Basketball now makes more analytical sense

The three-pointer’s final form

“To three, or not to three.” — Prince Hamlet, as he contemplates letting it fly

If you don’t care for theatrics, the TL;DR version of this thing is basically just the two charts at the bottom.

It was a typical Monday evening pickup session at the Syrian Club in Ikoyi. The cardio was good. The three-point shooting was bad.

Syrian Club’s basketball court in Lagos, Nigeria, overlayed with a “rouge” filter to compensate for the terribly low lighting

We were to follow the universally adopted but unspoken protocol of pickup basketball: one point for “two-pointers” and two points for “three-pointers”. Except on this particular Harmattan evening, a curious question was asked at mid-court. Why not just two for “twos” and three for “threes”? How silly, I thought, and proceeded to explain.

Since we don’t shoot as efficiently as NBA players from outside the arc, we need 2.0x the reward for making shots from outside the arc vs. inside the arc [2 points vs. 1 point], while NBA players get 1.5x the reward [3 points vs. 2 points].

Unbeknownst to my friend, I was only half-convinced myself.

I did what any self-respecting couch analyst would do, and spent a solid two hours later that evening on I found a titillating revelation about the state of the league’s three-point trend. I shared it with the Reddit NBA community (in particular the ever so supportive r/TorontoRaptors subreddit community), and was encouraged to do this long-form analysis.

Recap: rise of the three pointer

Since the three point line was first introduced to the NBA in 1979, virtually every subsequent year has seen more three-point shooting than the last.

The notable exceptions here are two seasons in mid-90s during which the three point line was moved closer as an experiment.

A tale of two citiez

2018–2019 best league record is as of the All-Star break (Milwaukee Bucks)

As of the All-Star break in the 2018–2019, 36% of all field goals in the league were attempted from outside the three point arc. Last year, Houston Rockets had the best regular season record in the league. They also became the first team in the history of the league to take more three point attempts than two point attempts over the course of the entire season. They’re on track to do the same again this year.

“I hate it… To me it’s not basketball but you get to used it… But you sort of feel like it’s cheating.” — June 2014
“I still hate it. I’ll never embrace it. I don’t think it’s basketball…. you know i think like a — it’s kind of like a circus type of thing… where does it stop?” — December 2015

Meanwhile, don’t tell Gregg Popovich, coach of the San Antonio Spurs, (pictured left, aging from top to bottom), that “hate” is a strong word. Because he has an Air Force background and seems like he likes to do strong person things (here’s a video). Point is, he hates the three-pointer.

“I hate it, but I always have… I’ve hated the three for 20 years… There’s no basketball anymore, there’s no beauty in it. It’s pretty boring.” — November 2018

And this is hands-down the most accomplished and celebrated coach in the NBA. He has won 5 championships, 3 coach of the year awards, and has NEVER missed the playoffs in his 23 years as coach.

He’s said that three pointers feel like cheating. He’s compared it to a circus. Called them boring.

Joke’s on Pop cause the circus is pretty fun.

Increasing three point shots have coincided with a brand of basketball commonly dubbed as “small ball” or “pace and space”. It has more passing (e.g., more behind the back passes, more between the legs passes, more no look passes, more alley oop passes). It’s a more offense-oriented game. It’s a speedier game. More ankle-breaking. Unrelated, but there’s also more Twitter. What’s there not to love? Sure, some might rather like to see big guys clog the paint, but I for one get enough of that at pick-up sessions.

The NBA is actually NOT getting better at shooting threes

Ignorant me: NBA is probably shooting more threes because they’re getting better at it.

Enlightened me: Wrong.

Ignorant me: Well, look at Steph Curry.

Enlightened me: He is an outlier. Which makes his legacy even more compelling.

The increased spacing which coincides with more three point shooting, along with increasing bias against mid-range twos, has actually enabled more efficient two point shooting. Meanwhile, league-wide three point shooting efficiency has remained historically consistent.

So why are they shooting more threes?

The concept I was trying to explain to my friend at the beginning of the post was that of expected value.

Expected value = (probability of success * award for success), or Expected points = (field goal percentage * points per field goal)

If you take the above two field goal percentage charts, and multiply them with the points they yield (three and two, respectively), you get the expected value of each, as shown below.

The grey area is a value gap, representing analytical inefficiency

The grey area represents the value lost attributed to a suboptimal mix of 3pt FGA vs 2pt FGA. It’s this gap that the league has been trying to exploit by taking more and more threes every year. Expediting this over the last few years has brought us to this season, where the mix of the two shots are more… analytically correct.

I was inclined to claim it’s a “new normal” but that would imply that there was an old normal. It just didn’t make sense analytically before. I think it’s starting to do so now.

The expected value of a field goal attempt has to capture the probability that a player will be fouled while shooting and subsequently be awarded free throws. This is more common with two point field goals than with three point field goals. Accordingly, the yellow line in the above chart should be adjusted upwards a bit to reflect this, further reflecting a more perfect 2pt/3pt shot mix (less grey area). Similarly, in the purple bar chart, all bars should be a little smaller (in absolute terms/magnitude) than they are.

Dramatic conclusion, but true nonetheless:

30 years after the introduction of the three point line, the league has finally perfected how to use it in the 2018–2019 season.

Answering Pop’s question

“Where does it stop?”

Around now. Volume of three point shooting in the league should finally plateau next season. So will the pace and space of the game. And so will two-point shooting efficiency.

Couple of notes / caveats

  • These stats for the 2018–2019 season are as of the All-Star break (~59 / 82 games into the season), so we are assuming that efficiency and volume mix hold steady until the end of the season.
  • Efficiencies and volumes of more granular shot types should probably be analyzed. i.e. instead of 2pt FGA vs 3pt FGA, one should analyze efficiencies of several distances from the basket (e.g. 0–5 feet, 5–9 feet,… etc.).