Dec 19 2013

3-Pointers and Pace, The New Synergy

Three-point shots are the most efficient in basketball. They’re worth 50 percent more than 2s,don’t go in 50 percent less, and even when they’re off target, they lead to offensive rebounds at a better clip than mid-range misses. The league is shooting more 3s than ever before (25.3 percent of all shots taken are now triples), and, the numbers say, loudly and clearly, that this still isn’t enough: everyone should be chucking more of them. In the modern NBA, three is the magic number.

MCW (1)“The debate on this stuff is over. Math has won,” Zach Lowe wrote in Grantland on Tuesday in a piece that mapped out the rise of the 3 and captured in strange and vivid detail the discomfort with the changing game that exists in some very influential league circles. (That long jump shots are somehow morally superior to 3-pointers and dunks is a belief that’s deeply held by handful of very successful NBA coaches and executives. The lesson, as always: smart people are capable of believing manifestly crazy things.)

There is a problem with the 3, however. While a triple-heavy attack is, in game theory parlance, a dominant strategy, it’s also a high-variance one. 3s are worth more than other shots and they go in less frequently, reducing the predictability of individual games. This makes a 3-centric offense well-suited for an 82 game regular season, where, over six months, the variance is ironed out–you lose a game you shouldn’t have here, steal one there–but in, say, a seven game playoff series, it can be a risky way for a favorite to play.

And so an analytic tension has emerged: in the modern NBA, the most efficient offenses (i.e., the ones that shoot the most 3s) will also be the most prone to playoff upsets. What’s a contender to do?

Well, for starters, they can go much faster.


In a tremendous (and paywalled) article that ran last week on ESPN.com, Kevin Pelton profiled the Rio Grande Valley Vipers–the Rocket’s D-League affiliate–and the unusual brand of basketball they’re playing. The Vipers are not only taking nearly 50 percent of their shots from beyond the arc, which would blow away the NBA record, but they’re averaging 107.2 possessions per 48 minutes. This, according to Pelton, is faster than any NBA team has played in 20 years.

Why does this matter? Well, in addition to being a dominant strategy in its own right, playing at a fast pace reduces variance by increasing the number of samples. To crib a Tom Haberstroh analogy, if you’re a kid who’s playing his older brother in basketball, and you’re just playing to first bucket, you may well win. As soon as he checks it to you, you might bounce it off the backboard and in and take bragging rights. But if you’re playing to 10, or 20, you’re much less likely to get so lucky. Things get a little more complicated in the NBA, but the basic principle holds: the better team benefits from more possessions.

All of which makes fast-paced basketball a perfect complement to the 3: by increasing the size of the sample, it mitigates the variance inherent in 3-point shooting. (And the fact that both strategies are dominant doesn’t hurt either.) If they use enough possessions, contenders who are built on 3-point marksmanship can have their cake and eat it too.

The Vipers are already having success with this fast/3 approach. They started the season 9-0 and didn’t lose their first game until Friday night. Oh, and you may have heard about the team that’s second in the D-League in 3-point attempts: the Delaware 87ers.

Know hope, Sixers fans. Know hope.

  • robbybonfire23

    The pace of these games would be much more significant, were there no 24-second clock. At it is, all teams are mandated to monotonously just “run and gun,” for the full 48 minutes, which renders surveys like this almost superfluous.

    I maintain that in the era of the trashy 3-point basket, the 24-second clock is virtually obsolete, given what it was originally intended for – to prevent teams with a lead or some kind of perceived physical disadvantage from “freezing the ball.” Teams now routinely overcome double-digit deficits in NBA games, so omnipresent has the “softie” 3-point shot attempt become.

    • Hank Hill

      Damn kids these days! I vote we not only abolish both the three point line and the 24 second shot clock (which will, god willing, revert the game back to the glorious days of terribly low scoring, “intelligent”outcomes), but also make the players walk uphill both to and from the arena.

  • robbybonfire23

    One of the (specious) reasons given for the adoption 3-point basket was to “unclog the lane.” This is the most myopic, idiotic rationale for a major rules change in a professional sport I have ever witnessed. This cheap (in terms of “difficulty”) 3-point shot PUNISHES teams which are adept at inside penetration for high percentage shots in a basketball game. It punishes teams for having a stout, basket-protecting defense. It rewards teams with porous defenses and /or a weak inside offensive arsenal. It has made a sham out of what used to be the objective of playing good, solid, disciplined high-percentage basketball, as the key to success and winning.

    But rather than correct this glaring inequity, I look for the NBA/television monolith to further corrupt the integrity of the outcome of these games via the addition of more gimmicky rules, in the years to come, to the delight of the “professional” wrestling- mentality crowd the NBA now panders to.

  • Joe

    Please keep writing articles like this so we can continually watch robby’s head explode. Thanks!

    • Joe


  • Hank Hill

    Love the 3, and I love pairing it with an emphasis on pace, but you still have to get good looks. Arbitrarily claiming that shooting tons of threes as quickly as possible (especially without prefacing said philosophy with any discussion of personnel) is downplaying the ultimate goal of basketball: to get the best look possible. Sprinting down the court and popping a three that’s successful 36% of the time is obviously an inferior strategy if a dunk is available…

    My only point is, I love and support analytics. But this article strikes me as fairly close to the dangerous realm of looking at the game of basketball through the lens of mathematics in a vacuum. Analytics can help us understand and expand upon our knowledge of how the game should be played, but they aren’t the only tool that should be used to do so.

    • tsunnergren

      Fair point Hank. Thanks for reading,

  • robbybonfire23

    Perhaps someone would like to even mention the real problem with the “made for TV,” “showtime” 3-point shot? And that is the fact that the NBA disguises, statistically – by just listing composite floor shooting percentage, and three point shooting percentage, t the shooting percentage on 2-point attempts. You have to compile that by extrapolation, yourself. Not that two “fans” in a hundred take the trouble to do that..

    The reason the NBA is not forthcoming, as regards this situation, is because that, when you break each category down by points scored per attempt, you will see that the 3-point attempt is disproportionally more rewarding than is the 2-point shot.

    And maybe you don’t think this represents a problem, but the NBA is at least looking at it, knowing that, in time, more 3’s than 2 point attempts will comprise your typical NBA game. I do think there is a (small) chance they will move the arc back a couple feet to rectify this inequity. It certainly would restore balance and provide consistently true results to these playground romps which reek of the most egregious “entertainment” monotony on the planet.

    Until you study and address this imbalance of difficulty-to-reward pertaining to these two and three shot categories, your input is superficial, at best, given that it can be taken as an indication that, until now, have not even been aware of this imbalance that is distorting the flow of every damn farcical exhibition game this league puts on.

    • JulianW

      In my day, we didn’t have this “three-point” shot shenanigans! We also had to make our own basketballs out of pig bladders, on account of the war! Did I ever tell you about the war, sonny? Well it was back in aught-six when I was but a shoe cobbler…

  • Andrew Johnson

    Tom- Good article, but my research indicates that three point misses are less likely to end in offensive rebounds. Looking at both Kirk Goldsberry’s visualizations and NBAWowy, I found that three point misses were the least likely shots to lead to offensive rebounds.


    • tsunnergren

      Interesting Andrew, but I think Goldsberry draws different conclusions from his data.
      “In the NBA, 3-point shots are much better options than midrange shots for 2 reasons: 1) The decreased FG% is more than compensated by a higher reward in terms of points per attempt, and 2) not only do made 3-point shots obviously result in more points, missed 3-pointers are more likely to result in offensive rebounds than missed midrange jumpers.” http://courtvisionanalytics.com/where-do-rebounds-go/

      • Andrew Johnson

        I guess it’s a further research needed area. The Kobe Assists Deleted Scenes post is after the Where Do Rebounds Go post, and the contour lines clearly don’t match up with the data in the earlier one. Also the Wowy data may have a different definition of “mid-range.”

        In any case the difference doesn’t seem to be great.

        • tsunnergren

          Well, keep at it man and keep us posted on what you find. I think it’s really neat stuff

  • madeiramustangs

    Can you share the stats which verify that 3-point shots lead to offensive rebounds at a better clip than mid-range misses?