The three-point revolution: how the NBA rebuilt its offence

A shot from a step inside the arc and a shot from a step outside it are close to the same shot. Same range, roughly the same difficulty, the same defender contesting it in the same way. One pays two points and one pays three. Everything that people file under the three point revolution in the NBA follows from taking that sentence literally, and the strange part of the story is not that teams eventually did. It is that the line sat painted on the floor for about three decades first, in plain view, while coaches taught players to step in front of it.

The arithmetic was never hidden. It was available on day one, to anyone with a pencil. What was missing was the evidence that the arithmetic described real shots taken by real players, the personnel who could shoot from that distance in volume, and the willingness of a coach to be publicly wrong for a season while he found out.

The arithmetic that started the three point revolution

Score a shot the only way that matters, which is points per attempt.

A two-point shot made at a rate of q produces 2q points every time it is taken. A three-point shot made at a rate of p produces 3p. Set those equal and the whole argument falls out in one line:

3p = 2q, so p = (2/3)q.

A three-point shot needs two thirds of a two-point shot's make rate to be worth exactly the same. Not the same rate. Two thirds of it. That ratio is fixed by the scoring rules and holds at every distance, for every player, in every era. It does not depend on data, and no season's numbers can move it.

Turn it round and it is even blunter. Whatever a two-point shot is being made at, a three-point shot from the same possession is worth 1.5 times as much per make, so the shooter can miss materially more often and still be doing the better thing. Nothing in the rulebook says a three has to be harder by any particular margin. It just has to be harder by less than a third.

That is the entire engine. Everything else in this article is a consequence.

• 23.75Feet to the arc at the top of the key
• 22Feet to the arc in the corner
• 1.5Points a three pays for every two-point basket
• 0.67Share of a two's make rate a three needs to tie

The two distances are the rule-defined court measurements. The two ratios are arithmetic, derived from the fact that a three pays three and a two pays two, and hold for any player at any make rate.

Two other things fall out of the same line of algebra, and both were missed for years.

The first is that this is a statement about shots, not about shooters. It does not say that a bad shooter should shoot threes. It says that for any given player, a three from twenty-four feet beats his own two from twenty-two feet unless his accuracy falls by more than a third across those two feet. For most players it does not fall by anything like that much, because the difficulty of a jump shot is driven far more by the contest and the footwork than by the last two feet of range.

The second is the reason the corner three exists as a separate object in every scouting report. The arc is not a circle. It is a circular section joined to two straight lines that run parallel to the sidelines, and those lines sit closer to the basket than the top of the arc does. A corner three is a foot and nine inches shorter than a three from the top of the key and pays exactly the same three points. It is the only place on the floor where the rulebook simply hands the offence a discount, which is why the corner is the first spot a modern offence fills and the last place a defence wants to be forced to rotate from.

Why the long two became the worst shot on the floor

Run the same arithmetic over the shots a basketball team actually takes and one of them lands in a hole.

Here is a worked example. Every make rate below is invented and deliberately round, chosen so the arithmetic stays legible. None of it reports a real season, team or player.

Say a shot at the rim goes in at 60 per cent. That is 1.2 points per attempt. Say a corner three goes in at 40 per cent. That is also 1.2 points per attempt. The two shots that look least alike on a television screen, a dunk and a set shot from twenty-two feet, are worth the same.

Now the shot in the hole. Say a long two-point jump shot from nineteen feet goes in at 40 per cent, exactly the rate we gave the corner three. It produces 0.8 points per attempt. Same shooter, same release, same difficulty in this example, and a third of the value has vanished because of where his feet were.

Shot at the rim, made at 60%1.2pts

Corner three, made at 40%1.2pts

Above-the-break three, made at 35%1.05pts

Floater from ten feet, made at 45%0.9pts

Long two from nineteen feet, made at 40%0.8pts

All five make rates are invented and round, chosen so the arithmetic is easy to check. Multiply the rate by the points the shot pays. Nothing here reports a real season, team or player.

Show the numbers

Worked example: points per attempt by shot type

Item	Value
Shot at the rim, made at 60%	1.2pts
Corner three, made at 40%	1.2pts
Above-the-break three, made at 35%	1.05pts
Floater from ten feet, made at 45%	0.9pts
Long two from nineteen feet, made at 40%	0.8pts

That is the shot chart in one figure. The rim is efficient because the make rate is high. The arc is efficient because the payout is high. Between them sits a shot with a mediocre make rate and the lower payout, and no compensating virtue at all. A nineteen-foot jump shot is nearly as hard as a twenty-four-foot jump shot, does not draw fouls the way a drive does, generates a long rebound, and pays two.

The natural response is to point out that this compares shots when the unit of account should be possessions, and that is a fair objection which cuts both ways.

Shots at the rim draw shooting fouls at a far higher rate than jump shots, so their true value is understated by any calculation that ignores free throws. That is precisely why the standard efficiency measures do not stop at the field goal. Effective field goal percentage credits a made three with an extra half of a make, which is the same 1.5 ratio wearing a different hat, and true shooting percentage goes further by folding free throws into the denominator with a fixed multiplier for the attempts that came from shooting fouls. Any argument about shot selection conducted in raw field goal percentage is being conducted in the wrong currency.

Offensive rebounding cuts the other way. A missed three produces a longer carom than a missed layup, and the team that shot it is standing further from the basket when the ball comes off. Threes therefore cost something in second chances, and a shot diet built purely on points per attempt quietly overstates the case. The correction is real. It is also nowhere near a third.

Now the compounding step, which is where a spreadsheet turns into a strategy. Take the invented rates above and give two teams a hundred shots each.

Team A takes 30 at the rim, 60 long twos and 10 above-the-break threes. That is 36 points from the rim, 48 from the midrange and 10.5 from the arc: 94.5 points.

Team B takes 40 at the rim, 10 long twos, 20 corner threes and 30 above the break. That is 48, plus 8, plus 24, plus 31.5: 111.5 points.

Same shooters. Same make rates. Seventeen points per hundred shots, produced entirely by moving feet.

Midrange-heavy diet94.5pts

Rim-and-arc diet111.5pts

Constructed illustration using the invented make rates from the previous figure. Team A takes 30 at the rim, 60 long twos and 10 threes. Team B takes 40 at the rim, 10 long twos, 20 corner threes and 30 above the break. Nothing here reports a real team.

Show the numbers

Worked example: two shot diets, one hundred shots each, same make rates

Item	Value
Midrange-heavy diet	94.5pts
Rim-and-arc diet	111.5pts

Seventeen points is not a marginal gain. It is the difference between a good offence and an unwatchable one, and it was sitting on the floor for years, free, requiring no better players.

Why the three point revolution in the NBA took thirty years to arrive

If the arithmetic was always true, the interesting question is not why teams changed. It is why they did not change immediately. Five things had to move first, and they moved in sequence rather than together.

The shot arrived with a reputation. The NBA did not invent the three-point line, it inherited the idea from a rival league that used it as a novelty, and the framing stuck. For years the three was understood as what you did when you were behind, a comeback device rather than an offence. Novelty shots do not get practice time, and things that do not get practice time do not get good.

Coaching orthodoxy defined a good shot by distance. The inherited teaching was that the closer you get, the better the shot, which is true for two-point shots and stops being true the moment a line is drawn on the floor. An entire profession had internalised a rule of thumb that the scoring system had quietly invalidated. Orthodoxies of that kind do not fall to argument. They fall when somebody wins with the opposite.

The players did not exist yet. Shooting from twenty-four feet, off the catch, with a hand in your face, off a hard cut, on legs that have run for forty minutes, is a specific and deeply trained skill. It takes something like a decade of daily repetition from childhood to build, which means the supply of players who could do it in volume lagged the demand for them by a full generation. A coach in the early years who wanted a five-out offence could not have staffed it. The high schools had not been asked to produce those players yet, and by the time they were, the ones already in the league had spent their formative years being taught to post up.

The evidence did not exist either. You cannot compute points per attempt by location without knowing the location of every attempt. That means shot coordinates logged for every game, then the same for every team over multiple seasons, then optical tracking that adds the defender's distance and the time on the clock. Until that existed, the case for the three was a piece of algebra with no way to check whether the make-rate assumptions inside it survived contact with a defence. Coaches were not being irrational in ignoring an untested model. They were being ordinary. The same lag shows up wherever a sport gets a measurement it previously lacked, from what expected goals did to the argument about shot selection in football to the way ball-tracking changed field settings in cricket, and in every case the model arrived years before the belief did.

The incentives were asymmetric. A coach who loses a game while taking twelve threes is criticised for taking twelve threes. A coach who loses the same game on contested midrange jump shots is criticised for losing. The failure modes are not punished equally, and a coach whose job depends on the second kind of criticism being avoided will pick the orthodox loss every time. That asymmetry is worth more than any spreadsheet, and it is why the change required people who could survive being wrong in public.

Underneath all five sat a slower constraint. Rebuilding an offence around shooting means changing the roster, and rosters are made of guaranteed multi-year contracts. A team with two non-shooting bigs on long deals cannot become a five-out team by deciding to, and the cap rules that govern how quickly a roster can be turned over put a floor of several seasons under any structural change. Strategy in a capped league moves at the speed of contracts, not at the speed of ideas.

The shot chart with a hole in the middle

Plot every shot a modern team takes and the picture has a shape that would have been unrecognisable to the league that first painted the arc. There is a dense cluster in the restricted area. There is a band of shots strung along the outside of the three-point line, heaviest in the two corners. Between the two, across the huge area from about eight feet out to the arc, there is a hole.

That hole is not an accident of style. It is exactly the region the arithmetic condemns, and its boundaries are drawn by two different pressures. The inner edge is set by where the floater and the runner stop being viable, which is roughly where a guard can no longer get the ball over a retreating big. The outer edge is set by the paint on the floor.

A few shots survive inside the hole, and the survivors are instructive.

The short midrange shot, from around ten feet, persists because it is what a driver has left when the rim is walled off and he is already in the air. It is a salvage shot, not a choice.

The post-up against a mismatch persists because the alternative is not a three, it is a switch nobody punished. When a defence puts a small guard on a large scorer, the fifteen-footer over the top of him is not being compared with a corner three. It is being compared with nothing.

The late-clock two persists because the shot clock does not care about efficiency. With three seconds left and no advantage created, the choice is a contested eighteen-footer or a turnover, and the eighteen-footer wins that comparison easily. A meaningful share of the midrange shots taken in any game are shots taken by a possession that has already failed.

The playoff two persists because a defence that has spent a series taking away the rim and the arc has, by construction, left the middle open. More on that below, because it is the most important limitation on the whole idea.

What actually disappeared was the chosen long two. The pull-up from nineteen feet with fourteen seconds on the clock, taken because it was open and because everyone had always taken it. That shot was the industry's largest single leak, and closing it did not require a better player, a new play or a philosophical revolution. It required a step backwards.

Spacing is the prize, not the shot

If the story stopped at points per attempt it would be a story about shooting. It is not. The three-point line's real effect on basketball is geometric, and it lands on the defence.

Start from the constraint the defence is under. Five defenders have to cover five attackers, protect the basket, and be close enough to every shooter to contest a jump shot. Those are three jobs and there are only five bodies, so the defence is always solving an allocation problem: how far can each man stray from his assignment before the cost of leaving exceeds the benefit of helping?

The answer depends entirely on what his man can do.

If his man cannot shoot from range, he can stand several feet off him, in the gap, with one foot in the paint. He is guarding two things at once and it costs him nothing. Multiply that across three non-shooters and the defence has effectively fielded an extra defender in the middle of the floor, without breaking any rule, without any special scheme, purely because the offence has told it that a third of the court is safe.

If his man can shoot, none of that is available. He has to start within a closeout of the arc. He is guarding one thing.

This is why spacing is not a decorative concept and not a synonym for standing apart. Spacing is the distance a defence must travel to be in two places at once, and every additional shooter on the floor lengthens it. Put five shooters out and the five defenders are pinned near the arc; the space between the arc and the rim, which is where every drive, cut and roll happens, is emptied out. A defence stretched all the way to the line simply cannot also wall off the basket, because the help has to come from somewhere and every somewhere now has a shooter standing on it.

The corner is where this pressure is highest, and the geometry is worth spelling out. A defender guarding a corner shooter is stuck in a dead end. He has the sideline on one side and the baseline behind him, so he is the least useful helper on the floor; if he steps in and the ball goes to his man, the closeout he has to run is the longest one available, along a path with no room to recover. That is why the corner is both the best shot on the arc for the offence and the worst assignment on the floor for the defence. Filling both corners is not a stylistic preference. It is a way of removing two of the five defenders from the rim-protection problem before the ball has even moved.

One rotation, and why it cannot be right

Prose describes the state of a defence badly. What it describes worst is the sequence, because a spaced floor does not beat a defence at any single instant. It beats it one step at a time, with each step forced by the last.

Here is a single pick-and-roll against a five-out floor, played out. No player in it does anything wrong.

1. 1The screen is set at the topThe ball handler comes off it with half a step. Two defenders are now attached to one ball, which leaves three to cover four attackers.
2. 2The big drops instead of switchingHe retreats towards the rim, conceding the pull-up jump shot to protect the layup. That is the standard trade, and against a good pull-up shooter it is already a loss.
3. 3The driver gets into the paintHe is now inside the arc with a retreating defender in front of him and nobody between him and the basket. Somebody has to step up or it is a dunk.
4. 4Only one man has a short routeThree of the remaining defenders are attached to shooters on the arc. The weak-side corner defender is the only one who can reach the ball in time.
5. 5He takes two steps inThat is the entire break. Not a mistake, not a lapse. Two steps, taken because the alternative was conceding a shot at the rim.
6. 6The pass beats the helpThe driver read the rotation as it started, so the ball is already in the air to the corner before the helper has arrived to contest anything.
7. 7The next man runs the longest closeout on the floorThe wing defender has to cover the distance from the middle of the floor to the corner. He arrives late, and he arrives moving.
8. 8The offence takes whichever half he givesContest hard and he flies past, opening a straight-line drive to a rim now guarded by nobody. Pull up short and the corner three goes up uncontested.
9. 9The defence is a man behind for the rest of the possessionEvery subsequent rotation starts late. One extra pass and the offence is choosing between an open three and a layup, with the shot clock barely moved.

A step-by-step account of a single possession. No figures are reported; this describes the sequence of decisions, each of which is individually correct.

Read the sequence again and notice that the defence never made an error. It made a series of forced choices, each one correct given the previous one, and arrived at a bad shot conceded. That is the difference between a scheme that is beaten and a scheme that is dominated: there was no branch of the decision tree that ended well.

The offence did not need a great shot-maker for any of that. It needed four men who could be believed from the arc, and one who could get into the paint.

Gravity: what a shooter does when he never touches the ball

The clearest evidence that the three-point line changed the game through geometry rather than through scoring is what happens on possessions where the best shooter never touches the ball.

Call it gravity: the defensive attention a player commands regardless of whether the ball comes to him. A genuinely elite shooter is guarded by a man who has been told, explicitly, that he does not help. Not on a drive, not on a roll, not on a post-up. He stays attached, which means that for the whole possession the defence is playing four against four in a space designed for five against five.

Watch what that does. The screener rolling to the rim meets one defender instead of two. The driver reaches the paint against a retreating big with no low man arriving. The cutter has an entire side of the floor to himself. None of it appears in the shooter's line in the box score, and all of it is caused by him.

Gravity also travels off the ball, which is the part that turns a shooter from a threat into a system. A shooter sprinting off two screens forces his defender to fight through both, forces the screeners' defenders to make a decision about helping, and shifts the whole shape of the defence towards the strong side while the ball goes the other way. Actions that used to be decoration become genuinely dangerous, because the defence cannot afford to treat any of them as decoration.

This is also where the standard statistics fail hardest. There is no column for a shot that was not contested because somebody else was standing in the corner. Attempts have been made to price gravity by comparing what a team's other players do with the shooter on the floor and off it, and those numbers are useful and noisy in equal measure, because on-off comparisons carry every other difference between the two lineups along with them. The honest position is that gravity is real, large, and measured badly, which is an uncomfortable combination for anyone building a roster on it.

There is a hard-edged consequence for the middle of the roster. A player who can shoot but does little else is worth more on a floor that needs spacing than his individual production suggests, and a player who does several things well but cannot shoot is worth less. That is the origin of the specialist wing who shoots and defends and does nothing else, a role that barely existed when the line was painted and is now the most reliably employable job in professional basketball.

What it did to the centre

No position absorbed more of this than the centre, and the change was not gradual.

The traditional job description was to score with his back to the basket, rebound, and protect the rim. Every one of those three things was devalued by the geometry, and the first was devalued almost to zero. A post-up occupies the exact area of the floor that a spaced offence is trying to empty. The scorer stands in the middle of the paint, which is where the defence would like everybody to be, and he invites a double team from the very help defenders that a five-out alignment is designed to pin to the arc. A post-up is, in spacing terms, an act of self-sabotage unless the mismatch is severe.

The second devaluation came from the other end. A centre who cannot switch onto a guard is a target. Once every possession begins with a screen designed to get him defending in space, the ability to slide his feet for four seconds twenty-five feet from the basket became a more important skill than the ability to block shots, because the offence gets to choose which of those two skills he is tested on.

Put those together and the modern requirement is brutally simple. A big man must be able to do at least one of two things: shoot from the arc, or defend on the perimeter. A big who can do neither is not a player with limitations. He is a liability the opponent can attack on every possession at both ends, and the market for that player collapsed accordingly. A big who can do both is among the most valuable assets in the sport, which is why the price of one now runs into the kind of money that forces teams to think hard about the roster-building penalties that arrive above the second apron.

The positional vocabulary changed with it. The five traditional positions described where a player stood in a half-court set that no longer exists. What replaced them is a set of questions: can he shoot, can he handle it under pressure, can he guard a guard, can he guard a big, can he pass out of a short roll. A player is now a bundle of those answers, and lineups are assembled to cover all of them rather than to fill five labelled slots. It is the least romantic development in modern basketball and the most useful.

The romantic reading of this, that the big man was killed off, is wrong. What was killed off was a specific job, the low-post scorer whose value came from being immovable close to the rim. Large players are as valuable as they ever were, provided the largeness comes with range or mobility. The premium simply moved from mass to versatility.

The defensive answers, and why none of them closed the hole

Defences did not sit still. They produced four serious answers, and every one of them trades a problem for a different problem. That is not a failure of imagination. It is the structure of the situation, and understanding why is the difference between watching basketball and understanding it. The full menu of coverages is a subject of its own, and how NBA defensive schemes actually fit together deserves more room than it gets here.

Switch everything. If every defender can guard every attacker, a screen achieves nothing, because the defence simply trades assignments and nobody is ever forced to help. It is the most direct answer available and it is why teams spent years collecting interchangeable six-foot-seven athletes. What it costs is mismatches. Switching by definition hands the offence the right to choose which defender guards which attacker, and a patient offence will screen until it finds the pairing it wants, then attack it. Switching does not eliminate the advantage, it converts it into a different advantage that takes longer to exploit and is easier to defend with a single extra body.

Drop the big. Keep the screener's defender near the rim, concede the pull-up, protect the basket. This is the coverage the flow above describes, and it is coherent as long as the pull-up jump shot is a bad shot. Against a shooter who is comfortable from twenty-seven feet it is not a coverage, it is an invitation. The drop was designed for an era when the ball handler coming off a screen wanted to get to the rim. When he wants to shoot from where the screen was set, dropping hands him the thing he was trying to create.

Blitz or hedge. Send two at the ball, take it out of the best player's hands, force somebody else to make the decision. This works, and the cost is arithmetic: two defenders on the ball leaves three covering four, which is the exact situation the offence was engineering anyway. It just happens further from the basket and with more time to rotate. Against an offence with four passers it is a losing trade. Against an offence with one decision-maker and three finishers it can be the right one.

Run them off the line. Close out hard and high, take the three away, accept the drive. This is the closest thing to a genuine solution, and it is the one that explains why the game has not simply become a shooting contest. If a defence refuses to concede any threes, it must concede everything the drive creates, and the modern answer to that is the shot the arithmetic supposedly banned: the midrange pull-up. A team that takes away the rim and the arc has spent all five defenders doing it, and what is left over is a fifteen-footer.

Which is the honest limit on the whole model. Shot quality is not a property of the shot, it is the outcome of a negotiation. As soon as an offence stops taking midrange shots entirely, the defence stops paying to prevent them, and the shot becomes efficient again precisely because it is undefended. The equilibrium is not "nobody shoots from the midrange". It is a distribution in which the midrange is taken often enough that ignoring it is punished. The efficiency numbers that condemned the long two were measured in a world where teams defended it. They cannot be read as a permanent verdict.

This is why the game tightens in a playoff series. Seven games against one opponent, with three days of preparation, allow a defence to build a plan around one offence's specific personnel, take away its two best shots, and dare the third-best option to beat them. The shots that get conceded in that situation are exactly the ones the regular-season model says to avoid, and taking them can be entirely correct, because the comparison is never against an average shot. It is against the alternative available on that possession.

The rules that made all of it legal

None of this would have worked in the game as it was previously officiated, and the rule changes deserve more credit than they usually get.

Hand-checking. For years a defender was permitted to place and keep a hand or forearm on a ball handler outside the paint, which let a strong defender ride a smaller player away from where he wanted to go. The league tightened that progressively and then removed it, and the effect was immediate: a quick guard with the ball became almost impossible to keep in front using strength alone. Once the drive could not be contained by one man, help became mandatory, and once help became mandatory, the shooter that help left open became the most valuable object on the floor. Freedom of movement rules for players without the ball did the same work off the ball, making it far harder to disrupt a shooter running a route to the corner.

The end of illegal defence, and the defensive three-second rule. The league used to forbid zone defence outright through a set of illegal-defence rules, and replaced them with a simpler bargain: zones are permitted, but a defender may not remain in the paint for three seconds unless he is actively guarding an opponent. That single clause is the reason a five-out offence cannot be answered by simply parking a seven-footer under the basket. The rule forces the rim protector to be attached to somebody, which means the offence can pull him out by putting his man on the arc, which means the rim is only as protected as the shooting of the man the centre is guarding.

The restricted area. The arc under the basket, inside which a secondary defender cannot draw a charge, tilted the collision at the rim towards the offence. It made driving less costly and rim protection harder, and every increment of that pushes the defence to help earlier, which pushes the offence to space wider.

There is also a natural experiment in the league's own history that is usually mentioned as trivia and is genuinely informative. The NBA shortened the arc to a uniform distance all the way round for three seasons in the mid-1990s, then moved it back. Attempts and makes both rose while it was short, which is what anyone would have predicted, and the league reversed the change on the grounds that it had distorted the game. What it demonstrated is the thing the current debate needs: the volume of threes is highly responsive to the distance, and the lever works in both directions.

The honest costs: sameness, variance and a narrower game

The strongest criticism of the three point revolution in the NBA is not that the arithmetic is wrong. The arithmetic is not wrong. It is that optimisation is a process that removes variety, and variety is a large part of what people were watching for.

Aesthetic convergence. When every team solves the same problem with the same data, they converge on the same answers. Offences look more alike than they did, sets look more alike, and the range of body types that can hold a job has narrowed at both ends. A sport in which every participant plays correctly is a sport in which every participant plays similarly, and the pleasure of watching two genuinely different ideas collide is a real thing to have lost. This is not nostalgia for inefficiency. It is a complaint about the by-product of efficiency, and it is legitimate.

Variance. A three-point shot is a higher-variance event than a layup, so a team that shoots more of them has a wider distribution of outcomes around the same average. Over a long season variance washes out and the better shot diet wins. Over seven games it does not, and over one game it certainly does not. That has a strategic implication people usually get backwards: the underdog should want variance, because a wide distribution is the only way an inferior team lands above a superior one, while the favourite should want to reduce it. A weaker team shooting a lot of threes is not being reckless. It is buying the only thing that can save it.

The rhythm of the game. More threes means more long rebounds, more transition, and a faster pace, which some people prefer and some do not. It also means longer stretches where nothing goes in, because a cold shooting night from the arc produces droughts that a diet of layups and free throws does not.

Development pressure. If shooting is the gate through which a young player must pass to be employable, then young players will spend their practice hours shooting. Some of that is pure gain, since the technical standard of shooting across the sport has risen enormously. Some of it is a loss, because the hours have to come from somewhere, and the skills that get squeezed are the ones the professional game currently prices at zero.

The defence of the change is equally honest and worth stating. The game is played at a higher technical standard than it was, spacing has made passing better rather than worse, and a great deal of what people miss was not beautiful at the time. Contested nineteen-footers were not an art form. They were the best available answer to a problem that has since been solved.

Should the line move?

The proposal comes up whenever scoring rises, and it deserves a serious answer rather than a reflex in either direction.

The case for moving it back is straightforward. Distance lowers make rates, lower make rates lower the value of the shot, and the arithmetic that condemned the long two starts to bite on the three itself. Push the line far enough and the break-even ratio stops being comfortably clearable, and shot selection re-diversifies without any need for a rule that dictates behaviour directly.

The case against is a second-order effect that most versions of the proposal ignore. Moving the line moves the defence too. Every defender guarding a shooter has to start further from the basket, which means the space between the arc and the rim gets larger, which means drives get easier and rim protection gets harder. It is entirely possible to move the line back, reduce the number of threes, and increase scoring, because what you have really done is widen the floor. The change is not a dial that reduces offence. It is a redistribution with an ambiguous sign.

There is also the practical point that the corners cannot move much. The straight sections exist because a full-radius arc would run off the court, and the sidelines are fixed by the size of the building. Any meaningful extension of the arc requires either a wider court, which almost every existing arena would have to be rebuilt to accommodate, or corners that stay where they are while the top moves back, which increases the discount on the corner three and makes the shape of offences more extreme rather than less.

Given all that, the more targeted interventions are the interesting ones.

Lengthen only the corners. Straighten the geometric anomaly rather than the whole line. It removes the cheapest three on the floor and leaves everything else alone, and it is the only version of the change whose direction is unambiguous.

A four-point line. The reverse move: add a deeper arc worth four. It sounds like a gimmick and it has a serious argument behind it, which is that it would pull defences out further still and open the rim dramatically. It would also make late-game deficits recoverable in ways that would change the shape of endings. Whether that is a feature or a defect is a matter of taste rather than analysis.

Change nothing and let the equilibrium work. The strongest argument of the lot. Defences are already adapting, offences are already meeting resistance, and the marginal three is a much worse shot than the average three: the thirtieth attempt of a night comes from a worse shooter, later in the clock, under a harder contest. Diminishing returns are a real force and they operate without any help from the rulebook. A rule change made at the peak of a trend has a habit of arriving just as the trend was correcting itself.

Where the frontier is now

The interesting work has moved past "shoot more threes", which is now settled and no longer confers any advantage on anyone. Four fronts are live.

Rim pressure as a scarce resource. If every team can space the floor, spacing stops being an edge, and the constraint becomes the man who can actually get into the paint against a set defence. Spacing without penetration produces a lot of open threes taken by nobody in particular, because a defence that never has to help never has to leave anyone.

Offensive rebounding as a counter-cycle. Crashing the glass was written off during the transition years, on the grounds that the possession cost of losing transition defence exceeded the value of the second chance. As shot diets shift, that trade is being reopened, and a longer average miss makes the geometry of the rebound different rather than simply worse.

Deep shooting as a weapon against the drop. The pull-up from several feet behind the arc is a bad shot in isolation and a devastating one in context, because it removes the last coverage that made the drop coherent. Its value is not the points it scores. It is that it forces the big man to leave the rim, and everything else on this list gets easier once he does.

The revival of the things that were squeezed out. Cutting, passing out of the short roll, and the deliberate midrange shot are all worth more now than they were five years of consensus ago, precisely because defences are built to stop something else. That is the equilibrium argument in action, and it is why the smartest teams are not the ones that shoot the most threes. They are the ones that correctly identify which shots the opposition has decided to concede, which is a question with a different answer every series.

There is a wider point in that, and it is not confined to basketball. Every sport that acquires a good measurement passes through the same three stages: the metric is ignored, then the metric is obeyed literally, then the metric becomes the thing opponents plan around and its naive form stops working. Golf went through it when shot-level accounting replaced the traditional box score, and the same arc is visible anywhere a number has been given the authority to overrule a coach. The three-point line is simply the loudest example, because the evidence of the change is visible from the back row of the arena.

What to look at on a shot chart

Four things, in this order, and none of them is the number of threes.

Where the threes come from. Corners are cheaper by a foot and nine inches and pay the same. A team taking most of its threes off the dribble from twenty-seven feet and a team taking them from the corners off the pass have completely different offences that look identical in a total.

Whether the rim attempts survived. The change was supposed to replace long twos, not layups. A team whose midrange volume fell and whose rim volume fell with it has not optimised anything, it has just moved outside, and it will be found out in a series against a defence that runs it off the line.

Who is taking them, and how late. The thirtieth attempt of a night is not the same shot as the tenth. Volume tells you about a philosophy; distribution across players and across the shot clock tells you whether the philosophy is disciplined or merely loud.

What the opponent conceded. A shot chart is a record of a negotiation between two teams, not a statement of one team's preferences. The right question about any midrange shot is never whether the model likes it. It is what else was available on that possession, and who decided.

The line has been on the floor the whole time. The only thing that changed is that somebody finally did the arithmetic, and then somebody else built a roster that could act on it. There is more of both to come. Anyone who wants the next version of this argument will find it wherever the geometry of the professional game is being pulled apart by people willing to be wrong in public for a season.