Has the secret value of the 3-pointer finally been completely exposed?

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When discussing the history of the 3-pointer, many people like to begin with the longest shot ever made in major professional basketball.

In the ABA’s inaugural season, the Indiana Pacers trailed the Dallas Chaparrals by two points with two seconds remaining. Pacers guard Jerry Harkness heaved a desperation 92-foot hook shot toward the basket, and to everyone’s surprise, the ball went through the net. That wasn’t the biggest surprise of the moment, though. As the story goes, the entire arena prepared for overtime – the entire arena except one official, who reminded everyone the long shot, now worth three points, gave the Pacers the win in regulation.

The shot – 92 feet! – and the novelty of situation – teams unnecessarily preparing for overtime – make the story great.

But what always stuck out to me was the game was played Nov. 13, 1967 – a full month after the ABA season began. Thirty-one full days, and the teams still don’t know the rule.

The NBA didn’t institute the 3-pointer until the 1979-80 season, well after the ABA had demonstrated the usefulness of the shot. But the NBA didn’t take a lesson from its more radical counterpart and embrace the triple right away. The NBA’s reluctant acceptance of the 3-pointer, 31 years after it’s introduction, might finally be near completion.

Growth of the 3-pointer

The deliberate treatment of the 3-pointer when the NBA first instituted it makes sense. Ryan Wood of iHoops.com explains:

In the late 1960s, when the ABA introduced the 3-pointer, a generation of coaches had to rethink everything they knew about the game, and it made things hectic. One ABA coach admits that at first, he never used the 3-pointer unless his team was losing late in the game and was desperate for points.

Other coaches had similar problems adjusting to its reality.

"You have to tell your players to remember who the shooters are, and when those guys are 25 feet from the basket, get in their jocks and guard them," former ABA and NBA coach Hubie Brown said in Loose Balls. "Don’t give them the 25-footer, which is something players had been conditioned to do all their lives. And as a coach, if you have a shooter with range, you have to give him the freedom to take the 25-footer, which is a philosophy that goes against what you learned as a young coach–namely, pound the ball inside."

It wasn’t just the coaches, either. The fans loved it right away, but there were growing pains among the players.

"It took a while for players to understand time and score situations, when to take it," said Len Elmore, the CEO of iHoops who played in both the ABA and NBA. "You also recognize that players who hadn’t been accustomed to playing with a 3-point line really had to work to develop the range."

Teams are taking more than 10 times as many 3-pointers per 100 possessions this year as they did the first season the NBA instituted the shot, 1979-80.

Sheet 4

That’s a statistically significant increase in 3-point attempts per 100 possessions. As players have taken more 3s, they’ve also gotten much better at making them. There’s also a statistically significant increase in 3-point percentage since the league introduced the shot.

Sheet 3
Sheet 3

I won’t play the chicken-or-the game, and this is is a good place to point out correlation does not equal causation. I think it’s a safe bet teams shooting more 3-pointers and making more 3-pointers both play off each other.

Value of the 3-pointer

A team at its peak efficiency receives equal value for a 2-point attempt and a 3-point attempt. If it’s receiving more value for its 2-point attempts, it should shoot more 2-pointers. Conversely, if it’s receiving more value for its 3-point attempts, it should shoot more 3-pointers.

Save for a few years in the late 1980s and early 1990s, the NBA hasn’t experienced that optimization.

Before then, teams got more value for 2-pointers. After then, teams got more value for 3-pointers. Charting the effective field-goal percentage of each type of shot demonstrates the trend. The blue line represents 2-pointers, and the red line represents 3-pointers.

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Sheet 6

Shooting-foul adjustment

The above graph should give you an idea of the value of 2-pointers and 3-pointers in a given year, but it doesn’t tell the entire story.

We must account for shooting fouls. Unfortunately, I can’t attain the data for most years. Fortunately, Scott Sereday of Basketball-Analysis.com provided the data necessary to analyze the 2005-06 through 2009-10 seasons.

Instead of using effective field-goal percentage, I’m going to use points per shot, including shots when a player draws a foul.

Obviously, 2-pointers will draw more fouls than 3-pointers. On the other hand, players who draw fouls on 3-pointers tend to shoot free throws better than players who draw fouls on 2-pointers.

  • Average free-throw percentage* for a player fouled on a 2-point shot: 75.2
  • Average free-throw percentage* for a player fouled on a 3-point shot: 80.1

*Weighted by free throws drawn on that type of shot. I also used players’ free-throw percentages after shooting fouls, not their overall percentages.

If you consider both factors, the value of 2-pointers benefits more from this adjustment than the value of 3-pointers does. Averaging the last five years, shooting fouls add .0848 points to the value of a 2-point shot, and shooting fouls add .0107 points to the value of a 3-point shot.

Still, that doesn’t completely close the gap, which is shrinking. Again, blue represents 2-pointers, and red represents 3-pointers.

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Other adjustments

There are factors I haven’t taken into account – namely what happens before and after a shot. Before each shot, a team tries to hold possession and maybe draw a non-shooting foul. Following each shot, a team tries to secure an offensive rebound and defend its own basket.

  • Do teams turn the less over more when looking for a 2-pointer or a 3-pointer?
  • Do teams draw more non-shooting fouls when looking for a 2-pointer or a 3-pointers?
  • Are 2-pointers or 3-pointers more likely to lead to offensive rebounds?
  • After grabbing an offensive rebound, is a team more likely to score when the missed shot was a 2-pointer or a 3-pointer?
  • Do teams defend better after 2-points or 3-pointers?

If I had to guess, here’s how I’d answer those questions:

  • Do teams turn the ball over less when looking for a 2-pointer or a 3-pointer? 3-pointers, because play becomes more sloppy in a more confined area.
  • Do teams draw more non-shooting fouls when looking for a 2-pointer or a 3-pointers? 2-pointers, play becomes more physical in a more confined area.
  • Are 2-pointers or 3-pointers more likely to lead to offensive rebounds? 2-pointers, because 3-point attempts pull at least one offensive player away from the basket.
  • After grabbing an offensive rebound, is a team more likely to score when the missed shot was a 2-pointer or a 3-pointer? 2-pointers, because putback attempts are efficient enough to skew the data in that direction.
  • Do teams defend better after 2-points or 3-pointers? 2-pointers, because they avoid long rebounds, which can lead to fastbreaks.

Again, those are only guesses, but four of my five guesses indicate 2-pointers are more valuable than I can demonstrate with the data available to me.

The answer to those questions – and determining the added value for each scenario – would tell teams whether they’re attempting 2-pointers and 3-pointers at an optimal ratio.

I don’t have the resources to answer these questions, but NBA teams do. If one of them is smart, they’ll commit those resources to solving these questions.

If one of them is smarter, they already have.

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