True shooting percentage explained: the formula and its limits

Field goal percentage answers a question almost nobody is asking. It counts how often a shot went in and refuses to care what the shot was worth, so a tip-in and a step-back from twenty-six feet arrive in the same column, get divided by the same denominator, and come out the same size. Then it discards free throws completely. The most reliable scoring event in the sport, the one taken with nobody guarding you from a fixed distance, is invisible to the number most often used to judge scorers.

That is two separate failures in one statistic, and they push in different directions, which is why the mistakes they cause are so hard to spot by eye. Here is true shooting percentage explained from the scoring rules upwards: what it is actually measuring, how the formula is built rather than merely stated, why the free throw term carries the odd coefficient it does, why that coefficient is an estimate and not a fact, and the four things the metric still cannot see no matter how carefully you read it.

The two things field goal percentage refuses to count

Take the first failure on its own. A field goal is any shot from the floor, and the percentage treats every one of them as a single unit of success or failure. The rulebook does not. It pays two points for some of them and three for others, which means the statistic and the scoreboard are using different currencies.

The consequence is not subtle. A player who takes nothing but shots at the rim and a player who takes nothing but threes are being measured on a scale that systematically flatters the first and punishes the second, by an amount fixed at 50 per cent of the payout. No amount of context solves this, because the error is baked into the definition. A three-point shot is worth half as much again as a two, and field goal percentage is built on the assumption that it is not.

The second failure is stranger, because it involves a shot the statistic does not merely mis-weight but excludes.

Free throws are not field goals. They do not appear in the numerator or the denominator of a field goal percentage. So a player who drives hard, absorbs contact, and lives at the line has an entire category of his scoring hidden from the number, while a player who settles for jump shots has all of his scoring visible. Two players can produce identical points from identical possessions and separate by ten points of field goal percentage purely on the basis of whether the contact was whistled.

Push that to its limit and the absurdity is complete. Imagine a possession in which a player drives, is fouled in the act of shooting, and converts both free throws. He has scored two points. In the field goal column he has recorded nothing at all. Not a make, not a miss, not an attempt. The most efficient thing that can happen to an offensive player, scoring without risking a live-ball miss, registers as a non-event.

So the statistic answers this question: of the shots this player took from the floor, ignoring their value and ignoring every shot he took from the line, what share went in? Nobody has ever wanted to know that. What people want to know is how many points a player produces from each opportunity he uses, and that is a different question with a different answer.

Building the measure: points per scoring attempt

Start from the question rather than the formula, because the formula is only interesting once you can see what it was forced into.

The thing worth measuring is points produced per scoring opportunity. A scoring opportunity is a possession that ends with this player attempting to score, whether that attempt happens from the floor or from the line. Everything after this is bookkeeping.

The numerator is easy. Total points. Not makes, not weighted makes, just the points that went on the scoreboard, which already contains the correct weighting because the rulebook did the weighting for us. There is nothing to derive here.

The denominator is the whole problem. Field goal attempts are straightforward: one attempt, one opportunity, whether it was a layup or a heave. Free throws are not, because free throw attempts and scoring opportunities are not the same thing and never have been. A standard shooting foul awards two shots from one possession. Counting those as two opportunities would double-charge the player for a single trip and drag his efficiency towards nonsense.

So the denominator has to be field goal attempts plus some fraction of free throw attempts, where the fraction converts shots at the line into trips to the line. Call that fraction c for the moment and leave it unresolved. The measure is:

points ÷ (FGA + c × FTA)

That is points per scoring attempt, and it is already a complete and honest efficiency metric. It reports a number somewhere around one, because a decent offensive possession produces about a point.

One more step turns it into the thing everybody quotes. Divide by two.

TS% = points ÷ (2 × (FGA + c × FTA))

The division by two is pure presentation, and it is presentation with a purpose. It rescales the answer so that it lines up with the field goal percentages people have been reading for a century. Check the calibration on the simplest possible case. A player who takes only two-point shots, never gets to the line, attempts n shots and makes m of them, scores 2m points. His true shooting is 2m ÷ 2n, which is m ÷ n, which is his field goal percentage exactly.

That is the design goal, and it is why the factor of two is there rather than some other number. For a player who does nothing but shoot twos, true shooting percentage and field goal percentage are the same number. Every point of difference between the two figures for any real player is caused by threes, by free throws, or by both. The metric is constructed so that the old number is the special case and the new number is the general one.

Two useful anchors fall out of the same scaling. A true shooting of 50 per cent means exactly one point per scoring attempt. A true shooting of 60 per cent means 1.2 points per scoring attempt. Once you hold those two in your head, every true shooting figure you ever read converts instantly into the only unit that matters on a scoreboard.

Effective field goal percentage, and exactly where it stops

Before the free throw term, there is an intermediate measure that fixes one of the two failures and leaves the other alone. It deserves precision, because the difference between the two metrics is the single most common confusion in this corner of the sport.

Effective field goal percentage weights makes by what they were worth. The derivation takes one line. Points scored from the floor are 2 × FGM + 3PM, since every made three has already been counted once as a made field goal worth two and needs one more point added. Factor out the two:

2 × FGM + 3PM = 2 × (FGM + 0.5 × 3PM)

Divide by field goal attempts and by two, exactly as before, and the twos cancel:

eFG% = (FGM + 0.5 × 3PM) ÷ FGA

The famous half-credit for a made three is not a convention somebody chose. It is what falls out of the algebra when you insist that the statistic be expressed on the same scale as a field goal percentage. A made three counts as a make and a half because it is worth a make and a half. Everything else about the way effective field goal percentage is built and used follows from that single substitution.

Now say precisely what each measure contains, because the boundary is the point.

	Counts made twos	Weights threes correctly	Counts free throw points	Counts free throw attempts
Field goal percentage	yes	no	no	no
Effective field goal percentage	yes	yes	no	no
True shooting percentage	yes	yes	yes	yes

Effective field goal percentage is not a worse version of true shooting. It is a different tool with a legitimate job, and there are questions for which it is the better instrument. If you want to judge shot selection from the floor, free throws are noise: they tell you about contact and officiating, not about where a player chose to shoot from. A team deciding whether its midrange diet is defensible wants effective field goal percentage, cleanly, without the foul-drawing of its guards muddying the picture. That argument is the whole subject of what the three-point line did to shot selection, and it is conducted almost entirely in effective field goal percentage for exactly this reason.

If you want to judge a scorer, free throws are not noise. They are points, produced from possessions, by a skill that is trainable and repeatable. That is where effective field goal percentage stops and true shooting has to take over.

Why the free throw term carries 0.44

Now resolve c, the coefficient sitting in front of free throw attempts. This is the part that most explanations state and almost none derive, which is a shame, because the derivation is the most interesting thing about the metric.

Start with the default case. A foul committed against a player in the act of shooting a two-point attempt awards two free throws. One possession, two attempts at the line. If every foul in basketball were that foul, c would be exactly 0.5, and the formula would have a clean, memorable half in it.

Four categories drag it below a half, and each one is a rule, not a statistical artefact.

Three-shot fouls. A foul on a player attempting a three awards three free throws. Still one possession, now three attempts. Each of those attempts represents a third of a trip rather than a half, so every three-shot foul pulls the average coefficient down.

And-one free throws. When a shooter is fouled and the field goal still counts, he gets one free throw. That possession has already been counted once, as a field goal attempt in the denominator. The bonus free throw does not represent a new opportunity at all. Its correct weight is zero.

Technical fouls. A technical free throw is awarded for conduct, not for a scoring attempt, and the ball goes back to whoever had it. No possession is consumed. Correct weight, zero again.

Flagrant and clear-path free throws. These award shots and then return possession to the shooting team. The trip to the line did not end anything; the team keeps the ball and can score again on the same possession. Zero once more.

Put those together with an invented worked example. The mix below is constructed to be round and legible, not reported from any season.

80%9%

• Two-shot shooting fouls80
• Three-shot shooting fouls9
• And-one bonus free throws7
• Technical and flagrant free throws4

An invented, deliberately round mix of foul types, used to show how the coefficient is built. Nothing here reports a real season, team or player. Two-shot fouls give one possession per two attempts, three-shot fouls one per three, and-one bonus shots and technical or flagrant shots give none.

Show the numbers

Worked example: where 100 free throw attempts come from

Item	Value
Two-shot shooting fouls	80
Three-shot shooting fouls	9
And-one bonus free throws	7
Technical and flagrant free throws	4

Count the possessions those hundred attempts represent. The eighty two-shot attempts are forty trips. The nine three-shot attempts are three trips. The seven and-ones are attached to possessions already counted as field goal attempts, so they add nothing. The four technical and flagrant shots add nothing. Forty-three possession-ending trips from a hundred free throw attempts gives a coefficient of 0.43 for this invented mix.

Change the mix and the number moves. Give the example more three-point fouls and the coefficient falls; give it fewer and-ones and it rises. That is the honest position on 0.44, and it needs saying plainly rather than buried:

The coefficient is an approximation, not a truth. It is an average of a distribution that varies by team, by season, by competition and by how the game is being officiated in a given year. A player whose fouls arrive disproportionately on three-point attempts is having his opportunities slightly overcounted by 0.44; a player who draws mostly and-ones is having his slightly undercounted. Analysts have argued for years that the conventional figure is a shade too high for the modern shot diet and have proposed recalculating it season by season, which is straightforwardly correct and which nobody does in casual use because 0.44 is memorable and the difference is small.

There is a further point that makes the approximation less defensible than it once was, and more forgivable. When the formula was designed, all anyone had was a box score. A box score records free throw attempts as a single number with no breakdown, so the coefficient had to be a fixed guess applied to everybody. Play-by-play data removes that constraint entirely: the exact number of possession-ending trips is now countable, for every player, with no estimation at all. The 0.44 survives because it is embedded in every published table and because replacing it would break comparability with decades of stored figures, not because it is the best available answer.

Treat it as what it is. A well-chosen constant standing in for a quantity that is now measurable, accurate enough that it will not mislead you about a season and not accurate enough to settle an argument about two players separated by half a point.

• 2.27Free throw attempts counted as one scoring attempt
• 0.5Extra half-make a three earns in effective field goal percentage
• 1Points per scoring attempt when true shooting reads 50 per cent
• 85.2True shooting per cent of a trip to the line converted at 75 per cent

Every figure here is arithmetic derived from the scoring rules and the 0.44 convention. None of them is a season, team or player statistic. The last row assumes a free throw conversion rate of 75 per cent, which is an invented round figure used to make the point.

That last row is worth sitting with, because it explains a great deal about how modern offences are built. If 0.44 free throw attempts make one scoring attempt, then one scoring attempt is 1 ÷ 0.44, which is 2.27 free throws. A player who converts free throws at 75 per cent turns those 2.27 attempts into 1.70 points, which is 85.2 per cent on the true shooting scale. Getting to the line is not a good outcome. It is very nearly the best outcome available on a basketball possession, and it beats an uncontested layup taken at any make rate below 85 per cent.

Run the comparison explicitly with invented numbers. A drive that produces a contested layup made 60 per cent of the time yields 1.2 points per attempt, which reads as 60 per cent true shooting. The same drive, if it instead produces a shooting foul and a pair of free throws converted at 70 per cent, yields 1.59 points per scoring attempt, or 79.5 per cent. The foul is worth nearly twenty points of true shooting more than the shot it replaced. Every coaching instruction about attacking the chest of the defender rather than avoiding him is that piece of arithmetic wearing a tracksuit, and it is the reason how fouls are defined and called has become a competitive subject rather than an administrative one.

True shooting percentage explained in eight steps

Prose is a poor medium for arithmetic with several stages. Here is one invented shooting line taken all the way through the formula, with every intermediate number shown so the whole thing can be checked with a calculator and nothing has to be taken on trust.

1. 1Start with the raw line20 field goal attempts, 8 made. Of those, 10 attempts and 4 makes came from behind the arc. Six free throw attempts, five made.
2. 2Notice what field goal percentage saysEight makes from twenty attempts is 40 per cent. That single figure is the entire input to the traditional number, and it is about to be shown up.
3. 3Count the points instead of the makesFour made threes are 12 points. Four made twos are 8 points. Five free throws are 5 points. Total, 25 points. This is the numerator, and it needs no weighting because the scoreboard already did it.
4. 4Count field goal attempts onceTwenty. The ten three-point attempts are inside that twenty, not added to it. Double-counting threes here is the most common arithmetic mistake people make with this formula.
5. 5Convert free throws into scoring attemptsSix free throw attempts multiplied by 0.44 gives 2.64. That is the estimated number of possessions that ended at the line, not the number of shots taken there.
6. 6Add them for total scoring attempts20 plus 2.64 is 22.64. This is the number of opportunities the player used, in the only unit that matters.
7. 7Double it to set the scale22.64 multiplied by 2 is 45.28. That is the points a perfect two-point shooter would have produced from the same opportunities, which is the yardstick the metric measures against.
8. 8Divide and read the answer25 divided by 45.28 is 0.552. True shooting of 55.2 per cent, from a player shooting 40 per cent from the field. Equivalently, 1.10 points per scoring attempt.

A constructed example. The line is invented: 20 field goal attempts with 8 made, of which 10 attempts and 4 makes were from three, plus 6 free throw attempts with 5 made. Nothing here reports a real player.

Notice what the last step actually reports. It is not the share of shots that went in. It is the share of a hypothetical maximum, where the maximum is defined as making every two-point attempt. That framing is the reason the metric is so much harder to misread than field goal percentage, and also the reason its name causes so much confusion.

Why true shooting percentage is not a percentage

The word percentage in the title is a historical accident and it does real damage. A percentage is a share of a whole, bounded by zero and one hundred. This is a ratio of points to twice the attempts, and there is nothing in the arithmetic that stops it exceeding one.

Work an example. A player takes one three-point attempt and makes it. Three points, one scoring attempt, denominator of two. His true shooting is 150 per cent. Nothing has gone wrong; he scored three points from one opportunity, which is one and a half times what a made two would have given him, and the metric is reporting that faithfully.

The and-one is the everyday version. A made two-point field goal plus a converted bonus free throw is three points from 1 + 0.44 attempts, so 3 ÷ 2.88, which is 104.2 per cent. Over a full season these events are diluted by everything else and the aggregate lands in a range that looks like a percentage should, which is exactly why people forget the ceiling is not real.

There is a small, instructive unfairness hiding in that and-one calculation. The bonus free throw consumed no possession, so its correct weight is zero, which would give 3 ÷ 2, or 150 per cent. The fixed coefficient charges the player 0.44 of an attempt for a shot that cost him nothing. It is a tiny penalty on the most valuable single event in basketball, applied because the box score cannot tell an and-one from any other free throw. Nobody would design it that way from scratch. It is the price of a formula that has to run on data collected before anyone thought to record the difference.

Two habits follow. Say "a true shooting of 58" rather than "58 per cent of his shots", because the second is not a thing that happened. And convert to points per scoring attempt whenever a figure needs to be reasoned about rather than merely quoted, since 1.16 points per attempt is a quantity with physical meaning and 58 per cent is a scaled abstraction.

How a 40 per cent shooter outscores a 50 per cent shooter

The example above was constructed to make a point, and the point is best made by putting it next to its opposite. Both lines below are invented, both are round, and neither reports anybody.

Player A takes twenty field goal attempts, all of them two-pointers, and makes ten. He never reaches the line. He shoots 50 per cent from the field, which in most conversations about basketball is the mark of an efficient scorer. He produces twenty points from twenty scoring attempts, so one point per attempt, so a true shooting of 50 per cent.

Player B is the line from the flow above. Twenty field goal attempts, eight made, ten of the attempts from three with four converted, plus six free throws with five made. He shoots 40 per cent from the field, which in most conversations about basketball is the mark of a chucker. He produces twenty-five points from 22.64 scoring attempts, so 1.10 points per attempt, so a true shooting of 55.2 per cent.

Ten points of field goal percentage separate them in one direction and five points of true shooting separate them in the other. Same number of field goal attempts, same team, same night. Player B scored five more points.

• Player A
• Player B

Field goal percentage50%40%

Effective field goal percentage50%50%

True shooting percentage50%55.2%

Both shooting lines are invented and described in full in the text. Player A takes 20 two-point attempts and makes 10. Player B takes 20 field goal attempts including 10 threes, makes 8 including 4 threes, and adds 6 free throws with 5 made. Nothing here reports a real player.

Show the numbers

Worked example: the same two players under three measures

Item	Player A	Player B
Field goal percentage	50%	40%
Effective field goal percentage	50%	50%
True shooting percentage	50%	55.2%

The middle row is the one that repays attention, because it isolates exactly where each metric stops.

Effective field goal percentage calls them identical. That is not a failure of the metric; it is the metric doing its job correctly and reporting that, from the floor alone, these two players produced the same points from the same attempts. Player B's shot mix converts his lower make rate into an equal points-per-shot, and effective field goal percentage sees that and says so.

Everything that separates them is the six free throws, and only true shooting can see those. Five points from what the formula counts as 2.64 scoring attempts is 1.89 points per attempt, or 94.7 per cent on the true shooting scale, and it drags the whole line upward.

That is the practical lesson, and it generalises well beyond the constructed case. When a player's true shooting sits far above his effective field goal percentage, he is a foul-drawer, and his efficiency depends on contact being called. When the two figures are close, he is a jump-shooter whose value rests entirely on the ball going in. Those are different players with different playoff risk profiles, and the gap between the two numbers is the cheapest way to tell them apart.

What true shooting percentage cannot see

A metric is only usable once its blind spots are as familiar as its formula. This one has four, and they are structural rather than fixable.

Turnovers are invisible. The denominator counts possessions that ended in a shot. A possession that ended in a stolen pass or a travel is not in it at all. So a player who commits a turnover on a fifth of his possessions and a player who never loses the ball can post identical true shooting figures while producing very different amounts of offence. This is the single largest omission, and it is why the possession-level measures that do count turnovers, of which offensive rating is the standard example, exist alongside true shooting rather than being replaced by it. Reading a scorer's efficiency without also reading his turnover rate is reading half a sentence.

Shot difficulty is invisible. Every field goal attempt weighs the same in the denominator whether it was a wide-open corner catch or a fadeaway over two defenders with one second left. The metric was designed before shot-quality models existed and has never been retrofitted. Tracking data now produces expected values for individual shots based on distance, defender proximity, time on the clock and shot type, and the gap between what a player actually scored and what his shot profile suggested is a far more interesting number than either figure alone. That comparison is the whole use case for the optical tracking layer that sits under modern shot models, and true shooting on its own has no access to any of it.

Creation is invisible. A player who catches and shoots an open three off a teammate's drive and a player who created the same shot for himself off the dribble are recorded identically. The second did substantially more work, and that work has value that shows up somewhere else on the floor or nowhere at all. Assisted rate is the crude proxy for this and it is genuinely useful: a very high true shooting figure attached to a very high assisted rate describes a finisher, and a merely good figure attached to a low assisted rate can describe a more valuable player.

Defensive attention is invisible. The player the opposition has built a game plan around is shooting against a different defence from the one his teammates face, and the metric cannot know that. Worse, the effect is circular. A great scorer draws the extra defender, which lowers his own efficiency and raises everyone else's, so the box score credits his teammates with the value he generated. This is the same measurement failure that makes gravity so hard to price, and it is a reason that shooting efficiency and offensive value are related but distinct quantities.

One further limitation is about samples rather than concepts. The 0.44 coefficient is an average, and averages behave badly on small numbers. Across ten games a player's actual mix of foul types can sit a long way from the assumption baked into the formula, so the free throw part of his denominator is estimated with real error. Over a season the error washes out. Over a week it does not, and a true shooting figure computed from a handful of games carries more uncertainty than its two decimal places suggest.

Usage is not context for true shooting, it is the other half

Here is the most common misuse of the metric, and it is not a subtle one: comparing the efficiency of two players who are being asked to do completely different jobs.

Efficiency and volume trade against each other, and the trade is not a mild statistical tendency. It is the central fact of offensive basketball. A player asked to end five per cent of his team's possessions gets to choose which five per cent. He shoots when he is open, when the pass arrives in rhythm, when the defence has already broken. A player asked to end thirty-five per cent of them does not get that luxury. He takes the shot at the end of a possession that produced nothing, against a defence that has spent the whole night preparing for him, with four seconds on the clock and no help coming.

Usage percentage estimates the share of his team's possessions a player ends while he is on the floor, counting field goal attempts, trips to the line and turnovers. The same 0.44 appears in it, doing the same job of converting free throws into trips, which is a good reminder that the two metrics are built from the same materials and are meant to be read together. The detail of how usage rate is calculated and what it does and does not capture matters here, because it is the axis along which every efficiency comparison has to be normalised.

The relationship runs in one direction with grim reliability. Push a player's usage up and his true shooting falls, because the marginal shot is always worse than the average shot. Drop his usage and his efficiency rises, because he sheds the hardest attempts first. Which means:

A high true shooting at low usage is a fact about role as much as about skill. The corner specialist who takes four wide-open catch-and-shoot threes a night and never dribbles is doing something valuable and difficult, and his efficiency figure is not evidence that he could carry an offence. Give him twenty attempts a game and the defence will simply guard him, and the shots that made his figure will stop existing.

A merely good true shooting at very high usage can be worth more than an excellent one at low usage. Absorbing difficult possessions has value even when the possessions are inefficient, because the alternative is that somebody less capable takes them. This is the argument every general manager has about every primary scorer, and it cannot be settled from a shooting line alone.

The blunt version: never compare true shooting across usage tiers without saying so. A scatter of efficiency against volume, with the league's own tradeoff curve drawn through it, tells you more in one glance than any ranked list of shooting figures. It is also why single-number summaries that fold volume and efficiency together, of the kind player efficiency rating attempts, keep being built despite their well-catalogued flaws. The demand for one number is enormous, and the honest answer is always two.

Why the raw number drifts across eras

A true shooting figure has no fixed meaning, because the environment that produces it changes constantly and sometimes abruptly. Anyone quoting a threshold for what counts as good is quoting a threshold with an expiry date on it.

The drivers are all rules and personnel rather than anything statistical.

Shot diet. As threes became a larger share of attempts, the average points per attempt across the league moved with them, because the payout per make is higher even though the make rate is lower. A league that takes a third of its shots from behind the arc has a structurally higher efficiency baseline than one that takes a twentieth.

Contact rules. Restrictions on hand-checking and the freedom-of-movement standards made it much harder to disrupt a ball handler with physical contact. Offences got easier, efficiency rose, and shooting figures rose with it. Rule changes of that kind reset the baseline in a single summer.

Defensive geometry. Permitting zone defence while forbidding a defender from camping in the paint changed where help can come from, which changed which shots are available. Any rule that alters the shots on offer alters the efficiency that gets recorded taking them.

Officiating emphasis. Free throw rates move with how tightly a season is called, and free throws are the most efficient scoring event in the game. A year in which more contact is whistled is a year in which league-wide true shooting rises without a single player getting better.

Skill supply. Shooting standards across the sport have risen steadily as each generation arrives having practised more of it from a younger age. That is a genuine improvement rather than an artefact, and it also means a raw comparison across decades measures the era as much as the player.

The fix is to stop reading the number in isolation and start reading the difference. Relative true shooting subtracts the league average for that season from the player's own figure, which is the only version of the comparison that survives a change in rules. It also reframes the question usefully: not how efficient was he, but how much more efficient was he than the environment he was playing in. League-wide averages for each season are published by the league and the standard reference sites, and they should be looked up rather than remembered, precisely because they move.

Every historical debate about scorers becomes more tractable once this is applied, and several of them reverse. A player whose raw figure looks ordinary today may have been the most efficient high-volume scorer of a low-scoring era, and the raw figure will never tell you so.

What the metric did to shot selection and rosters

Metrics do not merely describe behaviour, they change it, and this one changed a great deal once front offices started using it to price players.

The midrange volume scorer lost his market. A player whose profile was long two-point jump shots at a respectable field goal percentage read as a scorer under the old number and as an inefficient one under the new. Nothing about him changed. The instrument changed, and the contract offers changed with it. This was the first and largest repricing, and it happened faster than the corresponding change in coaching, because the people writing cheques adopted the metric before the people drawing up plays did.

Foul-drawing became a specified skill. Once the arithmetic showed that a trip to the line carries a true shooting in the eighties at ordinary conversion rates, drawing contact stopped being a by-product of aggression and became something coached explicitly. Sweeping the arms, shooting into the defender's body, jumping into a closeout: all of that is a rational response to a payout structure the metric made legible. The league has since legislated against the most obvious versions, which is itself evidence of how effective the response was.

Free throw shooting was repriced. A big man who cannot convert from the line does not merely miss free throws, he converts the single most efficient event in basketball into a mediocre one and gives opponents a strategic option they would not otherwise have. That is now a first-order roster consideration rather than a quirk, and it shows up in playing time in the final minutes of close games.

The three-and-D role became the most employable job in the sport. A player who takes only high-value shots posts a strong efficiency figure at low usage, and a roster needs several of those to make room for the one or two players carrying the volume. The whole structure of a modern rotation, one or two high-usage creators surrounded by high-efficiency low-usage specialists, is an efficiency-and-volume portfolio built directly on the tradeoff described above.

Shot charts were rebuilt around the payout, not the make rate. Once points per attempt replaced makes per attempt as the operative unit, the shots at the extremes of the floor won and everything in between lost. The consequences for spacing, for defensive rotation, and for which body types can hold a job are the largest structural change in the sport in decades, and they follow from a change in arithmetic rather than a change in athletes.

There is a counter-movement worth naming, because the metric is now old enough to be gamed. Defences adapted by refusing to give away the events the formula rewards: contest with verticality rather than contact, concede the shot the model dislikes, and take away the line. A defence that gives up midrange jump shots and prevents free throws is deliberately steering an opponent towards the parts of the shot chart where true shooting is lowest. The efficiency figures that made the case for the current orthodoxy were recorded in a world that defended differently, which is a caution that applies to every metric that becomes influential enough to be planned around.

The wider methodological lesson is one that shows up wherever a sport acquires a good measurement. A number gets built, it is ignored, then it is obeyed literally, then opponents plan around it and its naive form stops working. That is not a reason to distrust the number. It is a reason to keep asking what it was blind to, which is the same instinct that produces the various all-in-one impact metrics such as the family of plus-minus estimates built on lineup data, each of which sees something the shooting line cannot.

Reading a shooting line properly

The point of understanding the formula is to be able to look at a set of shooting numbers and extract what is actually in them. Five checks, in this order.

Convert to points per scoring attempt first. Double the true shooting figure and you have the number in the only unit the scoreboard recognises. A figure of 0.58 becomes 1.16 points per attempt, which can be reasoned about, compared against a possession's alternatives, and multiplied by a volume. Percentages invite the wrong intuitions; points do not.

Read it against the league, not against a threshold. The environment moves, so a raw figure quoted without a season is a figure quoted without a meaning. Look up the league average for the year in question and subtract.

Read it against usage, always. Efficiency at low volume and efficiency at high volume are different quantities that happen to share a scale. Any comparison that ignores the difference is comparing a specialist's best shots with a creator's worst ones.

Split the line into its three sources. Twos, threes and free throws produce very different amounts of the same total, and they are not equally repeatable. Compare the true shooting figure with the effective field goal percentage: a wide gap means the efficiency is built on contact and will move when the officiating does, a narrow one means it is built on the ball going in and will move when the shooting does.

Ask what the number could not see. Turnovers, shot difficulty, who created the shot, who the defence was guarding. None of it is in there, and all of it is in the game. A player with an excellent shooting line and a turnover problem is a worse offensive player than the line suggests, and the line will never say so.

Field goal percentage survives because it is simple and because it is printed on every screen in the building. It answers a question about makes in a sport that pays in points, and it has been the wrong tool since the day somebody drew a line on the floor and awarded three for shots taken behind it. True shooting is not a perfect instrument, and the 0.44 sitting inside it is an honest approximation of a quantity that is now countable exactly. It is still the closest thing basketball has to a straight answer about how much a player scored for what he was given, which is a better place to start any argument about scoring than a column of makes. Anyone who wants to see how the rest of the measurement layer around the professional game fits together will find the same pattern everywhere: a number built to answer one question, quietly used to answer another, until somebody derives it properly and finds out what it was really counting.