Authors: Hunter Zhang (hunterzhang2024@u.northwestern.edu), Weinberg; Ian Braud (ianbraud2022@u.northwestern.edu), Weinberg 

“That’s a bad shot,” said Paul George about the 36-foot buzzer-beater that his opponent Damian Lillard hit to eliminate his team from the playoffs last year. Although a 36-foot shot seems like a “bad shot” as George commented, it is actually a high-percentage, highly efficient shot for Lillard, as he hit an astounding 44% of all the 30ft+ shots he took during the fourth quarter of the 2019 playoffs. The brilliance of Lillard’s marksmanship is just another reminder of the shifting style of play the game has seen in the past decade. Not only have players been shooting further away from the basket, they also have become so much better at it. Since 2010, the percentage of shots taken from 30+ feet has increased by 66%, and the league’s field goal percentage for those shots skyrocketed by 385%. Witnessing this growing trend, basketball fans have long fantasized what it would be like to have a four-point line in the NBA. Fans were teased with a 27ft four-point line at the 2020 All-Star Celebrity Game. This prompts us to try to answer the question: if the NBA were to introduce a four-point line on its courts, where should they put it and what effects it might have on the game?

The answer to the first half of this question would depend on how efficient the NBA wants a four-point shot to be. And to decide how efficient we want the four-point shot to be, we have to first take a look at the efficiency of the two-point and the three-point shot, which would give us a baseline of comparison. 

To do that, we borrow the concept of the Points Per Shot (PPS) metric, which measures the efficiency of a player’s shot((Total Points of Player)/(Field Goal Attempts of Player)). Instead of using PPS to measure a player’s expected shot value, we use it to measure the expected shot value of different types of shots: 

Expected shot value(n) =  (Total “n” pointers made * n) / (Total “n” pointer attempts), n=2, 3, or 4

Using the data from the last three seasons (2017-2019), the expected shot value for every two-pointer is 0.9834 points, and for every three-pointer, it is 1.0566. To understand how efficient four-pointers could be, we use the same method with the same set of data to estimate the expected value for four-pointers at distances beyond the three-point line (23.75ft). For example, At 24 feet, which is just outside the three-point line, the numbers show that the expected shot value of a four-pointer is 1.399, making it significantly more efficient than both the two-point and three-point shot, whereas at 36 feet, which is Lillard’s game winner’s distance, it is 0.158. Charting the four-point line distance with the respective expected shot value, we get figure-2 that shows a decreasing expected value curve with a larger distance. 

So, where should the four-point line be? Our answer is to put it around 30ft from the rim. Here’s why. If the NBA doesn’t want the four-point line to turn its games into long-distance shoot contests, the efficiency of the four-point shot should not be greater than that of the three-pointer and the two-pointer, which means that its distance should be greater or equal to 29 feet (where the expected value of four-pointers is 0.9229). Additionally, since we estimated the expected value for four-pointers using past data, we should also account for the future increase in four-pointers’ accuracy as players train on that shot. Finally, taking into account that it should not be too far away as it would make it more of a gamified trick shot, we settle that the line should be at around 30ft from the rim, with an expected value at 0.693, which is slightly below that of two-pointers. At this distance, we won’t see players hoisting too many four-pointers but it would still be taken at desperate moments or when a player needs a heat-check. This would give more excitement for tight game scenarios and players with extreme marksmanship the opportunity to let their unique skills shine. 

The Effect

If the NBA listens to us and does introduce a 30ft four-point line in the NBA, what might it change about the game? 

You could say the NBA has already been moving toward a shooter-heavy league for some time now, with players like Steph Curry, Dame Lillard, and James Harden. Compared to the teams in the 2011-12 season, in which only one team (Orlando, 32.2%) had greater than 25% of their points coming from three-pointers, all teams in the 2019-20 season had at least 27% of their points coming from three-point land. 

If a four-point line were to be implemented, the reliance on shooting would likely increase even further. Slashing guards and forwards would likely become less of scorers, as shooting from deep would lead to more points than a lay-up. The importance of the big man, which has diminished tremendously over the last 10 years, would likely continue to decline, as small-ball lineups with five shooters on the floor might be more advantageous for teams. Additionally, having five mobile guys would be imperative. With the increase of jump shots, the number of screens used to get shooters open would increase as well. With screens being placed by bigger guys typically, the defense switches more times than not. Having a big guy then switched onto a little guy will inevitably happen, and in that case, the big guy must be mobile enough to guard that smaller shooter. 

Furthermore, just like the introduction of the three-point line back in the 1979-80 season, the four-point line would completely change the historic comparison between players. Since players have the opportunity to earn more points every possession, their career points would tally faster than players before. 

Conclusion

In this short study, we found that a four-point line can feasibly be introduced in the NBA without changing too much about the game. At about 30 feet, the four-point line could potentially create more excitement at the final minutes and seconds of a tight game; meanwhile, players with extreme marksmanship who we have witnessed to emerge in the past decade would have a better platform to showcase their ability. With that said, the introduction of the line would continue to push the NBA to change and adapt. Many might view it as a gimmick, as many did in 1979 for the newly installed three-point line, but who knows what the future may hold? Maybe a few years from now, the legendary “bang” calls from Mike Breen will be for four-point shots.

All Statistics used via Basketball Reference