In today’s new data-driven world, every major league in sports has, in some significant capacity, turned to analytics in order to optimize the way the game is being played. The NBA has followed this trend, in large part due to the immense quantity of data that can be collected, down to the very movements and steps taken on the court. One avenue that analysts have explored is quantifying the best players, creating all-encompassing statistics like Wins Above Replacement Player (WARP), Player Impact Estimate (PIE), Real Plus Minus (RPM), and so forth. Elsewhere, there has been a mission to optimize the game on a team level, and this is where the biggest breakthroughs have been taking place.

Team play is a different beast compared to quantifying an individual, as there is a geospatial element added to the equation. Deep analysis has been conducted in analyzing where teams are best off taking their shots and how to best generate those shots. The theory behind optimizing basketball made its first significant impact on the league through Daryl Morey’s work, which concluded that threes and layups are the optimal shots in the game. Take a look at any chart like the one below dealing with points per location, and this becomes exceptionally clear.

This makes sense because dunks are virtually assured two points, layups are almost equally safe, and there is a further propensity for fouls that would lead to free throws (a shot any pro should be hitting at a strong clip). In fact, the “more than 1.20” zone underneath the rim equates to over a 60% field goal percentage from that location. What Morey led the league in was realizing that the three point shot was actually a very close second place in terms of efficiency. This is especially visible with the corner three, which stands out by being the closest three available as well as a primarily catch and shoot location (a higher percentage shot from any distance compared to off the dribble). The three point shot generates this inflated value from the simple idea of being worth 1.5 two pointers, meaning 33% on threes actually equates to shooting 50% on twos. Thus, the long two becomes a useless shot, given that the conversion rate is only marginally higher than threes, yet results in two thirds of the points.

Morey took this philosophy and implemented an offense called four out for the Rockets, which involves a ball handler/center combination with great pick and roll chemistry, as well as three perimeter shooters. 

James Harden, since arriving in Houston, has played the 1 in this setup, while Clint Capela has played the 5 for the majority of Harden’s time here (aside from Dwight Howard’s stay early on). The surrounding shooters have been a revolving door over time, though Morey has interestingly contradicted himself by recently adding guard Russell Westbrook and defending the move by saying starpower in raw amounts can also get the job done. Harden and Capela engage in a pick and roll, forcing the defense to choose from strategies like hedging, sagging, or double teaming the ball handler. The end result, more often than not, is either a decent look for one of the two players involved or a catch and shoot opportunity for a perimeter player. The reason the latter option is popular is because the PnR frequently requires help defenders to collapse in order to stop the action towards the rim, leading to open looks from three. Four out provides optimum spacing and provides not only the second best shot in the game, but a catch and shoot variation. Fill the shooter position with the strongest shooters and the efficiency begins to directly threaten attempts at the rim. Harden has since developed an unparalleled isolation game that puts further pressure on the defense. With the four out scheme, defenses must still choose between facing his talents one on one or doubling and leaving open players.

The bottom line is that the Rockets’ system is efficient. There is no need to have four allstars like the dynastic Golden State Warriors and ball movement resulting in 30 assists per game. There only needs to be one true star and a collection of role players who are great at their jobs within the system. The Rockets could have beaten the Warriors in this manner in the 2018 Western Conference Finals if it wasn’t for Chris Paul’s injury. Other teams have borrowed the approach as well, most notably the Milwaukee Bucks, who made the Eastern Conference Finals this past year and pace the league with the best record today by surrounding MVP candidate Giannis Antetokounmpo with a bevy of shooters. In fact, the reason all of the top superstars today accumulate previously unheard-of stats is because the four out offense generates such one star systems.

This movement has been rapid in changing the landscape of shot attempts, as the league has collectively increased from 20 threes attempted per game in the 2012-2013 season to 32 in the 2018-2019 season. The game has become visually quite predictable, as the isolation dances to find a midrange shot have fallen out of favor. Shooting specialists like Ryan Anderson have found their way into large contracts, while immobile and/or non shooting threats like Roy Hibbert and Kenneth Faried rapidly fell by the wayside. There is no longer a yin to the yang, as the variety of ways to approach the game has fallen. The San Antonio Spurs, a team that has not missed the playoffs since the Jordan Bulls were in the midst of domination, are in danger of doing so as a result of their two centerpiece scorers (Lamarcus Aldridge and DeMar Derozan) living out of the midrange.

It is essential to counter the unanimous approach being taken within the league, and I am a big supporter of Kirk Goldsberry’s proposal to let each NBA team draw their own three point line for their own arenas. While it sounds like a ridiculous solution, something even Goldsberry has acknowledged, I believe there are countless positive effects this will have on the game that transcend actual gameplay.

Before discussing the impact of the line, I first hold some opinions on potential ground rules on the line itself. It should be redrawable each season to accommodate new signings and releases, but must maintain constant between the regular season and playoffs. The line must be symmetrical across the midline of the court. This is so that the line still presents more of a skill-based challenge of an absolute distance and not an unnecessary mental distraction of having to remember different locations based on wing of the court. There also ought to be a minimum distance this line can be placed (like high school distance) as well as a maximum (30 feet as an arbitrary example).

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Math is an endless abyss of numbers, and the beauty of this is that teams will have countless ways to decide where to set their line, not to mention they all have different data sets to peruse. Amidst my tinkering with league statistics, I found that a great metric to further explore was effective field goal percentage (EFG). EFG adjusts regular field goal percentage by scaling the conversion rate of three pointers up by 50%, acting on the fact that a 40% rate from three is functionally a 60% clip from two. Since EFG now values all points equally, it provides a very strong view into what teams are the most efficient. The two components to the game are, of course, offense and defense, meaning a team is interested in maximizing their own EFG and minimizing their opponent’s EFG, with the difference between them being called the EFG gap. There is a strong correlation between having a higher EFG gap and a higher winning percentage. My proposed method of determining a three point line would be to maximize the EFG gap between your own team and your opponent’s season-long cumulative results. The approach would be graphical. A team like the Warriors could look at their 2018-2019 EFG and see that they had a 56.5% EFG and allowed a 50.8% EFG. That in itself is a positive 5.7% gap that explains their dominant campaign last year. 

But, the real question is: could it have been better? What if the three point line was deeper? Were the Warriors’ opponents relying on success from directly behind the line while the Warriors succeeded with Klay Thompson, Stephen Curry, and Kevin Durant shooting from 2-3 feet behind the line? Given that the geospatial data exists for shot attempts, it would be simple to draw a new line and calculate new EFGs given the new line, reclassifying specific previous threes as twos. Let’s pretend the Warriors’ EFG fell to 51.9% while their opponents fell to 45.9%. It is a given that both of theirs would fall from a deeper line, but the new 6% gap in EFG suggests a relative boost to the Warriors. At every theoretical distance, there would be a gap in EFG. Graphing all possibilities can provide an interesting result.

(Note: the graph above contains hypothetical data line, although it follows the premise)

The team’s best interest is to place the three point line at the distance that maximizes the EFG gap, which is relatively simply found. A team with many standard specialists like the Rockets may prefer to keep the line at the same distance as today, given that their role players are particularly adept at the current distance. Other teams like the Warriors or Trail Blazers may end up moving the line backwards in order to leave only a distance that Curry or Damian Lillard are capable of proficiently hitting from. Yet others like the Spurs would move the line forward in order to maximize the value of Derozan and Aldridge’s deep twos. Already, we can see how various types players can gain value simultaneously, which actually increases competitive balance while diversifying the types of offenses we see.

Teams will have more difficulty forecasting the optimal line if experiencing plenty of roster turnover. The 2018-2019 Warriors shot chart would not help the team determine what to draw up for the 2019-2020 season’s decimated roster, given the team lost half of its previous season’s player minutes even before Stephen Curry broke his hand. However, it is possible to take individual player shot charts from the past season or career and overlay those to create a custom theoretical team. The options are endless, and the lack of a clearcut path is, in fact, exactly what the league needs to spice up the competition.

Custom three point lines create a home court advantage, which means the regular season suddenly gains even more value for playoff positioning. This, on its own, whittles away on the recent trend of load management pioneered by Kawhi Leonard, as the combination of both home court fans as well as an optimal line is more appealing. This also means that the home team win rate across the entire league will tick upwards, pleasing fans and raising both ticket sales and prices. Furthermore, it will be intriguing to see if teams develop multiple strategies to roll out during their different road games, providing TV audiences with a more diverse experience over the course of the season. Another benefit I foresee is that coaching will become more valuable, as only the truly great coaches will be able to develop successful schemes for the suddenly many variations of the court that they face over time.

Over the course of the NBA, there have been rule changes with significantly larger impacts than this current proposal would have. In 1954, a 24 second shot clock was introduced, which overhauled the pace of play across the league to faster levels. 1979 brought the three point line to the NBA for the first time at all. In 2001, illegal defense was eliminated while zone defense was allowed. This change is directly responsible for the shift from Kobe and Iverson type players even before the “Moreyball” concept doubled down on it. The league has even collectively brought the line in to an even 22 feet for three years in the 1990s , and players showed they could easily adapt to the change. All players, as it stands, progress through multiple lines across high school, college, and the NBA, and summer FIBA competitions provide a change of pace to the NCAA line for the NBA’s best. The NBA’s shortened line was in an effort to increase scoring across the league, but what instead happened was a decrease in scoring. However, that should not be a harbinger of things to come with the newer proposal. The league is full of better shooters, the ban of illegal defense has changed the physical dynamic of the game, and only the teams who are analytically better off with a shorter line will be the ones implementing it this time around.

This proposal could also be a short term process used for data collection that would serve a greater purpose. By averaging all selected three point lines for 30 teams each year over 5 years, a grand mean can be found that would suggest the true equilibrium line distance the league collectively needs. 

At the very least, this proposal should merit consideration in an experimental setting such as the preseason or the G League, as tangible results will speak better than any hypothetical.

In professional sports, various teams have unique home field advantages. In the MLB the fields have distinctly unique dimensions and only half the league incorporates a designated hitter. In the NFL, fields are subject to different weather patterns. Meanwhile, the NBA has identical courts all in indoor climates. A variety of unique three point lines will diversify the playstyle of the league, allow a wider range of players to maintain higher value, require more innovative coaches, and generate money for the league. At bare minimum, the opportunity merits greater consideration by the gurus of the league and should not be written off as a lunatic proposition.

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