Basketball
How The Three-Point Line Arrived
Rewarding distance shooting was a rejected novelty for decades before it became the defining feature of the sport, and its arc shape was chosen for a specific reason.
Rewarding shots from distance was treated as a gimmick for decades before it reshaped the sport entirely. The line's arc shape and its distance were both chosen deliberately.
The problem it was introduced to solve
Without a distance bonus, the optimal shot is always the closest one, which concentrates play near the basket and rewards height above all other attributes.
Defences collapsed inward accordingly, and offences became congested, with little reason for anyone to stand far from the hoop.
A scoring premium at distance gives defenders a reason to guard the perimeter, which pulls them away from the basket and opens the interior.
Why it took so long to be accepted
Early trials in minor competitions were dismissed as a novelty that distorted the game and rewarded a narrow skill disproportionately.
The established view held that basketball was a game of movement towards the basket, and that paying more for a lower-percentage shot was incoherent.
Adoption came through leagues that needed differentiation, and the rule spread only once its effect on spacing became visible rather than theoretical.
The geometry of the line
The arc is a circle centred on the basket, so every point on it is equidistant from the hoop and the reward matches the difficulty consistently.
The straight sections near the sidelines exist because a full circle would run off the court, and the corners are consequently closer than the top of the arc.
That shortened corner distance makes the corner three the most efficient shot on the floor, an unintended consequence of fitting a circle into a rectangle.
How the arithmetic changed strategy
A shot worth three points needs a lower success rate than a two-pointer to produce the same expected return, and the required rate is easily achievable.
Once that arithmetic was widely understood, shot selection shifted towards attempts at the rim and attempts behind the line, with mid-range shots declining sharply.
The mid-range shot is not worse than it was. It is simply worth the same as before while the alternative became worth half as much again.
The spacing effect on everything else
Defenders committed to the perimeter cannot also protect the basket, so driving lanes opened and scoring at the rim became easier as well.
Player roles changed as a result, with interior players expected to shoot from distance so that their defender cannot sit under the hoop.
A rule intended to add a scoring option ended up determining which body types and skill sets the sport values, which few of its early advocates anticipated.
