced NBA Stats Basics

By Ted Knutson

By Jesse Mason

superman_DHoNow is a great time to be a supporter of basketball analytics. The ‘advanced stats’ approach has been creeping into front offices, with ESPN’s John Hollinger getting hired by the Grizzlies as a vice president, forward-thinking Masai Ujiri getting named executive of the year and earning a big pay bump from the Raptors, and long-admired Houston Rockets GM Daryl Morey has had his approach vindicated when it landed his team James Harden and that other dude whose name I forget. [Dwight something? – Ed]

But, as any intro-level college class or 1950s instruction film would ask: what does ‘advanced stats’ or ‘analytics’ mean?

It’s more than just watching games, knowing the points per game of Kobe Bryant, and yelling to the next cubicle that your team’s rookie is “completely unstoppable.” At its most basic, it’s about using stats that explain what we want them to explain, rather than the traditional ones that’ve been used since people first saw a tall guy and went “wow, that guy is good at basketball.” And that starts with the complete destruction of all “per game” statistics.

The basic unit of a basketball game is the possession. Each team gets the same amount of possessions per game (plus or minus a small number due to who uses the last possession in a quarter), and the team wins if they use them more efficiently (ie, more points) than their opponent. Thus, when looking at a bunch of games from a team, what matters is not how many points they scored per game, but how many they scored and allowed per possession. To make the numbers easier to look at, this is usually stated as per 100 possessions, since that’s roughly the number in an average game. Why does this matter in the real world? Because it lets us look at how good an offense actually was, rather than having it affected by how many possessions there were in a game. Running up and down the court doesn’t make your offense necessarily good, and slowing things down to a crawl doesn’t make it necessarily bad, and our stats should reflect this.

For example, this past season, the league’s best offense was the Thunder, with their 112.4 points scored per 100 possessions (also called offensive rating or ORTG) barely edging out Miami’s 112.3. This matches much better with what we can see than if we had used points per game, where the Nuggets had the most with 106.1, and Houston close behind with 106.0. Those were offenses that, while very good, were also the top two in possessions per game (also called pace), at 96.1 for Houston and 95.1 for Denver. The per-game statistics would punish Miami, who played at the eighth-slowest speed, despite their excellent offense.

Similarly for defense, both points allowed per game and per possession (defensive rating, or DRTG) show that Indiana and Memphis were the best on that side of the ball. But DRTG reveals the uptempo Spurs were the third-best there, whereas the snail’s-pace Nets, sixth in points allowed per game, were actually below average in DRTG.

These differences might seem like a whole lot of effort for some minor movement around meaningless rankings, but they’re important: the same logic that applies to teams applies to individual players, and here’s where the shocking revelations come pouring through. By looking at per possession stats for points, for example, we can see who’s truly unstoppable and who is entirely stoppable, but just taking tons of shots.

Some stats should be immediately adopted by everyone, whether they’re the biggest cheerleaders for advanced stats on the planet or a basketball insider stick-in-the-mud who thinks the game died with the retirement of Bill Russell. One of these is True Shooting % (TS%). Instead of the absolutely useless FG% that cares not whether a player was shooting from two, three, or how often they got to the line, TS% is strictly the points a player generates per shot, no matter how they got them. A player that takes three shots and gets three points off of them has a TS% of .500, regardless of whether they took three three-pointers and made one of them, or missed a shot, drunked, then went ½ from the line. Since it doesn’t care how a player got their points, it’s a stat that we can apply equally to Steve Novak, Tyson Chandler, and Monta Ellis. (One of these players had a terrible TS%. Guess which!)

There are a lot of other stats that are percentage-based replacements of their conventional counterparts, which makes evaluating starters against bench players a lot easier. Offensive and defensive rebounding percentage are the percentage of available rebounds that team or player got; assist percentage is the percentage of teammates’ shots the player in question assisted on; steal%, block%, and turnover% are fairly easy to figure out.

(By the way, whoever saw offensive and defensive rebounds, thought “well, those are pretty much the same,” and then put them in one column, deserves whatever death he has surely already suffered. They do totally different things: offensive rebounds give the team an entire new play, and are rare relative to defensive rebounds, which a team would get anyway most of the time.)

Reevaluation of What Matters
You might be asking: so what, stats man? Per possession stats are a replacement for per game ones, but how could that possibly be a whole new way of thinking about the game?

Well, once we start looking at teams and player on that per-possession basis… doesn’t the same thing apply to individual in-game decisions? Since we want to maximize our points per possession and minimize our opponents’, doesn’t everything have a per possession value?

sergeibakaIt’s led to a reprioritizing of shots. The best shot, obviously, is the dunk: instant two points. Hard to beat that. After that are free throws. They’re not just to bail someone out when they miss a shot; since the league average was 75.3% at the line, getting fouled while shooting has a base rate of 1.5PPP. That is worth crafting strategy over. The best offenses are ones that draw a lot of fouls, and the best defenses (contrary to the smashmouth, old-school “no layups” philosophy) see fouling as something to be avoided at all costs. Not because of “foul trouble,” but because it’s just a terrible way to end a possession for a defense. A shooter only has to hit 56.3% of free throws before sending them to the foul line every play would result in the league’s best offense.

After free throws in the hierarchy are three-point shots. Specifically, the corner three, which has come to symbolize all that Stats Nerds stand for: a seemingly insignificant differentiation, a high-efficiency shot taken by oft-overlooked players, and a smart point on the risk-reward spectrum. Analysis by 82games shows them to produce an incredible 1.18PPP, which makes them worth building an offense around. The Spurs, who have been The Smartest Team in Basketball for quite a long time, have done so.

After that come straight-ahead threes, then wing threes, and after that… the dreaded Midrange Shot. Surprisingly, shots that would seem “easier” just outside the paint are not. Everything outside the paint but within the three point line is almost equally bad, and shots that come from there as the result of designed plays are becoming less and less frequent (though they can still be seen in the horrifically boring old-school East coast teams like the Celtics, Bulls, and Pacers, which are not coincidentally not good offensive teams). Great offenses like the aforementioned Rockets and Nuggets were able to essentially ignore that entire area of the court from a shoot perspective.

Almost everything I’ve said about stats on a per-play and per-player basis has been about offense: how good a player is at shooting, where they take their shots, how good they are at assisting and grabbing offensive rebounds. The sad fact is that defensive stats are way behind offensive ones. There is no easily-calculated equivalent to TS%. Steals and blocks, analysts have known for years, are overrated as box score stats, since a player can get a stop by forcing a missed shot, or a bad pass, or taking a charge, or even just making the player break the play to pass out desperately.

Synergy Sports has a rather brute-force solution to this: they analyzed every single play for play type, offensive players and defenders, as well as numerous other things, and gave the world offensive and defensive per-possession numbers for every team and player. This still has some weaknesses when it comes to defense, because it’s so fundamentally team-oriented, but it’s better than looking at who blocked the most shots and calling them the league’s best defender.

A similarly brute-force, but extremely useful, tool is looking at the +/- numbers for how the team did with that player on and off the court. This has more cautions than almost any other “advanced” statistic, because it can be subject to so many factors beyond the player’s control: who they played with and against, most obviously, but also issues of sample size and straightforward variance. Sometimes you’re playing against Nate Robinson and he hits five threes in a row. It happens. If you don’t see the court much, that’ll affect your +/- in a big way even if you did everything perfectly. That being said, for players that are in the regular rotation, it’s an invaluable tool for doing some rough fact-checking: if a broadcaster says Kosta Koufos was secretly a fabulous, I’ll check his last year with the Nuggets and see that, since the Nuggets defense was three points better in DRTG with him out there with a sample of almost 2000 minutes both on and off, they might really be onto something. If they say the same thing about JaVale McGee (“look at all those blocks!”), I’ll see that the team was two points worse in DRTG and dismiss it.

What I love so much about basketball statistics is how, despite these enormous amounts of fascinating and useful data, there is still so much left to be discovered. Advanced stats have not “solved” basketball; they have not definitively made a ranking of the best or worst players of this or any other era; and anyone making far-reaching and specific declarations about certain teams based on Their Statistical Model is probably at least slightly full of shit. But still, every year we learn a little more about the statistical rules underlying the game, and now’s a great time to be a stats-minded basketball fan.

Before I go, a few quick winners and losers from this analytic era of basketball:


  • Anyone that can shoot a three-pointer at an elite rate. Steve Kerr was a one-of-a-kind specialist once upon a time; now a team is thought of as incomplete without someone taking that role. (Examples: Steve Novak, Ersan Ilyasova, roughly half the Spurs roster.)
  • The big man equivalent of the above: the guy who doesn’t use an above-average amount of his team’s possessions, but makes the shots dunks he does take. (Tyson Chandler, DeAndre Jordan, Serge Ibaka.)
  • Offensive rebounders. These are incredibly offensively valuable, and roughly one-third as common as the defensive rebounds that go in the same column. (Reggie Evans, Zach Randolph, KENNETH FARIED.)
  • Anyone that provides good defense without getting a lot of blocks or steals. Old stats would be completely blind to who was a useless seven-footer taking up roster space, and who is the invaluable anchor of a defense. (Tony Allen, Andre Iguodala, Marc Gasol.)
  • The foul-drawing machines, who might have a lower FG% than their peers, but make up for it with constant trips to the line. (This is basically a list of superstars, but James Harden stands out.)
  • And now a moment for the non-specialists: those players who excel in something that’s often overlooked for their position, like rebounding guards or big men who can really pass. (Kyle Lowry and Russell Westbrook for their rebounding, either of the Gasols and Blake Griffin for their passing.)


  • The high-usage, low-efficiency gunner. (Examples are almost too easy to find: Monta Ellis, DeMarcus Cousins, Rudy Gay, Michael Beasley… notice how they’re either highly paid, high draft picks, or both?)
  • Overlapping with the above: the back-to-the basket big who takes shots from there rather than passing out. This is basically just Al Jefferson now, but there’s a good reason they’ve gone away.
  • Big men who get a lot of blocks, at the expense of playing good defense. (JaVale McGee, DeAndre Jordan, who gets to be both a winner and loser for different reasons.)
  • One-way scorers that the team has to go outside of their way to hide on defense. (Pretty much the same list as the gunners above.)
  • Midrange specialists, especially big men, who live at that god-forsaken area between the three point line and the paint. (Carlos Boozer, and anyone a broadcaster over 50 refers to as “fundamentally strong.”)

Hopefully, this introduction to basketball analytics shed some light on a nebulous concept. Keep in mind that, much like a political philosophy, basketball analytics are not a monolith. There can be extreme disagreement among people in this community, especially when two stats-based models clash or provide different causes for the same outcome. I’m sure that someone could accept all of my premises and reject all my conclusions as complete trash.

-Jesse Mason

Article by Ted Knutson