Offensive rating and defensive rating in the NBA, explained

A team can finish third in the league for points scored and eleventh for offence in the same season, and both statements can be exactly right. Nothing has been miscounted. Points per game answers a question nobody meant to ask, which is how much scoring happened while this team was on the floor, and offensive rating answers the one they did mean, which is how well the team played each time it had the ball. Everything that separates the two comes from a single substitution in the denominator: divide by possessions instead of by games.

That substitution is the whole idea behind offensive rating and defensive rating in the NBA. It looks like a technicality. It is not. Changing the denominator changes what the number is about, and it fixes a distortion that sits inside points per game so quietly that most people never notice it is there.

Points per game measures how fast the clock is spent, not how well

A basketball game is 48 minutes long, and that is the only fixed quantity in it. The number of times a team gets the ball inside those 48 minutes is not fixed at all. It depends on how quickly both teams shoot, how many turnovers happen, how many misses are rebounded by the offence and thrown straight back up, and how often the game is stopped for free throws. Two teams can play the same 48 minutes and have wildly different amounts of basketball happen in them.

Points per game divides by the constant and ignores the variable. That is the defect.

Two entirely separate mechanisms push a team's points per game upward, and only one of them has anything to do with being good at basketball. The first is playing quickly on purpose: shooting early in the clock, running after every defensive rebound, taking the first advantage the defence offers. The second is having a bad defence. If the opposition scores easily and quickly, your team gets the ball back sooner and more often, which raises your scoring total. A leaky defence inflates your offence in the scoring table. There is no version of that which makes sense as a measure of quality.

The mirror image is worse. Points allowed per game, still quoted every night, is close to useless as a description of a defence, because the simplest way to allow few points is to play slowly. Hold the ball for twenty seconds on every trip, take the last shot of each quarter, never gamble for a steal, and the opposition's total falls without a single stop being made any better. A patient offence flatters its own defensive numbers.

So the two most commonly quoted team statistics in the sport are both partly measuring tempo. They are not wrong about anything, they are answering a question about pace while being read as an answer about quality. Once you see that, the correction is obvious. Stop dividing by games.

The possession is the unit, and both teams get almost exactly the same number

A possession starts when a team gains control of the ball and ends when it gives that control up. There are four ways to give it up: score a field goal, make the last free throw of a trip, turn the ball over, or miss a shot that the other team rebounds. Miss a shot that your own team rebounds and nothing has ended. You have the ball, you had the ball, and the possession continues.

That definition has one property which makes the entire statistical apparatus of modern basketball possible, and it is worth stating plainly because it is almost never said out loud.

Possessions alternate. Every possession that ends puts the ball in the other team's hands.

Which means that over a full game the two teams have used, to within a possession or so, the same number of them. The only sources of difference are the beginnings and ends of periods: whoever has the ball when a quarter expires, whoever gets the ball to start the next one, and the odd half-court heave at the buzzer. That is a tiny discrepancy, and it is a structural feature of the sport rather than a matter of skill or effort.

The consequence is enormous. It means dividing by possessions gives you a genuinely fair comparison, because the two teams in any game were handed the same number of opportunities. Not roughly the same. Almost exactly the same, guaranteed by the way the game alternates. Neither team can hoard chances. Neither can be denied them.

Very few sports offer this. Football teams can hold the ball for two thirds of a match. A cricket team's innings can end in an over or last two days. American football gives each side a different number of drives depending on how the possessions ended. Basketball hands both sides an identical count without anybody arranging it, which is why per-possession analysis arrived in basketball earlier and stuck harder than in almost any other team sport.

One distinction is worth getting right, because it causes a lot of confusion. A possession is not the same thing as a play or a chance. If a team misses, rebounds its own miss, misses again, rebounds again and finally scores, that is one possession and three chances. Some statistics divide by chances rather than possessions and produce different numbers on purpose. Per-possession efficiency treats the offensive rebound as what it is, a way of getting more out of the same opportunity, and rewards it. Per-chance efficiency treats the second shot as a fresh attempt and does not. Both are defensible. They answer different questions, and mixing them up is the most common way to get an efficiency argument wrong.

Possessions are not written down, so they have to be estimated

Here is the awkward part. The box score does not have a column for possessions. It never has. What it has is the wreckage each possession left behind, and the count has to be reconstructed from that.

The reconstruction follows straight from the definition. Count the events that end a possession, then take back the ones that did not.

Field goal attempts are the bulk of it. Most possessions end with a shot, made or missed.

Turnovers end a possession every time, with no ambiguity.

Trips to the free throw line end possessions too, but attempts are not trips, and this is where the estimate stops being exact. A two-shot foul is two attempts and one possession. A three-shot foul on a missed three is three attempts and one possession. An and-one is one attempt and no possession at all, because the made basket already ended it. A technical free throw belongs to no possession whatsoever. And a missed final free throw that the shooting team rebounds ends nothing. Every one of those cases pulls the average number of possessions per free throw attempt below one half, which is why the conventional coefficient sits a little under half a possession per attempt rather than at exactly 0.5. It is an average across a league's worth of trips, and it is applied to every team including the ones whose foul-drawing habits do not match the average.

Offensive rebounds are then subtracted, because each one means a shot that looked like the end of a possession was not. The more careful estimators do not subtract the raw count. They scale it, using the team's share of available rebounds and a coefficient slightly above one, because a rebounded miss and a possession are not quite in one-to-one correspondence.

Then most published versions average the two teams' figures for the game. That is not laziness. Since the true counts are nearly identical, any gap between the two estimates is mostly error, and averaging cancels half of it.

The estimate is good. It is not exact, and the imprecision has a specific shape: it is largest for teams whose free throw patterns or offensive rebounding are unusual, which is to say precisely the interesting teams. Every rating built on top of it inherits the error, because possessions are the denominator of all of them. The same estimate sits underneath the pace adjustment inside player efficiency rating, and underneath every per-100 statistic on every reference site. One approximation, made once, propagates through the entire field.

1. 1Start with the two box score linesPoints, field goal attempts, free throw attempts, offensive rebounds and turnovers for each team. Nothing else is needed, which is why this works on any box score from any competition in any decade.
2. 2Count the events that end a possessionField goal attempts plus turnovers. These are the unambiguous cases: a shot ends the trip unless your own team rebounds it, and a turnover ends it always.
3. 3Convert free throw attempts into tripsMultiply attempts by a coefficient a little under a half, because a trip can be one, two or three shots, an and-one ends no possession at all, and a technical belongs to no possession.
4. 4Take back the offensive reboundsSubtract them, because each one means a shot that looked like the end of a possession was not. The careful estimators scale the count by the team's rebounding share rather than subtracting it raw.
5. 5Average the two teams' estimatesThe true counts are nearly identical, so the gap between the two estimates is mostly error, and averaging removes a good part of it. One possession figure now stands for the whole game.
6. 6Divide points by possessions, multiply by a hundredEach team's points over the shared possession count gives its offensive rating. Each team's offensive rating is the other team's defensive rating, by definition. The pair is one number seen from two ends.
7. 7Subtract to get net ratingOffensive rating minus defensive rating is point differential per 100 possessions, which is the single best one-line summary of how a team has played.
8. 8Compare each rating to the season's league averageRatings drift across eras, so a raw figure means nothing on its own. The distance from that season's average is the part that carries information across time.

The order of operations. Every number in this article's worked examples is invented and deliberately round; no season value, league average or team figure is reported here.

A worked example, all the way from the box score

Invent a game. Every figure below is made up and round, chosen so the arithmetic can be followed with a calculator and nothing else.

The home team scores 112 points on 88 field goal attempts and 24 free throw attempts, with 12 offensive rebounds and 14 turnovers. Its possession estimate is 88 plus 14, plus 24 multiplied by 0.44 which is 10.56, minus 12. That comes to 100.56.

The away team scores 106 points on 86 field goal attempts and 26 free throw attempts, with 11 offensive rebounds and 15 turnovers. Its estimate is 86 plus 15, plus 11.44 from the line, minus 11, which comes to 101.44.

The two estimates differ by 0.88 of a possession, which is what you should expect, since the real counts cannot differ by much and the gap is mostly noise in the free throw coefficient. Average them and the game contained 101 possessions.

Now the ratings. The home team's 112 points over 101 possessions is 110.9 per 100. The away team's 106 over the same 101 is 105.0 per 100. So the home team's offensive rating is 110.9 and its defensive rating is 105.0, because its defensive rating is nothing more than the opponent's offensive rating written from the other side. Net rating is plus 5.9.

Notice that the home side won by six points and its net rating is 5.9. In a game that happens to contain almost exactly 100 possessions, net rating and margin of victory are nearly the same number. That coincidence is why the scale feels intuitive to people who have never used it. In a game with 90 possessions or 110, the two come apart, and the rating is the one that transfers.

71%11%10%

• Field goal attempts88
• Turnovers14
• Offensive rebounds, subtracted12
• Free throw trips, at 0.44 each10.56

An invented box score line, built so the arithmetic is legible: 88 field goal attempts, 14 turnovers, 24 free throw attempts counted at 0.44 of a possession each, and 12 offensive rebounds. The offensive rebound term is subtracted rather than added, since a rebounded miss means the possession never ended; it is shown here at its magnitude so the four contributions can be compared. No real team's figures are reported.

Show the numbers

The four terms in the invented home team's possession estimate

Item	Value
Field goal attempts	88
Turnovers	14
Offensive rebounds, subtracted	12
Free throw trips, at 0.44 each	10.56

The shape of that is worth a moment. Field goal attempts dominate the estimate, which is reassuring, because they are the term recorded exactly. The two terms carrying real uncertainty, the free throw conversion and the offensive rebound adjustment, are small and they partly cancel. That is the reason a formula this crude produces a denominator good enough to build a whole analytic tradition on.

Pace is a description of a team, not a compliment

Once possessions are estimated, pace comes free. Pace is possessions per 48 minutes, which in a game without overtime is just the possession count itself. College basketball uses 40 minutes and the same idea.

Pace is the statistic that points per game was accidentally measuring. Separating it out and reporting it on its own is a large part of what per-possession analysis achieved, because it turned a confound into a fact about the team.

And having separated it, the honest thing to say is that pace does not tell you whether a team is any good. There is no reliable relationship between tempo and quality in either direction. Teams have won championships playing quickly and playing slowly. A fast team is a team that has decided, or been forced, to fit more basketball into 48 minutes, and the decision says nothing about how well those extra possessions are played.

Pace is also not entirely a choice, which people forget. A team that forces turnovers and rebounds defensively gets the ball in space and can run, so its pace rises through its defence. A team that concedes quick baskets also plays fast, because the ball keeps coming back into play. A team that misses a lot of shots which the other side rebounds and pushes is playing fast without ever having chosen to. Tempo is an outcome as much as an intention, which is exactly why it deserves its own column rather than sitting hidden inside a scoring average.

What pace does change is the variance of a result. More possessions means more independent trials, and more trials means the better team wins more often. A slow game is a smaller sample, and a smaller sample is friendlier to the worse team. That is the real strategic content of tempo, and it explains why a weaker side shortening a game is not being defensive out of timidity but is playing the odds correctly. It also explains why games tend to slow when the stakes rise and the defences tighten. The relationship between tempo, spacing and shot quality in the modern game is a subject of its own, and what pace and space actually changed about NBA offence covers the tactical half of it.

The point to hold on to is that pace belongs next to the ratings, not inside them. It tells you what kind of game a team plays. The ratings tell you how well it plays it.

Net rating is a better description of a team than its record

Net rating is offensive rating minus defensive rating, which makes it point differential per 100 possessions. Over a short stretch of games it describes a team better than that team's own win-loss record does, and the reason is not statistical sophistication. It is information.

A record throws almost everything away. Every game is compressed into one bit, won or lost, and a one-point win and a thirty-point win are stored identically. Point differential keeps the margin. Per-possession differential keeps the margin and removes the tempo. A team that wins six games by two points and loses two by twenty-five has a fine record and has been playing badly, and the record is the only one of those numbers that will not tell you.

The mechanism underneath is that close games are close to coin flips. Results decided in the final possession turn on a shot going in or rimming out, and no team sustains an unusual hit rate on them. Blowouts are much stickier, because a large margin is the accumulated product of a hundred possessions rather than the outcome of one. So a record built on close wins is fragile in a way a record built on comfortable ones is not, and net rating sees the difference immediately while the standings do not.

None of which makes net rating a verdict. It has three specific blind spots, and they all point the same way.

It does not know who was available. A team's rating includes every possession played by every lineup, including the weeks when the best player was injured, and the resulting number describes a team that may no longer exist.

It does not know the schedule. Playing a run of the league's worst teams raises both ratings in a way that has nothing to do with improvement, which is why schedule-adjusted versions exist and are worth preferring where they are published.

And it is inflated at both ends by blowouts, which brings us to the least glamorous problem in the whole subject.

• Offensive rating
• Defensive rating

Team Quick111.3per 100109.4per 100

Team Even116per 100110per 100

Team Slow110.6per 100105.3per 100

A constructed illustration. Team Quick scores 118 and allows 116 in an invented 106-possession game; Team Even scores 116 and allows 110 in 100 possessions; Team Slow scores 104 and allows 99 in 94 possessions. Ranked by points per game the order is Quick, Even, Slow. Ranked by net rating it is Even at plus 6.0, Slow at plus 5.3, Quick at plus 1.9. Every figure here is invented and no real team's numbers are reported.

Show the numbers

Three invented teams whose scoring order reverses when you divide by possessions

Item	Offensive rating	Defensive rating
Team Quick	111.3per 100	109.4per 100
Team Even	116per 100	110per 100
Team Slow	110.6per 100	105.3per 100

Team Quick scores fourteen more points a night than Team Slow in that invented example and is comfortably the worse team. The scoring gap is almost entirely the twelve extra possessions. Divide by them and the two offences are within a point of each other, while the defences are four points apart, and the whole apparent difference between the sides reverses.

That is the substitution doing its work, and it is the reason the pair of ratings is the first thing to look at rather than the last.

The individual versions, and the thing nobody likes saying about defensive rating

Team ratings are simple and trustworthy. The individual versions are neither, and they fail in interestingly different ways.

Individual offensive rating asks how many points a player produced per 100 possessions he personally used. Both halves of that need unpacking.

"Points produced" is not points scored. A player who scores a basket does not receive full credit for it if he was set up, because the pass created part of the value. A player who assists receives a share of the basket he created. A player who takes an offensive rebound receives credit for the possession he salvaged. The published construction splits the value of every scoring possession among the people who contributed to it, using team-level assist rates to decide the split because the box score does not record who assisted whom. So the credit is apportioned by a rule rather than observed.

"Possessions he personally used" is the denominator, and it counts the possessions that ended in his hands: shots that were not rebounded by his own team, turnovers, and trips to the line. A closely related figure, floor percentage, asks a different and sometimes more useful question: of the possessions this player finished, on what share did his team actually score? That is a hit rate rather than a points rate, and the two can disagree, because a player who scores rarely but produces three points when he does is not the same as one who scores often for two.

The important habit with individual offensive rating is never to read it without the volume next to it. A rating and the share of his team's possessions a player finishes have to be read as a pair, because efficiency is easy at low volume and hard at high volume, and a rating alone cannot distinguish the specialist who takes four open shots from the man asked to create twenty-five times against a set defence. The relationship between those two quantities is the central trade-off in offensive evaluation, and the shooting measure that prices twos, threes and free throws on one scale is the third number that makes the picture legible.

Now the individual defensive rating, and the honest problem.

The idea is a "stop", an estimate of how many defensive possessions the player personally ended. Steals and blocks are obvious ingredients. Defensive rebounds count, discounted because most of them were coming to the defence anyway. Forced misses count, but the box score does not record who forced them, so the construction estimates a player's share of his team's forced misses from the minutes he played and the events he did generate. Then the free throws he conceded through fouls are folded in.

Then comes the step that matters. The published individual formula does not simply report the player's own stop rate. It anchors the player to his team's defensive rating and lets his personal contribution move him only a fraction of the way from it. The published weighting puts most of the number on the team and a minority of it on the player.

Read that again, because it is the single most useful fact anyone can carry about this statistic. Most of what appears next to a player's name in a defensive rating column is his teammates' work.

The consequences are exactly what you would predict. Every rotation player on a strong defence looks like a good defender. A genuinely excellent defender stuck on a poor defence cannot post a good number, because the team term will not let him. Sort a league by individual defensive rating and you have mostly produced a list of the best defensive teams with their rotations attached, which you could have got from the team table in a quarter of the time.

This is not a flaw somebody failed to notice. It is a deliberate admission. The formula was built by people who understood perfectly well that a box score contains three defensive columns and that individual defensive credit cannot be extracted from them, and the team anchor is an honest way of saying so: in the absence of evidence about this player, assume he defended like his team. The dishonesty comes later, from anyone who puts the resulting column on a leaderboard and treats it as a ranking of defenders.

The gap only started closing when the data changed rather than the formula. What optical tracking systems actually record is the reason defensive measurement improved at all, because a contest, a rotation that arrived on time and a drive that was deterred before it began are all observable now and were not before.

So the pair is asymmetric in a way that deserves stating in one line. At team level, defensive rating is one of the most reliable numbers in basketball, because it is simply the opponent's scoring per possession and nothing is being inferred. At individual level, it is one of the least reliable, because almost everything is.

• 4Ways a possession can end
• 4Terms in the box score possession estimate
• 5Box score columns needed for a team rating
• 0.9Possession gap between the two teams in the invented game above

Structural counts of the published method rather than measurements, plus one figure from this article's invented worked example. The four possession-ending events are a made field goal, a made final free throw, a turnover and a miss rebounded by the defence. The four estimate terms are field goal attempts, turnovers, free throw attempts at a fraction, and offensive rebounds subtracted.

On-off splits look like the answer and are mostly noise

The obvious next move, once you have team ratings, is to compute them twice: once for the possessions a player was on the floor and once for the possessions he was not, then subtract. That difference is the on-off split, and it is the most over-interpreted number in public basketball analysis.

The appeal is genuine. It contains everything, including all the defence nobody records, because it does not ask what a player did. It asks what happened.

The trap is arithmetic. An on-off split is a difference between two estimates, and the uncertainty in a difference is larger than the uncertainty in either half. Worse, the two halves are not the same size. A star plays most of the minutes, so his on-court sample is large and his off-court sample is small, and the small one dominates the error. A month of on-off numbers for a heavy-minutes player is built on a bench sample that would embarrass anyone who wrote it down.

The second trap is that off-court minutes are not a random sample of anything. They are the minutes a coach chose to rest him, which means they are disproportionately played against the opponent's reserves, disproportionately at the start of second and fourth quarters, and disproportionately alongside a particular set of teammates. Whatever the split measures, it is not the player alone.

The third trap is the one that cannot be fixed by patience. If two players share the floor for nearly every minute they play, no quantity of data can separate them, because the evidence never varies. Their splits will be nearly identical no matter how different they are, and the statistic is not being noisy, it is being asked a question the season did not answer.

This is why the metrics that take the plus-minus idea seriously do not use raw splits. They solve for individual contributions across thousands of lineup combinations at once, and they apply a statistical brake so that estimates about players with little independent evidence get pulled toward the average rather than flying off. The box score metric that fits its weights against long-run plus-minus data is the hybrid answer: use the box score, which is stable, and let plus-minus decide what each column is worth.

For everyday reading, one rule covers most of it. An on-off split over a full season is a hint worth following up. An on-off split over ten games is a sentence somebody wrote to win an argument.

Garbage time is folded into everything and nobody agrees where it starts

Ratings count every possession. That includes the ones played with four minutes left and the result settled, by deep reserves against deep reserves, at an intensity that has nothing in common with the rest of the game.

The effect is systematic rather than random, and it runs in one direction. A team that is far ahead stops attacking, plays out possessions, and takes its best players off. A team that is far behind faces a soft defence and scores more easily than it did all night. So garbage time compresses ratings toward the middle: the good team's net rating is understated, the bad team's is overstated, and the more lopsided the season the more of this there is.

For team ratings the distortion is real and modest. For individual ratings it can be total. A twelfth man whose entire season is played in settled games has a sample composed of nothing else, and his per-possession numbers describe a version of basketball that stops being played whenever the result is in doubt. The same problem sits underneath every per-minute rate statistic, which is one reason a rating and the minutes it was accumulated in should never be separated.

The tidy solution would be to exclude those possessions. Several publishers do, and this is the reason two reputable sites can publish different net ratings for the same team without either being wrong. There is no agreed definition of garbage time. Any rule has to pick a score margin, a time remaining, and usually something about which players are on the floor, and every threshold is a judgement. A twenty-point lead with six minutes left is over in one game and not in another.

So the practical advice is unglamorous. Check whether the rating you are reading is filtered, and when comparing two figures make sure they came from the same source. Most public disagreements about a team's efficiency turn out to be disagreements about definitions rather than about basketball.

A rating means nothing until you know the season it came from

League-average efficiency is not a constant. It has moved substantially over the history of the league, and it moves inside a decade, not just across eras. Rule changes on hand-checking and contact on the perimeter, the defensive three-second rule, the way freedom of movement is officiated, changes in how shooting fouls are called, and above all the reorganisation of shot selection around the three-point line have all shifted how many points a possession is worth.

Which means a defensive rating that would have been elite in one season can be mediocre in another, with the same number printed on it. Comparing raw ratings across seasons is a category error, and it is committed constantly, usually by people arguing about which defence was the best of all time.

The fix is straightforward and it is what serious work uses: express each rating relative to the league average of its own season. Subtract the average from the team's figure and you get a relative rating, positive for offences above the league and negative for defences below it. Note the sign convention, since it catches everybody at least once. For defensive rating, lower is better, so a negative relative figure is the good one.

Relative ratings transfer across time. Raw ones do not. This is the same trick, applied at team level, that fixes an average in place inside a player rating so that seasons can be compared, and it has the same virtue and the same limitation: it tells you a team's distance from its contemporaries and it can never tell you that the whole league got better.

The current season's league averages, and the ratings themselves, are published by the league and by the reference sites throughout the year, which is where any figure you intend to quote should come from. Nothing about the method requires you to memorise them, and the method is the part that stays true.

How to read a team properly from the two numbers

Start with both, never one. A net rating on its own hides which half of the team produced it, and the two halves behave very differently under pressure. A team carried by its offence and a team carried by its defence can share a net rating and be entirely different propositions in a seven-game series, because half-court defence tightens when the stakes rise and the scoring team loses more of what it had than the defensive team does.

Compare each figure to that season's league average rather than to each other. A defensive rating of a given value is meaningless without the baseline, and the baseline moves.

Then go one level down, because ratings say how much and not why. Underneath both numbers sit the same four factors: shooting efficiency, turnovers, offensive rebounding and getting to the free throw line, in roughly that order of importance. Shooting dominates. If an offensive rating has fallen, the first place to look is the way shooting efficiency is priced across the three shot types, and only then the other three factors. Two teams with identical ratings can be built completely differently, and the four factors are where the difference shows up.

Check the sample and check the roster. A rating over ten games is a rumour, a rating over a season with a two-month injury inside it is an average of two different teams, and a rating that has not been schedule-adjusted has flattered or punished whoever the fixture list handed over.

Check the splits that matter. Home and away. With the starting group on the floor and without. Against teams with winning records, which is a crude filter and still catches most of what a full adjustment would catch.

And keep the individual and team versions in separate compartments. The team pair is close to the best evidence available about how good a team is. The individual offensive rating is useful with usage sitting next to it. The individual defensive rating is mostly the team's, and treating it as a player's is the commonest mistake made with these numbers, made daily, usually by people who would never dream of quoting points per game as a measure of an offence. The wider statistical record of the sport is full of both kinds of mistake, and the column in a table rarely tells you which one you are looking at, which is the recurring theme of how basketball measures itself.

Four things to look at before saying a team is good. Its offensive rating against this season's league average. Its defensive rating against the same. The gap between them, which is the summary. And the number of possessions those figures were accumulated over, because everything above this line is an estimate, and an estimate from a small sample is a guess wearing a decimal point.

Then look at the pace, last, and remember that it is telling you what kind of game the team wants and nothing whatsoever about whether it deserves to win it.