The Math Behind the Strokes Gained Formula

Most golfers meet strokes gained as a number on a screen. Your approach play was +0.4, your putting was -1.2, and somewhere behind that is math you have to take on faith.

You do not have to. The strokes gained formula is one subtraction, applied to every shot you hit, using a lookup table anyone can inspect. Everything else in a strokes gained report is bookkeeping on top of that subtraction.

The strokes gained formula, in one line

For any shot:

SG = E(start) − E(end) − 1

E is the expected strokes function: the average number of shots a reference golfer needs to hole out from a given distance and lie. You subtract 1 because you used a stroke to get from the start position to the end position.

If the shot moved you to a position better than the average result from where you started, the difference beats 1 and your strokes gained is positive. If it did not, the number goes negative.

Penalties add one term:

SG = E(start) − E(end) − 1 − penalty strokes

That is the entire calculation. Every category average, every round total, every trend line is built from repeated applications of those two lines.

Where the expected strokes numbers come from

E is not derived from a physics model. It is measured. Mark Broadie built the first versions from amateur data in his GolfMetrics project, then rebuilt them at scale using ShotLink, the laser tracking system that has recorded every shot on the PGA Tour since 2003. Take every tour shot that started 160 yards out in the fairway, count how many strokes each of those players needed to finish the hole, average it. That average is E(160, fairway).

Do that for every distance and every lie and you get a table. Here are real values from the PGA Tour baseline golfity uses:

Two details matter when you read a table like this. Green positions are indexed in feet and everything else in yards, because a putting baseline needs resolution that yards cannot give. And the lie matters as much as the distance: 160 yards from the rough costs a quarter of a stroke more than the same yardage from short grass, before you have swung the club.

Why the values are decimals

Expected strokes is an average over thousands of attempts, so it lands between whole numbers. The decimals also encode make rates you can recover with a bit of algebra.

Take the 10-foot putt. A tour player expects 1.615 strokes from there. Write that as one stroke for the putt itself, plus whatever is left if it misses:

1.615 = 1 + (1 − p) × 1.02

The 1.02 is the expected strokes from the tap-in range a missed 10-footer usually leaves. Solve for p and you get 0.397. Tour players make about 40% from ten feet, which is exactly what the tracking data shows. The baseline table is a compressed record of how often shots actually finish.

Working a hole shot by shot

A 420-yard par 4, tour baseline. Expected score from the tee: 4.016.

Shot 1 — drive into the fairway, 160 yards left. 4.016 − 2.964 − 1 = +0.052

Shot 2 — approach to 17 feet. 2.964 − 1.826 − 1 = +0.138

Shot 3 — first putt to 3 feet. 1.826 − 1.039 − 1 = −0.213

Shot 4 — tap-in. The ball is in the hole, so E(end) is 0. 1.039 − 0 − 1 = +0.039

The first putt is the interesting line. You hit the green in regulation and made par, and the round summary will call that a good hole. The math still charges you 0.213 strokes for leaving a three-footer, because tour players lag closer from 17 feet than you did.

For a second worked example with different lies, see the step-by-step strokes gained calculation.

Why the shot numbers always reconcile with your score

The hole total came to +0.016, and the expected score from the tee was 4.016 against a par of 4. That is not a coincidence.

Write the sum out and the middle terms cancel:

(4.016 − 2.964) + (2.964 − 1.826) + (1.826 − 1.039) + (1.039 − 0) − 4

Every E(end) is the next shot’s E(start), so each pair deletes itself. You are left with E(first shot) − (number of strokes taken), or 4.016 − 4 = +0.016.

This telescoping property is what makes strokes gained trustworthy as an accounting system. Sum every shot in a round and you get the baseline’s expected score for that course minus what you actually shot. Nothing leaks, and no shot is double counted or forgotten.

How penalties enter the math

Suppose the drive on that same par 4 finds the water and you drop, playing your third from 165 yards in the fairway:

4.016 − 2.986 − 1 − 1 = −0.970

The penalty stroke is charged to the shot that caused it. Inside golfity the penalty itself is recorded as its own row with a strokes gained value of zero, and the extra stroke is subtracted from the tee shot’s number. The bookkeeping keeps the telescoping sum intact while putting the damage where it belongs. There is more on this in how strokes gained handles recovery shots and penalties.

Category totals are a sorting step, not new math

Off the tee, approach, around the green and putting are not four different formulas. Each shot gets one strokes gained value from the same subtraction, then lands in a bucket based on where it started:

• Off the tee — tee shots on par 4s and par 5s
• Approach — shots from more than 30 yards out, plus par 3 tee shots
• Around the green — shots inside 30 yards that are not on the putting surface
• Putting — anything on the green

Add the four buckets and you are back to your round total. Nothing gets reweighted along the way, which is why a strokes gained breakdown can tell you where the strokes went rather than just how many there were.

Changing the baseline changes every number

The formula is fixed. The constants are a choice, and that choice moves the answers more than most golfers expect.

Run the same approach shot, 160 yards from the fairway to 17 feet, against two tables:

• PGA Tour baseline: 2.964 − 1.826 − 1 = +0.138
• 15-handicap baseline: 3.860 − 2.047 − 1 = +0.813

Identical shot, six times the credit. A 15-handicap expects 3.86 strokes from that yardage rather than 2.96, so hitting it to 17 feet is a genuinely strong result against that population and a slightly above average one against tour players.

Neither number is wrong. They answer different questions, which is why picking a benchmark you can actually learn from matters. Setting your own strokes gained benchmark covers how to choose.

What the arithmetic cannot fix

The formula is exact. The sample is not.

Individual shots carry a lot of variance, so single-round category numbers bounce around. Putting settles first because you hit roughly 30 putts a round; driving takes longer at 14 tee shots a round, and around-the-green numbers take longest because you might only face four or five of those shots in a round. Read how many rounds you need for accurate golf stats before you make swing changes off a small sample.

The math is also only as good as your inputs. Distances rounded to the nearest yard are fine. A lie logged as fairway when the ball was sitting down in rough is not, because you will be credited against the wrong column of the table.

To see the subtraction run on positions you choose, the strokes gained calculator lets you set a start and end position and returns the number, along with the baseline values it used. Change the lie from fairway to rough and watch how much a missed fairway costs before you have hit the next shot.