Player efficiency rating explained: what PER measures

A reserve centre who plays fourteen minutes a night, catches lobs, blocks the occasional shot and collects whatever falls near him can finish a season with a higher player efficiency rating than the wing who chases the opposition's best scorer for thirty-six minutes. Nothing has malfunctioned. That result is the rating working exactly as built, and the way it was built is the entire subject.

Most accounts of player efficiency rating explained on a stats page run through the inputs, then list the criticisms afterwards as though the two arrived independently, the formula from one person and the flaws from somebody careless. They did not arrive separately. PER set out to compress every column of a box score into one per-minute number, and each of its famous weaknesses falls directly out of that ambition. Compression is lossy. The argument is only ever about what got lost.

So the useful thing is not a verdict on whether the number is good. It is knowing precisely which information survived the compression and which did not, because that tells you exactly which questions the rating can answer.

The question the rating is answering

How much did this player produce, per minute on the floor, out of the events a box score records, priced against everything else a box score records, relative to his own league in his own season?

Every clause there is doing work, and the last two carry more weight than people expect.

"Out of the events a box score records" is a hard boundary, not a soft one. Thirteen columns of one player's line go into the calculation and nothing else does. A rotation that was blown up, a rebound secured by a box-out that a teammate collected, a drive walled off before it started: none of these exist in the arithmetic, because none of them exist in the source.

"Priced against everything else a box score records" is the ambitious part. An assist and an offensive rebound and a blocked shot and a turnover are not naturally comparable quantities. To sum them you must first convert them into a shared currency, and PER's currency is points. Every event is converted into an estimate of the points it gained or cost, then everything is added.

"Per minute" is a choice with consequences that reach further than any other design decision in the formula. It makes a substitute and a starter directly comparable, which was the explicit intention, and it silently assumes that a player's rate of production would hold up if his minutes doubled, which is not true and cannot be true.

"Relative to his own league in his own season" is the reason the number is readable at all. The final step of the calculation rescales the whole league so that the average comes out at exactly 15.00, every year, forever. That constant is not a discovery about basketball. It is a stipulation, and a great deal follows from it.

Notice what the question never asks. It does not ask whether the team was better with this player on the floor. It does not ask whether the shots he took were shots worth taking. It does not ask what his presence did to the four teammates around him. Those are the questions the plus-minus family was invented to answer, and they are a different subject with different failure modes.

Player efficiency rating explained one box score event at a time

Before anything can be added up, each event needs a price. The prices are not arbitrary and they are not fixed constants either. Most of them are derived from two league-wide quantities that are recomputed every season.

The first is the value of a possession: the league's total points divided by the league's total possessions. Possessions are not recorded directly, so they are estimated from field goal attempts, offensive rebounds, turnovers and free throw attempts, with free throws counted at a fraction of an attempt because most trips to the line take two shots and only the last one ends the possession. Around forty-four hundredths of a free throw attempt is the conventional coefficient, and it is an estimate that everybody in basketball analytics has agreed to live with. That estimate is buried inside the possession count that offensive and defensive ratings also rest on, so an error in it propagates a long way.

The second is the league's defensive rebounding rate: what share of all rebounds are collected by the defending team. Defences win most of them, which is why this number matters so much to the pricing.

Now watch what those two quantities do to each event.

A missed field goal is not charged the full value of a possession. It is charged the value of a possession multiplied by the chance the defence actually recovers it. A miss that your own team rebounds cost nobody anything, so the formula charges only the expected loss. This is genuinely sound reasoning and it is also the single most consequential line in the whole construction, for reasons that get their own section below.

A turnover is charged the full value of a possession, with no discount, because a turnover always hands the ball over. A turnover is therefore priced meaningfully worse than a missed shot, which is correct and which makes the rating quite sensitive to ball security.

A steal is credited the full value of a possession, being the mirror image of a turnover.

A blocked shot is credited the possession value multiplied by the defensive rebounding rate, on the reasoning that a block only helps if somebody then collects the ball, and blocks are recovered by the shooting team often enough to matter.

An offensive rebound is credited at the defensive rebounding rate, and a defensive rebound at one minus that rate. Read that twice, because it is the cleverest idea in the formula and almost nobody notices it. Rebounds are not priced by how many you got. They are priced by how surprising they were. A defensive rebound is largely expected, so it earns a small credit; the possession was probably coming to your team anyway. An offensive rebound overturns the expected outcome, so it earns considerably more. Since defences collect the clear majority of misses, the offensive board is worth more than double the defensive one in every season the formula has ever been run.

A made field goal is credited roughly the points it scored, less a share handed to the passers. That deduction is set by the team's assist rate: what fraction of the team's baskets are assisted overall. An assist collects a flat credit in return, the same credit whatever kind of basket it created.

A made three-pointer enters twice, once as a made field goal and once again as a flat one-point bonus. The first two points are docked for the passer's share. The third point is not.

A made free throw is credited a little under a point, adjusted slightly by the same team assist rate.

A missed free throw is charged a smaller fraction than a missed field goal, since a missed first free throw costs nothing at all and only the final miss surrenders the ball.

A personal foul is charged the league's average cost of a foul: the free throws it typically hands over, net of the possession value involved.

1. 1Start with thirteen columns and one playerMinutes, field goals made and attempted, three-pointers made, free throws made and attempted, offensive and total rebounds, assists, steals, blocks, turnovers, fouls. Nothing else about the player enters the calculation at any later stage.
2. 2Fetch the season's league constantsThe value of a possession, from league points divided by estimated league possessions. The league defensive rebounding rate. A factor derived from league assist, field goal and free throw totals. These are recomputed every season and they set every price below.
3. 3Price the creditsMade field goals at roughly their points, less a share for the passers. A flat bonus on top for each three. Free throws just under a point each. Assists at a flat rate. Steals at a full possession, blocks and offensive rebounds at a discount, defensive rebounds at a steeper one.
4. 4Price the debitsMissed field goals at the possession value times the chance the defence recovers them. Turnovers at a full possession, since a turnover always hands the ball over. Missed free throws at a smaller fraction. Fouls at the league's average cost per foul.
5. 5Add it all up and divide by minutes playedThis is unadjusted PER, and it is a rate: production per minute in points-equivalent units. Everything to this point used the player's own line and nothing about his circumstances beyond his team's assist rate.
6. 6Multiply by league pace over team paceA player on a slow team gets fewer possessions per minute through no fault of his own, so his rate is scaled up. A player on a fast team is scaled down. The correction uses the team's pace for the season, not the pace of the lineups he actually played in.
7. 7Multiply by fifteen over the league averageThe final step rescales every player in the league so the minute-weighted average comes out at exactly 15.00. This is the step that makes seasons comparable and it is the step that quietly changes what the number means.
8. 8Read the ratingA single figure with two decimal places, sitting on a sortable table, describing offensive production per minute and almost nothing about the half of the game played without the ball.

The order of operations, as published. Every price and constant in this article's worked examples is invented and round; no league value, season constant or player rating is reported here.

One invented box score line, all the way through

Numbers make this concrete in a way prose cannot, so here is a complete worked example. Every figure in it is invented and deliberately round. No league constant is being reported and no real player's line is being used.

Invent a season in which a possession is worth exactly 1.00 point and defences collect exactly 0.70 of all rebounds. Those two invented figures set the prices: a made two-point basket is credited 1.6 after the passer's share is deducted, a made free throw 0.9, an assist 0.67, a steal 1.00, a block or an offensive rebound 0.70, a defensive rebound 0.30. A missed field goal is charged 0.70, a turnover 1.00, a missed free throw 0.40, a foul 0.30.

Now invent a line. Thirty minutes. Nine field goals made from twenty attempts, three of them three-pointers. Five free throws made from six. Four assists, six rebounds of which two were offensive, two steals, one block, three turnovers, three fouls.

The credits come to 14.4 from the made baskets, 3.0 from the three-point bonuses, 4.5 from the free throws, 2.7 from the assists, 1.4 from the offensive rebounds, 1.2 from the defensive ones, 2.0 from the steals and 0.7 from the block. That is 29.9.

The debits come to 7.7 from the eleven missed shots, 0.4 from the missed free throw, 3.0 from the turnovers and 0.9 from the fouls. That is 12.0.

Net production, 17.9 over thirty minutes, or 0.597 per minute. Suppose his team played 5 per cent slower than the league, so the pace adjustment multiplies him by 1.05 and gives 0.627. Suppose the league's minute-weighted average worked out at 0.40 per minute in this invented season, so the final scaling multiplies by 37.5. The rating is 23.5.

48%15%18%10%9%

• Made field goals14.4
• Made free throws4.5
• Rebounds, steals and blocks5.3
• Three-point bonus3
• Assists2.7

Every figure is invented and deliberately round, chosen so the arithmetic can be followed. These are not any real player's totals and no league constant is reported. The three-point bonus is the flat extra credit each made three receives on top of its value as a made field goal.

Show the numbers

Where an invented player's 29.9 credits come from, before any debits

Item	Value
Made field goals	14.4
Made free throws	4.5
Rebounds, steals and blocks	5.3
Three-point bonus	3
Assists	2.7

Look at the shape of that. Scoring, in its two forms, accounts for more than three quarters of the credit before a single debit is subtracted. Four assists, six rebounds, two steals and a block together contribute less than the made field goals alone. That is not a distortion introduced by bad weighting. It is the honest consequence of pricing everything in points and then noticing that scoring is the thing that produces points.

Any single-number rating built on a box score will look like this, because the box score is mostly a record of scoring with a few other columns attached.

• 13Individual box score columns the formula reads
• 3Team-level figures it also needs
• 3Scaling stages applied after the raw sum
• 3Columns that record a defensive action

Structural counts of the published formula rather than measurements. The thirteen individual columns are minutes, field goals made and attempted, three-pointers made, free throws made and attempted, offensive and total rebounds, assists, steals, blocks, turnovers and fouls. The three defensive columns are steals, blocks and defensive rebounds; personal fouls appear as a penalty rather than a defensive credit.

The pace adjustment repairs one problem and leaves a smaller one behind

A player on a team that runs gets more possessions per minute than a player on a team that walks it up. More possessions means more shots, more rebounds, more of everything, including the mistakes. Comparing two players' per-minute production without correcting for that would rank teams as much as players.

The correction is a single multiplication: league pace divided by team pace, where pace is possessions per forty-eight minutes. Play slower than the league and your production is scaled up. Play faster and it is scaled down. It applies to the whole rating rather than to individual terms, which is a simplification but a defensible one, since almost everything in the sum scales with opportunity.

Two things it does not do.

It uses the team's pace for the whole season, not the pace of the lineups the player was actually on the floor with. A bench unit that pushes the ball while the starters grind is a real and common pattern, and both groups receive the same adjustment. Modern lineup-level tempo, of the sort that comes with the spacing and speed of the contemporary game, makes this a bigger gap than it was when the formula was written.

And it corrects for opportunity without correcting for context. Playing quickly changes what a possession is worth as well as how many you get. Early offence produces better looks than a possession that grinds to eight seconds on the shot clock, so pace is not purely a volume knob. Dividing by it treats it as one.

Fixing the average at 15 is what makes eras comparable and teams misleading

Here is the design decision that people find most surprising once they see it clearly. The last operation in the calculation looks at every minute played in the league that season, takes the average pace-adjusted rating across all of them, and rescales everybody so that average lands on exactly 15.00.

Not approximately 15. Exactly 15, by construction, every season since the formula was created and every season it is ever run.

The gain is real and it is the reason the number caught on. Because the average is pinned, a rating carries a fixed meaning across seasons. Scoring levels rise and fall, the three-point line reshapes the shot chart, the rules on hand-checking change what a guard can do to a driver, and none of it moves the average, because the average is not allowed to move. A rating from a slow, physical era and one from a fast, spaced era both describe distance from a contemporary league. That is a genuinely useful property and very few statistics have it.

The cost arrives in three parts.

The scale cannot tell you the league got better or worse. If every player in the world improved by 10 per cent overnight, every rating would be identical the following season. The number is a ranking device wearing the clothes of a measurement.

The population defines the average. Fifteen is the average of the minutes actually played, which includes every end-of-rotation player who logs garbage time. Change the composition of who plays, through expansion, deeper rotations, more resting of starters, and the meaning of 15 shifts underneath a scale that looks fixed.

And the normalisation is league-wide while several of the inputs are team-specific. This is the part that gets missed. The credit a player receives for a made basket is docked by his team's assist rate, so the same made basket is worth less on a team that shares the ball and more on a team that does not. The pace adjustment uses his team's tempo. Two players who did precisely the same things in precisely the same minutes on two different teams do not receive the same rating.

So the normalisation makes cross-era comparison coherent and cross-team comparison quietly unreliable, which is close to the opposite of what most people assume when they put two ratings side by side. Comparing a guard from one decade with a guard from another is the comparison the design supports. Comparing two players in the same season on different teams is the one it complicates.

Why the formula pays for shots taken more than shots made

This is the most cited criticism and it is usually explained badly, as though somebody simply chose careless weights. The real mechanism is more interesting and less forgivable.

Go back to the pricing. A made two-point basket is credited roughly the points it produced. A miss is charged the value of a possession multiplied by the chance the defence recovers it. Both of those prices are individually reasonable. Put them together and something breaks.

Using the invented prices from earlier, a made two is worth 1.6 and a miss costs 0.7. The shooting percentage at which those cancel is 0.7 divided by 2.3, which is 30.4 per cent.

Above roughly thirty per cent from two, in this invented season, taking more shots raises the rating. That is the arithmetic, and the arithmetic does not care that shooting thirty-five per cent from two-point range is dreadful basketball.

Now ask what percentage actually helps a team. A possession in this invented season is worth 1.00 point. A two-point attempt therefore has to convert at 50 per cent to be worth as much as an average possession would have been. So the threshold at which a shot helps the rating sits about twenty percentage points below the threshold at which it helps the team.

Five of ten, 50 per cent4.5credits

Four of ten, 40 per cent2.2credits

Three of ten, 30 per cent-0.1credits

A constructed illustration using the invented prices from this article: 1.6 credit for a made two, 0.7 charge for a miss. At three of ten the credits and charges almost exactly cancel, which is where the formula's break-even sits. An average possession in the same invented season is worth 1.00 point, so ten possessions used are worth 10 points, and only the 50 per cent row comes close to matching that. No real shooting percentage or league constant is reported.

Show the numbers

Net credit from ten invented two-point attempts at three make rates

Item	Value
Five of ten, 50 per cent	4.5credits
Four of ten, 40 per cent	2.2credits
Three of ten, 30 per cent	-0.1credits

The root cause is a single omission. PER charges a player for possessions he lost and never charges him for possessions he used. A missed shot loses a possession, sometimes, and is billed accordingly. A made shot also consumes a possession, one that a teammate could have had, and that consumption is never billed at all. The formula has no concept of opportunity cost.

Everything downstream follows. High-usage scorers are flattered because volume is nearly free. Efficient low-volume players are underpaid because the formula has no term that says "did more with less". A specialist who takes four shots a game and makes three of them accumulates credits slowly and finishes near the average, while a teammate who takes twenty and makes eight finishes well above him.

The metrics that came afterwards fixed exactly this, and they fixed it by adding the term PER lacks. Shooting efficiency measured against the points a shot is worth prices makes and attempts on the same scale. The share of a team's possessions a player finishes makes volume explicit rather than leaving it hidden inside a rate. Read those two alongside a rating and the volume problem stops being invisible, which is the practical answer for anybody who has to use the number as it stands.

Rebounds, turnovers and the weights that are genuinely arguable

Some criticisms of the formula are aimed at the wrong terms. Worth separating the ones that hold from the ones that do not.

Rebounds are handled better than their reputation. Pricing by surprise rather than by count is the right idea, and it means a big man cannot inflate his rating by hoovering up uncontested defensive boards, because those are cheap. What the treatment cannot do is distinguish a rebound won in traffic from one that bounced to a player standing still, or credit the box-out that let a teammate collect it. That is a limit of the data, not of the weighting.

Turnovers are charged hard, and defensibly. A full possession, no discount. The knock-on effect is that the formula rewards not handling the ball. A player who never initiates, never passes into traffic and never makes a decision under pressure accumulates no turnovers and pays nothing, while the creator who runs the offence pays for every mistake and collects a flat, modest credit for every assist. The passer's ledger is asymmetric.

The flat assist credit is the weakest weight in the formula. Every assist earns the same, whether it created a corner three, a layup at the rim or a long two. Since the assisted shot's value varies enormously, and since the modern game is organised around producing the highest-value assisted shots, a fixed price for a pass is a real loss of information rather than a rounding error.

The assist deduction on made baskets is applied at team level. A player's own baskets are docked according to how much his team assists overall, not according to how many of his own baskets were assisted. A player who creates all his own offence on a team that shares the ball is docked for his teammates' habits. The published formula does not have the data to do better, since who assisted whom is play-by-play information rather than a box score column.

Drawing fouls is barely rewarded. Free throw attempts appear, so a player who gets to the line collects the credit for what he makes. The pressure a driver puts on a defence, the fouls he draws that go uncalled, and the way his gravity moves defenders are absent. Committing a foul is charged. Forcing one is not credited beyond the free throws that follow.

Blocks are priced sensibly and still oversold. Discounting a block by the chance it is recovered is correct. What no box score can record is whether the block came from good positioning or from a gamble that left the rim open on the four possessions it did not work.

Player efficiency rating explained by what the box score never recorded

Defence is where the compression loses the most, and the reason is worth stating precisely, because the usual framing gets it backwards.

The problem is not that the formula weights defence badly. The problem is that there is almost nothing there to weight.

Three columns in a box score record a defensive action: steals, blocks and defensive rebounds. Fouls appear as a penalty. That is the complete inventory. Now list some things a defender does over forty-eight minutes that produce no entry anywhere on that sheet. Contesting a jump shot so it misses. Closing out under control so the shooter drives into help instead of shooting. Fighting over a screen so the ball handler never turns the corner. Rotating early so the pass to the roller is never thrown. Taking a charge, which enters the record as the other man's turnover and foul. Communicating a switch. Standing in the right place so that a possession dies without any event occurring at all.

The best defensive possessions in basketball produce no statistics whatsoever. A shot clock expiring on a well-defended team is recorded as a turnover charged to whoever last held the ball. The five defenders who caused it receive nothing.

Which means the two individually attributable defensive events, steals and blocks, carry the entire load. Both are events, and events are what get recorded. Both also correlate imperfectly with good defence, and in the specific direction that causes trouble: the gambling defender who jumps passing lanes generates steals and surrenders layups when he misses, while the disciplined defender who never leaves his assignment generates nothing at all. The formula rewards the first and is silent about the second. That is exactly the failure the author himself identified, and it is not a fixable one within the box score.

This is the point that matters most about the whole metric. It is a data problem, not a modelling problem. No amount of cleverness with weights applied to steals, blocks and defensive rebounds can recover information about closeouts and rotations, because that information was never written down. Every box score metric of the same family shares the ceiling, and any of them that claims a defensive component is inferring it from offence-adjacent evidence.

What changed the situation was not better formulas but better data. Optical tracking records where all ten players stood every fraction of a second, which finally makes it possible to observe a contest, a deterred drive or a rotation that arrived on time. What tracking systems actually capture and how teams use it is a separate technology story, and the honest summary is that defensive measurement improved because the cameras arrived, not because anybody found a smarter way to divide by minutes. The same applies to understanding what a defensive scheme is asking of each player, which determines whether a given action was a mistake or the assignment.

The per-minute basis is a standing favour to the bench

Dividing by minutes was deliberate and the stated reason was sound: a substitute and a starter should be comparable, and comparing raw totals means comparing playing time. Nobody disputes the intention.

The trouble is that per-minute production is not constant across minutes. It falls as minutes rise, for at least four reasons that all point the same way.

Opponent quality. Deep bench minutes are played against other deep bench players. A starter's thirty-six minutes are mostly spent against the other team's best, and the last four minutes of a close game are the hardest four minutes in the sport.

Fatigue. A player asked for fourteen minutes empties the tank. A player asked for thirty-eight paces himself, because he has to.

Defensive attention. The best player in a lineup is game-planned against. A reserve is guarded by whoever is nearest. Production per minute is partly a function of how much of the opposition's attention you attract, and attention scales with minutes.

Foul rate. A big man who fouls at a high rate cannot play thirty minutes. His per-minute production is a rate achieved precisely because he was never asked to sustain it, and the rating treats that rate as though it would survive being tripled.

Garbage time compounds all four. Minutes played with the outcome decided are the easiest minutes available and they are pooled with every other minute in the calculation.

The result is a systematic tilt. Reserves with small samples and favourable circumstances appear higher on the leaderboard than they should, and starters carrying the hardest assignments appear lower. This is not a subtle statistical artefact; it is the single most reliable prediction you can make about how a rating leaderboard will differ from a coach's ranking of the same roster.

The defence of the per-minute basis is that the alternative is worse. Rank on totals and you rank on availability, which is a different question again. The correct response is not to pick one but to read the rate next to the minutes and never let the rate stand alone.

What the successors fixed, one part each

Nearly every metric that followed repaired a specific piece of this, and knowing which piece tells you which to reach for.

Box plus-minus keeps the box score inputs and changes where the weights come from. Instead of asserting a price for each event from first principles, it estimates the weights by regressing box score lines against long-run plus-minus data, so the coefficients are fitted to what actually correlates with winning rather than to a theory of what a possession is worth. It is also expressed per hundred possessions relative to a league-average player rather than per minute against a fixed constant, and it includes a team-strength adjustment, which is the closest thing in the box score family to acknowledging context. How the regression against plus-minus produces those weights is the natural next step for anybody who has understood the pricing problem above.

Win shares takes a different route to the same destination, allocating a team's actual wins among its players by estimating each one's offensive and defensive contribution. It is a totals statistic rather than a rate, so it answers the availability question that per-minute ratings refuse.

The plus-minus family abandons the box score entirely. Raw plus-minus asks what happened to the scoreboard while a player was on the floor, which captures everything, including all the defence nobody records, and also captures every teammate and opponent he happened to share the floor with. Adjusted plus-minus attempts to solve for individual contributions from thousands of lineup combinations. Regularised versions add a statistical brake so the estimates do not fly apart when two players are almost never separated, which is a real problem: if two starters play every minute together, no amount of data can fully distinguish them.

Hybrid metrics blend both, using box score information as a stabiliser for noisy plus-minus estimates. These are the best public single-number ratings available and they need years of play-by-play, lineup logs and often tracking data to compute.

Each of those is more accurate than PER on the questions PER is bad at. Each one also requires data PER does not, which turns out to be the thing worth understanding about the original.

The honest case for the old number

PER can be computed from a box score. That is the entire argument and it is stronger than it sounds.

Not a play-by-play log. Not a lineup file with substitution timestamps. Not optical tracking. Thirteen columns from one player's line, three team figures, and a handful of league totals from the same season. Every one of those has been recorded, by hand where necessary, in essentially every organised basketball competition that has kept records at all.

Consider what that permits. A season played decades before anyone logged possessions. A domestic league in a country with no tracking installation. A women's competition whose broadcast partner does not fund a camera system. A college tournament, a youth international event, a second division anywhere in the world. In every one of those places the box score exists and the modern metrics do not, and the choice is not between PER and something better but between PER and counting points.

There is a second property worth as much. The formula is published in full and it is deterministic. Anyone can implement it, check it, and get the same answer. It does not change when a vendor retrains a model, it has no proprietary inputs, and nobody has to be trusted. Several of the best modern ratings are excellent and none of them can be independently reproduced from public data. For a public record that people will argue about for thirty years, auditability has a value that accuracy does not automatically supply.

And within its own boundary it does a real job. As a summary of offensive box score production per minute, corrected for tempo and pinned to a stable scale, it is a reasonable instrument. Most of the abuse it takes comes from being asked questions about defence, context and impact that it was never constructed to answer, by people who read one number and assumed it contained everything because it was presented as though it did. Compressing a season into a single figure that sits in a sortable column of basketball's statistical record is an invitation to exactly that misreading, and the invitation is issued by the format rather than by the formula.

When to reach for it, and when to put it down

Reach for it as a sieve. Sorting a hundred and fifty rotation players into a shortlist worth examining properly is a job it does well and quickly, and no argument about its precision affects that use at all.

Reach for it when the box score is all there is. Historical seasons, leagues without tracking, competitions outside the well-funded top tier. Here it is not a compromise, it is the only tool that exists.

Reach for it to compare seasons within one league. The fixed average is a real advantage and the comparison it supports is a genuine one.

Put it down for defence. Three columns and a penalty is not a defensive evaluation, and no reading of the number can make it into one.

Put it down when two players are within a point or so of each other. The difference is smaller than the uncertainty in the inputs, smaller than the effect of the team assist rate on both, and smaller than the gap between per-minute production and what either would do at the other's minutes load.

Put it down when comparing players across teams that play very differently, because the team assist rate and the pace figure are inside the calculation and they are properties of the team.

Put it down for low-minute players. A rate from a small, favourable sample sits on the same table as a rate from three thousand hard minutes, with nothing to indicate the difference.

Five things to check next to any rating before quoting it. Minutes per game, because the rate assumes a durability it never tested. Usage rate, because volume is nearly free inside the formula. True shooting percentage, because efficiency is the term the arithmetic underprices. The team's assist rate, because it sets the exchange rate on that player's own baskets. And one plus-minus derived metric, because the disagreement between the two is where all the defence you cannot see has gone.

The criticism that PER is a crude number is true and mostly beside the point. It was an attempt to answer an impossible question with the only data anybody had, and the surprise is not that the compression lost the defence, the context and the opportunity cost. The surprise is how much survived.