2.2: The Analytics That Drove It

Chapter 2: State of the game

Points per possession as the currency, the arithmetic of the corner three, gravity, and how much of the modern game follows from one division.

New terms introduced (2): Corner three, Gravity. No diagrams.

Lecture 2.1 measured what changed. This lecture is about the measurement that caused it, and it is short, because the idea at its center is one division.

1 Points per possession

Points per possession is points scored divided by possessions used. It is the currency of every argument in this site: a possession is the unit a team gets a fixed number of, so the only question about any action is how many points it returns per possession spent.

The reason this is the right unit and points per game is not is in the pace table of lecture 2.1. A team that plays fast scores more points per game without being better at scoring, and a team that plays slowly scores fewer without being worse. Dividing by possessions removes tempo from the comparison, which is what makes a 1979-80 offense and a 2024-25 offense comparable at all.

The figure this site already quotes for transition, in lecture 3.1, is of exactly this kind: a data set of college play-by-play since the 2010 season gives “the average points per transition play is 1.04” against “the average points per half-court play is 0.87”.¹ That is a difference of 0.17 points per play, and everything in lecture 3.1 is a way of getting more plays into the first category.

2 The arithmetic of the three

The whole of the shift measured in lecture 2.1 follows from one comparison, and it needs no data beyond the values of the shots.

A two-point shot made at rate p returns 2p points. A three-point shot made at rate q returns 3q. The three is the better shot whenever 3q > 2p, which is whenever q > (2/3)p. So a three taken at 35% returns 1.05 points, and a two must be made at better than 52.5% to match it.

That is the entire argument, and it was available on the day the line was adopted in 1979. What was missing for twenty years was not the arithmetic but the habit of counting. Lecture 2.1 shows the consequence: threes went from 3.1% of shots in 1979-80 to 42.2% in 2024-25, and true shooting rose from .531 to .576 over the same span.²

3 The corner three

The corner three is where that arithmetic is sharpest, and the reason is geometry rather than skill. The three-point line is a fixed arc around the basket with the corner segments cut off by the sidelines. The NBA rulebook states it in one sentence: “The three-point field goal area has parallel lines 3’ from the sidelines, extending from the baseline and an arc of 23’9” from the middle of the basket which intersects the parallel lines.”³ A shot from the corner is therefore taken from 22 feet rather than 23 feet 9 inches, the shortest three available, and worth the same three points.

That single fact is why the corner is a place in this site’s vocabulary rather than merely a region of the floor. The lift of lecture 3.7 exists to get a shooter out of it and back to the wing when the drive goes baseline; the kick-out and skip pass of lecture 3.10 exist to find him in it; the hammer of lecture 3.6 exists to put a shooter there against the grain of a defense’s rotation.

The corner three’s higher conversion rate is not sourced here. It is routinely reported that corner threes are made at a higher rate than threes from above the break, which is what the shorter distance would predict. This site has no shot-location table on file, for the reasons stated in lecture 2.1, so the claim appears here as the geometry (which is in the rulebook) and not as a conversion rate (which is not on file). What would close it: a public shot-location table by zone.

4 Gravity

Gravity is the name for what a shooter does to defenders when he is not involved in the play. A defender who will not leave a shooter is a defender who is not helping, so the shooter’s presence is worth points scored by somebody else. It is the clearest case in this site of a term that exists because of a measurement: the idea that a player’s value can be located in shots he does not take requires someone to have counted what happens when he stands still.

Gravity is also why spacing is a property of a team rather than of a floor plan. Five players spread to the arc create nothing if their defenders can safely leave them; the same five spots occupied by shooters force every helper to make a choice. That is the difference between the 5-out alignment and 5-out as an offense.

Gravity is not quantified here. Several public and private analyses have put numbers on it. None of them is on file, so this lecture defines the term and does not measure it.

5 How much of the modern game is downstream of one division

A reader can draw a line from 3q > 2p through most of Chapter 3.

• The floor. 5-out and 4-out 1-in exist to place shooters where help must come from.
• The gap. Spacing is measured in gaps because a double gap is the distance a helper cannot cover in time, and it only matters if leaving the man costs three points rather than two.
• The main action. The pick-and-roll of lecture 3.3 forces two defenders onto one attacker, and the pop exists because the screener’s defender now has to choose between the rim and the arc.
• The shot chart. The corner three became a designed shot, and the drive and kick-out became the pair of actions that produce it.

What does not follow from it is anything in Chapter 1. The eras there are bounded by dated rule changes, and the arithmetic in this lecture was true in every one of them. That is the honest summary of this chapter: the sport did not learn a new fact in 2004, it started acting on an old one, and the measurements in lecture 2.1 are the record of it doing so.

Footnotes

1. Jordan Sperber, “Should offenses play faster?”, Hoop Vision, 15 January 2020, https://hoopvision.substack.com/p/should-offenses-play-faster, retrieved 2026-09-17. Verbatim: “The average points per transition play is 1.04” and “The average points per half-court play is 0.87”, stated under the heading “Since the 2010 season”. The text does not name the league. The programs it names, Wisconsin, Davidson, Illinois and Cal State Bakersfield among them, with a WAC title and an NIT Final Four, are Division I men’s college teams, so these are college figures, used here for the shape of the effect and not as an NBA number. The publication’s own about page confirms the scope in its own words, quoted in the next footnote.[^hvabout] Saved as sperber-2020-play-faster.

2. Basketball-Reference, “NBA League Averages - Per Game”, https://www.basketball-reference.com/leagues/NBA_stats_per_game.html, retrieved 2026-09-21, regular-season table. Rows quoted: “season 1979-80” with “fg3a_per_g 2.8”, “fga_per_g 90.6”, “ts_pct .531”; “season 2024-25” with “fg3a_per_g 37.6”, “fga_per_g 89.2”, “ts_pct .576”. The percentages of shots are this site’s arithmetic from the two attempt columns. Saved as bbref-per-game.

3. NBA Official, “RULE NO. 1: Court Dimensions – Equipment”, https://official.nba.com/rule-no-1-court-dimensions-equipment/, retrieved 2026-09-21; the same page is quoted in tools/court.py, where this site’s diagram geometry is defined. Verbatim, in the page’s own characters: “The three-point field goal area has parallel lines 3’ from the sidelines, extending from the baseline and an arc of 23’9” from the middle of the basket which intersects the parallel lines.” The page’s text does not state the court’s overall width; the corner distance of 22 feet is this site’s arithmetic from the quoted 3-foot inset and the 50-foot width, which tools/court.py takes from a secondary source and marks as such. Saved as nba-rule-1-court.