Effective field goal percentage: what a three is really worth

Two players finish a game shooting the same percentage from the field and one of them scored a third more points. Nothing has gone wrong with the arithmetic. Field goal percentage is being asked to compare shots that the rulebook prices differently, and it refuses.

Effective field goal percentage is the repair, and it is a single substitution rather than a new idea. It counts a made three-pointer as one and a half made shots, because the scoring rules pay one and a half times as much for one. Everything else in this piece follows from that sentence: where the formula comes from, why it is the first of the four factors that decide basketball games, what it is genuinely the best tool for, and the four things it cannot see at all.

The one substitution the formula makes

Take the scoring values first, since they are the only external fact the whole construction depends on. FIBA's rules state them plainly: a goal from the two-point area counts two points, a goal from the three-point area counts three, and a free throw counts one.

Three divided by two is one and a half. That ratio is fixed by the rulebook, it is identical in every competition that uses an arc, and no season's data can move it.

Now build the statistic. What you want is a measure of how productive a player or a team was per shot taken from the floor. Points from the floor are straightforward to count: every made field goal produced two points, and every made three produced one more on top of that. Written out, points from the floor equal two times made field goals plus made threes.

Divide that by field goal attempts and you have points per shot. Divide by two as well and you have a figure on the same scale as a field goal percentage, because a player who makes half his two-point attempts and nothing else lands on exactly 0.50 either way.

Do the algebra and the twos cancel:

eFG% = (FGM + 0.5 × 3PM) ÷ FGA

That is the published formula, and the 0.5 in it is not a weighting anybody chose. It is what survives when you insist on the familiar scale. The cleanest way to hold it in your head is not as a half-point bonus but as a change in what counts as a make: a made three is one and a half makes. A player who goes four for ten with two threes has made five shots as far as this statistic is concerned, so his effective field goal percentage is 50.

There is a second form of the same identity that is more useful in practice and almost never written down:

eFG% = FG% + 0.5 × (3PM ÷ FGA)

Effective field goal percentage is ordinary field goal percentage plus a bonus, and the bonus is half the rate at which a player converts threes as a share of his total shots. That decomposition is worth having, because it separates the two things a shooter can do to raise the number. He can make a larger share of the shots he takes, or he can convert more threes per shot attempted. Those are different skills with different reliability, and a single figure hides which one is doing the work.

Points per shot, wearing a percentage's clothes

The scaling is the part that causes confusion, so it deserves stating directly. Multiply an effective field goal percentage by two and you get points per field goal attempt.

An eFG% of 50 is one point per shot. An eFG% of 55 is 1.10 points per shot. An eFG% of 60 is 1.20.

Once that conversion is automatic, the number stops being an abstraction and becomes a currency you can spend. Every shot type on the floor has an eFG% of its own, which is simply its expected points per attempt halved, and that is precisely why shot charts are shaded in this statistic rather than in raw field goal percentage. A shot chart coloured by field goal percentage tells you where shots go in. A shot chart coloured by effective field goal percentage tells you where points come from, and those are different maps of the same floor.

It also explains something that trips people up the first time they see it. The number can exceed 100. A player who takes one three and makes it has produced one and a half makes from one attempt, so his effective field goal percentage is 150. Nothing is broken. He produced three points from a shot the scale prices at two, and the statistic is reporting that faithfully. Over a season the extremes get diluted and the figure settles into a range that looks like a share of a whole, which is exactly why people forget it never was one.

The word percentage in the name is a convenience rather than a description, and the safest habit is to read every effective field goal figure back into points per shot before reasoning with it. Deciding whether 1.06 points per attempt is good is a question about basketball. Deciding whether 53 per cent is good is a question about a scale.

A good shot is not one above 50, it is one above the alternative

Treating the figure as a currency invites a fixed threshold, and there is not one. No absolute number separates a good shot from a bad one, because a shot is never judged against zero. It is judged against whatever the possession would have produced instead.

That comparison is what makes shot selection a real decision rather than a lookup. A pull-up two worth 0.94 points per attempt, an effective field goal percentage of 47, is a poor shot for a team whose offence generates 1.12 points per attempt when it runs properly. The same shot is a perfectly sensible one for a team whose alternative is a contested fadeaway at 0.88. The shot has not changed. The replacement has.

The clock supplies the other half of the comparison, and it is the half that gets forgotten when raw shooting numbers are used to judge a player. With two seconds left on the shot clock, the alternative to any shot is a violation, and the value of a violation is nothing at all. Every offence therefore takes a stream of attempts it knows are poor, deliberately, because a poor shot beats no shot. Those attempts sit in the denominator alongside everything else and drag the season figure down, and they drag it down hardest for the player the offence turns to when the first two options have failed.

So a low effective field goal percentage can mean a player shoots badly, or it can mean he is the one holding the ball when the clock runs out. Nothing inside the statistic separates those, and the difference between them is the difference between a problem and a job. This is the clearest case for reading the number against the situations that produced it rather than as a verdict, and it is why shot-quality models are built to compare an attempt against the alternatives available on that possession rather than against a constant.

A corollary catches teams as well as players. As an offence improves, its own threshold rises, and shots that were correct last season become mistakes this one. A club that has just added a shot creator should be taking fewer of the shots it used to accept, and a coach who has not moved his threshold along with his roster is leaving points on the floor while every individual figure on his sheet looks exactly as it did before.

Three routes to the same number

The decomposition above has a consequence that makes the statistic far more interesting than it first appears: two shooting lines that look nothing alike can produce an identical figure, and the figure is correct in both cases.

The published glossary makes the point with a small example of its own. A player who goes four for ten with two threes and a player who goes five for ten with no threes have both scored ten points from the floor, and both have an effective field goal percentage of 50. One made fewer shots and got the same result, because the shots he made were worth more.

Push that further with three constructed lines. Every number below is invented and deliberately round, chosen so the arithmetic can be checked in your head. None of it reports any real player.

Each of the three takes exactly one hundred field goal attempts.

• The first takes no threes at all and makes 55 of his 100 shots. His field goal percentage is 55, his three-point bonus is nothing, and his effective field goal percentage is 55.
• The second makes 45 of his 100 shots, of which 20 are threes. His field goal percentage is 45. The bonus is half of 20 divided by 100, which is 10. His effective field goal percentage is 55.
• The third makes only 35 of his 100 shots, but 40 of them are threes. His field goal percentage is 35, a figure that would get him benched. The bonus is half of 40 divided by 100, which is 20. His effective field goal percentage is 55.

• Field goal percentage
• Bonus from made threes

No threes, 55 makes55%0%

20 threes made, 45 makes45%10%

40 threes made, 35 makes35%20%

An invented illustration, not a report of anyone's season. Each line is 100 field goal attempts. The two bars in every row sum to that player's effective field goal percentage of 55, because eFG% equals field goal percentage plus half the ratio of made threes to attempts.

Show the numbers

Three constructed shooting lines that all land on the same effective field goal percentage

Item	Field goal percentage	Bonus from made threes
No threes, 55 makes	55%	0%
20 threes made, 45 makes	45%	10%
40 threes made, 35 makes	35%	20%

Look at the third line for a moment, because it is not a curiosity. A player shooting 35 per cent from the field is, by the traditional number, having a poor season. By the corrected number he is producing 1.10 points every time he shoots, which is a perfectly respectable offensive outcome. The gap between those two verdicts is the entire reason the statistic exists.

The same picture read backwards is a warning. Three players with identical effective field goal percentages have completely different risk profiles. The first depends on nothing but making shots he takes close to the basket. The third depends on a high-variance shot going in at a rate that will swing wildly over any short sample, and on the defence continuing to let him take it. A single figure cannot distinguish them, which is why the decomposition is worth carrying around.

The statistic was patched onto a box score that predates it

There is a reason the formula looks bolted on rather than designed, and it is historical.

Field goal percentage is older than the three-point line. When the arc arrived, the box score was not re-cut around it. A made three was folded into the existing field goal columns as one make and one attempt, exactly like any other shot, and two new columns were added beside them recording three-point makes and three-point attempts separately. The old statistic did not become wrong on the day the line was painted. It carried on reporting precisely what it had always reported, and the game underneath it turned into something the report no longer described.

Effective field goal percentage is a correction applied on top of that record, working from the columns that exist rather than the columns anyone would design now. A made three appears twice in the box score, once inside the field goal total and once in its own column, and the formula exploits that duplication: it adds half of the second appearance to correct the value of the first.

Which produces the single most common error people make computing this by hand. Three-point attempts already sit inside field goal attempts and must not be added to them, and three-point makes already sit inside made field goals. A shooting line of ten attempts including four from behind the arc is ten attempts, not fourteen. Anybody whose answer comes out suspiciously low has almost certainly inflated the denominator by counting the same shots twice.

The same structural point explains why the formula stops where it does. It can only correct what the record distinguishes, and the record distinguishes shot value. It does not distinguish an open shot from a contested one, a shot the player created from a shot he was handed, or a possession that ended at the line from one that never happened at all. Those corrections need data the box score was never built to hold.

What the box score actually records, ending by ending

Here is the mechanism that produces the statistic's largest blind spot, and it is a scorekeeping matter rather than a mathematical one. Follow one drive to the rim through five possible endings and watch what each one leaves in the record.

1. 1Ending one, the layup goes inOne field goal attempt, one made field goal, two points. The statistic sees a make worth one make, and the possession is fully represented in both the numerator and the denominator.
2. 2Ending two, the shot is a three and it goes inOne attempt, one make, one made three, three points. The numerator credits one and a half makes for the single attempt, which is the whole substitution the formula exists to perform.
3. 3Ending three, the shot misses cleanlyOne attempt, no make. The denominator grows, the numerator does not, and the figure falls. This is the only kind of failure the statistic is built to punish.
4. 4Ending four, he is fouled shooting and missesNo field goal attempt is charged at all. He goes to the line, converts a pair, and two points arrive on the scoreboard. Effective field goal percentage records nothing whatsoever: not a make, not a miss, not an attempt.
5. 5Ending five, he is fouled, scores, and converts the bonusOne attempt, one make, three points. Only two of those three points sit inside the statistic, and the third arrived from the line where the formula cannot follow it.

A trace of what the scoring record retains in each case, and what effective field goal percentage can therefore see. The point of the sequence is the fourth ending, where a possession that produced points leaves no field goal attempt behind at all.

Endings four and five are where the whole argument about this statistic lives.

A shooting foul that ends in a miss removes the possession from the calculation entirely. The player attacked, drew contact, produced points, and the record of that shot is simply absent from both halves of the fraction. The consequence is systematic rather than random: a player who lives at the rim and gets whistled has his best possessions deleted, while a player who settles for jump shots has every possession counted.

The and-one runs the other way and does its own quiet damage. A made basket plus a converted free throw is three points, and the statistic sees a two-point make on one attempt, which reads as an eFG% of 50 for a possession that produced 1.5 points per shot. The most valuable single outcome available to an offensive player is recorded as an ordinary one.

The free throw hole is deliberate, and it has a name

None of this is a defect that somebody failed to notice. It is a boundary, drawn on purpose, and the reason it was drawn is worth understanding rather than complaining about.

Free throws tell you about contact, about how the game is being officiated, and about the whistle. They tell you almost nothing about where a player chose to shoot from. If the question in front of you is whether a team's shot diet is defensible, whether the midrange volume is too high, whether the corner is being used, then free throws are noise in the signal and pulling them out sharpens the picture.

If the question is how efficiently a scorer produced points, free throws are not noise at all, and the statistic that folds them in is true shooting percentage, which adds free throw points to the numerator and an estimated count of trips to the line to the denominator. The two figures answer different questions and the gap between them is itself informative.

Dean Oliver's framework makes the division explicit in a way that settles the argument. In the four factors, shooting and free throws are two separate factors with two separate weights, and the free throw factor is measured as free throws made divided by field goal attempts. Free throws were never omitted from the model of how teams win. They were given their own line, because getting to the line and shooting well from the floor are different capabilities that different teams have in different proportions.

Why it is the first of the four factors

The four factors are the standard framework for explaining why a basketball team wins, and effective field goal percentage is the first and largest of them.

• Shooting40.0%
• Turnovers25.0%
• Rebounding20.0%
• Free throws15.0%

The approximate weights published alongside the four factors framework. Shooting is measured by effective field goal percentage, turnovers by turnover percentage, rebounding by offensive and defensive rebound percentage, and free throws by free throws made divided by field goal attempts. Each factor applies to a team's offence and to its defence, which in practice makes eight.

Show the numbers

The weights Dean Oliver assigned to the four factors

Item	Value
Shooting	40%
Turnovers	25%
Rebounding	20%
Free throws	15%

Two structural points follow from that chart and they are more useful than the weights themselves.

The first is that each factor has an offensive version and a defensive one, computed with the same formula from the other side of the ledger. A team's own effective field goal percentage describes how well it shot. Its opponents' effective field goal percentage describes how well it defended, and that second figure is one of the most direct defensive statistics available anywhere in the sport, because it collapses shot location and contest quality into a single number without needing to know who guarded whom.

The published four factors page works its example on the 2004-05 Phoenix Suns, and the pair of numbers is instructive. That team's offensive effective field goal percentage was .534 and the figure it allowed was .478. The gap between those two numbers, more than the size of either, is what a team is actually trying to build.

The second point is that shooting is the largest factor but not the whole story, and the three remaining factors are precisely the things effective field goal percentage cannot see. That is not a coincidence. The framework was designed so that the four factors between them cover the ground, which means each one is allowed to be narrow.

What effective field goal percentage is blind to

Four categories, and they matter in roughly this order.

It counts shots, not possessions. This is the big one and it is easy to miss. The denominator is field goal attempts, so a possession that ended in a turnover never appears. A team can shoot brilliantly and score badly by giving the ball away on a fifth of its possessions, and this statistic will report the brilliance and stay silent about the rest. That is the whole reason the possession-based team ratings measured per 100 possessions exist alongside it rather than being replaced by it.

Offensive rebounds cut the same way in the opposite direction. A missed shot that the offence collects and converts has cost the team nothing, but the statistic charges the miss at full price. A team built to hunt second chances is systematically understated by its own shooting figure, and its offensive rating will look better than its eFG% suggests it should.

It says nothing about volume, or about who created the shot. A specialist who takes six wide-open catch-and-shoot threes a game and a primary creator who takes twenty-two contested shots against a defence built to stop him can post the same figure, and the second is doing something far harder. Efficiency and difficulty trade against each other continuously, which is why the number should never be read without the share of possessions a player used sitting next to it. Efficiency at low volume is cheap; the interesting players are the ones who hold their efficiency as their volume rises.

The related point is that the statistic credits the shooter and nobody else. A wide-open corner three is the product of a drive, a rotation, a skip pass and a screen, and every one of those actions was performed by somebody who receives nothing in this column. Shot creation is invisible here by construction.

It conflates shot selection with shot making. Two teams at the same figure can have arrived by opposite routes: one taking excellent shots and converting them at an ordinary rate, the other taking poor shots and making an unusual share of them. The first is a repeatable process. The second is a hot month. Nothing inside the number distinguishes them, and separating the two requires shot-quality models built on player and ball tracking, which is the only way to ask what a shot was worth before it was taken.

The defensive version of the same problem is sharper still, and it is the reason opponent effective field goal percentage should be handled with care. A defence controls where the opposition shoots from and how contested those shots are. It has far less control over whether open threes go in on a given night, and three-point variance is large. A defence that has forced a good shot diet can look poor for weeks, and a defence that has been lucky can look excellent.

It is not comparable across eras. The formula prices a three at one and a half makes, so a competition where nobody takes threes and a competition where a third of all shots are threes will produce figures on the same scale that mean different things. Any comparison worth making is a comparison against the league average of the same season. That is true of most shooting statistics and it is especially true of this one, because the input that moves it most, three-point volume, is the input that has changed most, as the arithmetic that reshaped shot selection made unavoidable.

Two constructed teams, identical shooting, different offences

The claim that the statistic counts shots rather than possessions sounds abstract until it is worked through. Here it is with invented, deliberately round numbers, chosen so every line can be checked by hand. Neither team below is real, and free throws are left out of the illustration entirely so the possession arithmetic stays legible.

Both teams shoot at an effective field goal percentage of 55, which is 1.10 points per field goal attempt. Both play exactly 100 possessions. Everything else differs.

	Team A	Team B
Field goal attempts	90	105
Turnovers	10	5
Offensive rebounds	0	10
Possessions	100	100
Effective field goal percentage	55	55
Points from the floor	99	115.5

Follow the possession count, because the trick sits there. A possession ends in a shot, a turnover, or a trip to the line. An offensive rebound ends nothing: it hands the same possession back, and the extra attempt it produces is a second bite at one possession rather than a new one. So Team B's 105 attempts plus 5 turnovers, minus the 10 attempts that came from its own rebounds, still add up to 100 possessions.

Team A produces 99 points per 100 possessions. Team B produces 115.5. The gap is 16.5 points per 100 possessions, which is the distance between a poor offence and an excellent one, and every bit of it was created by turnovers and offensive rebounds while the shooting figure sat unchanged at 55 for both.

That is the honest scale of what the statistic leaves out. It is not a rounding error at the margin. Two teams shooting identically can be separated by more than the entire spread of offensive quality in a competition, and the shooting column will report them as twins.

Why the figure swings harder for a three-point shooter

There is a property of the formula that goes almost unmentioned and that matters enormously for how much weight a short sample deserves.

A made two adds one to the numerator. A made three adds one and a half. The numerator is therefore a sum of larger, lumpier increments for a three-point shooter, and larger increments mean a wider spread of outcomes over the same number of attempts, even when the underlying skill is identical.

Work it through with two constructed shooters, both invented. The first takes nothing but two-point attempts and converts 54 per cent of them, so his effective field goal percentage is 54. The second takes nothing but threes and converts 36 per cent, and since each make is worth one and a half, his effective field goal percentage is also 54. On skill they are indistinguishable, by construction.

Now the variance. For the two-point shooter, the spread of his figure over a given number of attempts is driven by 0.54 multiplied by 0.46, whose square root is about 0.498. For the three-point shooter it is driven by 0.36 multiplied by 0.64, whose square root is 0.48, and then multiplied by 1.5 because every make counts one and a half times, which gives 0.72.

Divide one by the other and the three-point shooter's figure is roughly 1.4 times as volatile as the two-point shooter's over the same number of attempts, at exactly equal true efficiency. That factor is arithmetic rather than a season's data, and it holds whatever the sample size.

Two practical consequences follow. A three-heavy shooter needs a materially longer sample before his figure means anything, which is why a five-game slump from a specialist tells you close to nothing and the same slump from a player who scores at the rim tells you a little more. And at team level, a roster whose scoring is concentrated behind the arc produces a noisier game-to-game record than a roster of the same quality that scores inside, which surfaces as the familiar complaint that jump-shooting teams are streaky. They are. The streakiness is a property of the scoring rule, not a character flaw.

Reading a team properly from the number

A few habits turn the figure from a scoreboard decoration into something that answers questions.

Always read it as a pair. A team's own effective field goal percentage and the one it allows are the two halves of the largest factor in the sport, and the difference between them predicts more about a team than either number alone. A club that shoots well and defends the shot badly is a very different proposition in a playoff series from one with the same net figure built the other way round, because shot defence travels and shooting variance does not.

Always split it into its two components. Field goal percentage plus the three-point bonus tells you whether a team is efficient because it makes shots or because it takes valuable ones. Those are different assets. A team whose figure is carried by three-point volume has a floor that moves with variance; a team whose figure is carried by conversion near the rim has a floor that moves with health and matchups.

Never read it without a turnover figure beside it. Shooting and giving the ball away are the two largest factors, they are close to independent of one another, and a team can be excellent at one and hopeless at the other. Judging an offence on its shooting alone is judging it on 40 per cent of the evidence, by the framework's own weighting.

And read a player's number against the shots he was asked to take. A high figure produced entirely from assisted catch-and-shoot attempts is a genuine skill and a fragile one, because it depends on somebody else generating the attempt. A slightly lower figure produced from shots the player made for himself is worth more than the arithmetic says.

• 1.5Makes a converted three-pointer is credited with
• 1Points per field goal attempt at an effective field goal percentage of 50
• 150Effective field goal percentage of a player who makes every three he takes
• 40Weight the four factors framework assigns to shooting

The first three are arithmetic that follows directly from the scoring values in the rulebook and from the definition of the statistic. The fourth is the approximate weight published with the four factors framework. None of these is a season, team or player figure.

Where to use it, and where to put it down

Reach for effective field goal percentage whenever the question is about shooting from the floor, and stop there.

Use it to judge shot selection, since that is the job it was built for and the job it does better than any other single figure. Use it to compare a team's offence with the shot diet it allows, which is the cleanest one-line summary of a defence available without tracking data. Use it to score individual shot types, because a shot's expected eFG% is just its points per attempt halved, and that conversion is what makes a shot chart legible.

Put it down when free throws matter, which is any question about how efficiently a player scored rather than where he shot from. Put it down when possessions matter, which is any question about a team's offence as a whole rather than its shooting. Put it down when volume matters, because a figure with no usage attached says nothing about difficulty. And put it down before comparing two seasons separated by a decade, unless both are expressed relative to their own league average.

The statistic is narrow on purpose. It performs one substitution, correctly, on the one input the rulebook prices unequally, and it declines to do anything else. That is a virtue rather than a limitation, provided you know which questions belong to it and which belong to the statistics built to sit alongside it. Ask it what a shot was worth and it will tell you exactly. Ask it anything else and it will answer anyway, which is the only dangerous thing about it.