Two teams finish a season three places apart in the standings and eleven places apart in the scoring table. The one that scores more loses more, and every explanation offered involves defence, character or the schedule.
Usually it involves none of them. It involves the number of times each team had the ball. A team that plays fast will score more points than a team that plays slowly while being worse at scoring, and points per game cannot tell the difference because it has no denominator.
What follows is the correction, done with nothing more than a standard box score: how to estimate possessions, how to convert points into a rate, why one odd-looking coefficient appears in the formula, and how many games have to pass before any of it means anything.
The four numbers worth computing
- Possessions. Estimated as field goal attempts, plus 0.44 times free throw attempts, minus offensive rebounds, plus turnovers.
- Pace. Possessions per forty minutes, which is the length of a game under international rules.
- Offensive rating. Points scored per hundred possessions.
- Defensive rating. Points allowed per hundred possessions. The difference between the two is net rating.
- What replaces shooting percentage. Effective field goal percentage, which counts a three-point shot as worth one and a half of a two.
- The rough sample. Shooting rates settle slowly; turnover and rebounding rates settle much faster.
Why the scoring table and the standings disagree
Points per game answers a question nobody is really asking: how many points did this team score in a fixed amount of time. The question that matters is how many points it scored with the opportunities it had, and those two are only the same when every team has the same number of opportunities.
In leagues where tempo is uniform, the distinction is small enough to ignore. In leagues where it is not, the two rankings can look almost unrelated. A team that pushes after every rebound, takes early shots and forces turnovers can generate ten or fifteen more possessions per game than a team that walks the ball up and uses most of the shot clock.
Fifteen extra possessions at a mediocre conversion rate produce more points than five fewer possessions at an excellent one. The scoring table records the first team as better. The standings, eventually, record the second.
What points per game is actually measuring
Split the metric and it becomes two separate things multiplied together: how often a team has the ball, and how well it uses the ball when it does. Only the second is a description of quality; the first is a description of style.
That matters because style is easy to change and quality is not. A coach can raise his team’s pace in a fortnight by pushing after defensive rebounds and shooting earlier in the clock, and the scoring average rises without a single player becoming better.
Defensive numbers suffer the same distortion in the opposite direction. Points allowed per game rewards a slow team automatically, which is why teams that grind out low-scoring games acquire defensive reputations they may not have earned. Both errors disappear the moment the denominator is added.
Estimating possessions from a standard box score
A possession ends in one of four ways: a field goal attempt that is not offensively rebounded, a turnover, a trip to the free throw line that ends the possession, or the end of a period. Everything needed to estimate that is in an ordinary box score.
The standard estimate is field goal attempts, plus 0.44 times free throw attempts, minus offensive rebounds, plus turnovers. Each term corresponds to one of those endings: shots taken, trips to the line, shots that did not end the possession because the ball was recovered, and possessions given away without a shot.
Two practical notes. The estimate is a team-level figure and should be computed for both teams and averaged, because in a single game the two totals must be very close and small differences reveal recording errors. And team offensive rebounds credited to the team rather than to a player can inflate the subtraction, which is a known source of noise in amateur data.
Basketball pace and offensive rating, defined
With possessions in hand, basketball pace and offensive rating are straightforward. Pace is the number of possessions a team uses per forty minutes of play, which under international rules is a full game. Offensive rating is points scored per hundred possessions; defensive rating is points allowed per hundred.
The choice of a hundred is arbitrary and useful. A typical game sits somewhere in the seventies or eighties for possessions, so ratings land in a range that reads like a percentage and can be compared across leagues, eras and rule sets without adjustment.
Net rating, the difference between the two, is the single most useful summary number available from a box score. It is close to point differential per hundred possessions, it correlates with winning far better than points per game does, and it does not reward a team for playing fast or slow.
The 0.44 on free throw attempts
The coefficient looks like a fudge and is not. It exists because not every free throw attempt ends a possession, and the number is an estimate of the proportion that does.
A two-shot foul produces two attempts and ends one possession, which would suggest a coefficient of 0.5. Several situations pull it downward. A shooting foul on a made basket produces one attempt after the possession has already ended, technical and flagrant free throws do not end a possession at all, and an offensive rebound of a missed final free throw continues the possession.
The value settles slightly below 0.5 as a result, and 0.44 is the figure that became standard. Anyone computing this on a small dataset should know that the exact value varies with the rule set and with how often teams foul deliberately, but the difference between 0.44 and 0.475 changes a rating by a fraction of a point and never changes a ranking.
Effective and true shooting
Field goal percentage treats a two-point shot and a three-point shot as the same event, which has been wrong for decades. Two corrections fix it, and both are one line of arithmetic.
Effective field goal percentage adds half a made three to the numerator: made field goals plus half the made threes, divided by attempts. A team shooting forty per cent while taking half its shots from behind the arc is producing more points per attempt than a team shooting forty-five per cent entirely from inside it, and this is the number that says so.
True shooting percentage goes further by including free throws: points divided by twice the sum of field goal attempts and 0.44 times free throw attempts. It is the best single summary of a player’s or a team’s scoring efficiency, and it is the number to use when comparing a player who lives at the line with one who does not.
The four factors and their rough weights
Offensive rating can be decomposed into four independent components, which is the most useful diagnostic in the whole toolkit because it says where a rating came from rather than only what it is.
Shooting, measured by effective field goal percentage. Turnovers, measured as turnovers per possession. Offensive rebounding, measured as the share of available offensive rebounds collected. And free throws, measured as attempts or makes relative to field goal attempts.
The weights usually quoted in the analytics literature put shooting at roughly forty per cent of the explanation, turnovers at about a quarter, rebounding at a fifth and free throws at the remainder. The practical consequence is that a team trying to improve should look at its shot profile first and its offensive rebounding third, which is the opposite of how most amateur post-match discussions run. The same decomposition applies to the defence, using the opponent’s four factors.
Net rating, and what a schedule does to it
Net rating is close to a complete summary and it is not a pure one, because it is measured against whoever a team happened to play. A team that has faced the three weakest sides in the league has a net rating flattered by exactly that.
The correction is strength of schedule, and it can be approximated without any modelling: compute the average net rating of the opponents faced, and adjust. In a league with an unbalanced early schedule this changes the ordering of the table more than any other single adjustment.
Home advantage is the second correction and is usually larger in basketball than people expect, particularly in leagues with long travel between host cities. Splitting ratings into home and away before drawing conclusions is worth the extra column, and coverage of continental qualifying windows shows how sharply results diverge between the two.
A worked example with round numbers
Take two hypothetical teams with round figures, purely to see the arithmetic move.
Team A takes 80 field goal attempts, 20 free throw attempts, collects 12 offensive rebounds and commits 14 turnovers, scoring 88 points. Possessions are 80 plus 8.8 minus 12 plus 14, which is 90.8. Offensive rating is 88 divided by 90.8, times a hundred: about 96.9.
Team B takes 68 field goal attempts, 30 free throw attempts, collects 8 offensive rebounds and commits 10 turnovers, scoring 85 points. Possessions are 68 plus 13.2 minus 8 plus 10, which is 83.2. Offensive rating is about 102.2. Team A scored three more points and was the less efficient offence by more than five points per hundred possessions, and the scoring table would have ranked them the other way round. That is the entire argument in one paragraph of arithmetic, and it is why any serious analysis of the sport begins by dividing.
Sample size: when the numbers start meaning something
Each of these measures settles at a different rate, and treating them as equally reliable after four games is the fastest way to reach a confident wrong answer.
Turnover rate and offensive rebounding rate are relatively stable early, because they involve many events per game and depend heavily on style, which does not fluctuate. Effective field goal percentage is the slowest to settle, because three-point shooting is high-variance and a team can shoot well above or below its true level for a month.
The practical rule is to trust the components in the order they stabilise. Early in a season, a team’s turnover and rebounding profile is close to real; its shooting numbers are a mixture of ability and luck; and its net rating inherits the uncertainty of the least stable component inside it. Anyone quoting a rating after five rounds should quote the schedule alongside it, a point that applies just as much to broader work on performance data in other sports.
A metric reference
| Metric | Formula | What it answers |
|---|---|---|
| Possessions | FGA + 0.44 x FTA – ORB + TOV | How many chances a team had |
| Pace | Possessions per forty minutes | How fast the team plays |
| Offensive rating | Points / possessions x 100 | How well the chances were used |
| Defensive rating | Points allowed / possessions x 100 | How well chances were denied |
| Net rating | Offensive minus defensive rating | Overall quality, pace removed |
| Effective FG% | (FG + 0.5 x 3PM) / FGA | Shooting, with threes valued correctly |
| True shooting % | PTS / (2 x (FGA + 0.44 x FTA)) | Scoring efficiency including free throws |
Where the whole approach still fails
Rate statistics fix a denominator problem and inherit every other problem in the box score. Three are worth naming before anyone builds an argument on them.
Garbage time contaminates everything. Possessions played with a twenty-five-point margin count identically to possessions played in a tied fourth quarter, and in a league with lopsided fixtures this materially distorts season ratings. Filtering them out requires play-by-play data that most competitions do not publish.
Recording quality is the second. Turnovers, offensive rebounds and assists are the fields most affected by who is typing, and a league where different venues use different scorers has systematic differences that look like team characteristics. And the third is that none of this describes how a team plays: two sides can reach the same offensive rating through entirely opposite methods, and the number will not distinguish them. The record of individual careers, such as that of the country’s most decorated centre, is a reminder that rate statistics describe a role as much as a level.
Frequently Asked Questions
Why not simply use point differential?
Point differential is good and it still carries a pace effect. A fast team’s differential is stretched and a slow team’s is compressed, so two teams of equal quality playing at different tempos produce different differentials. Net rating removes that.
Where does the 0.44 come from?
It estimates the share of free throw attempts that actually end a possession. A two-shot foul suggests 0.5, but shooting fouls on made baskets, technical free throws and rebounded final misses pull the figure down, and just below 0.44 is where it settles in practice.
Is pace itself good or bad?
Neither. It is a style choice with tactical consequences. A fast team increases the number of possessions for both sides, which raises variance and generally helps the weaker team; a slow team reduces the number of chances an opponent gets to be better than it is.
How many games before a rating is meaningful?
It depends on the component. Turnover and rebounding rates are informative early; shooting percentages take much longer, and the rating built on them inherits that uncertainty. Reporting a rating without the schedule behind it is the most common early-season error.
Can these be computed from a public box score?
Yes. Field goal attempts, free throw attempts, offensive rebounds, turnovers and points are all standard fields, and everything above follows from them with a calculator. The only figures that need play-by-play data are the ones that filter for score margin.
The correction is one division and it changes the ranking of a league. What it does not change is the harder part: understanding why one team converts its chances better than another, which no rate statistic has ever answered on its own.
