The strokes gained formula
Strokes gained for one shot is the expected strokes from where it started, minus the expected strokes from where it finished, minus one for the stroke. A holed shot leaves zero; a penalty makes the shot cost two. From a 420 yard tee (4.020 expected) a drive to 155 in the fairway (2.963) is worth +0.058.
The formula
strokes gained = expected strokes before − expected strokes after − strokes taken. Expected strokes is the published tour average number of strokes to hole out from a lie and a distance: yards for tee, fairway, rough, sand and recovery, feet on the green. The shot itself counts one; a shot that incurs a penalty counts two, and its finish is where the ball lies after the drop.
Seven shots, worked
The same arithmetic on seven very different shots. The two approaches from 155 yards show the lie in the number: the shot from the rough finishes in the same place and is worth more, because it beat a harder average.
Strokes gained shot by shot
| Shot | Before | After | Strokes | Gained |
|---|---|---|---|---|
| Drive, 420 yard tee to fairway at 155 | 4.020 | 2.963 | 1 | +0.058 |
| Approach, fairway 155 to 18 feet | 2.963 | 1.840 | 1 | +0.122 |
| Approach, rough 155 to 18 feet | 3.210 | 1.840 | 1 | +0.370 |
| Chip, rough 25 yards to 6 feet | 2.638 | 1.357 | 1 | +0.281 |
| Putt holed from 18 feet | 1.840 | 0.000 | 1 | +0.840 |
| Putt, 18 feet to 2 feet | 1.840 | 1.009 | 1 | -0.169 |
| Tee shot into water, drop at 200 in rough, penalty | 4.020 | 3.420 | 2 | -1.400 |
The identity
Add up every shot on a hole and the total must equal the expected strokes from the tee minus the strokes taken. The 420 yard par 4 above, played drive, approach, lag, tap in: +0.020 in total, and 4.020 − 4 = +0.020. They match, and they always will; it is the check that makes the method trustworthy.
The categories
Each shot is filed by where it started: off the tee for par 4 and par 5 tee shots, approach for shots to the green from outside the short game zone (including par 3 tee shots), around the green for short shots off the putting surface, and putting for everything on it. The formula is the same in every category; only the table changes.
In PinFlag
PinFlag runs this formula twice for every shot: before you swing, on the target you are considering with your own dispersion, and after you log where the ball finished. Both use the same published tables, and the round view lists every shot with its own number.
Frequently asked questions
What is the strokes gained formula?
How is a penalty handled in strokes gained?
Why does the lie change the number?
Do the shot values always add up?
Which golf app does this on the course?
Related
Sources
- PGA TOUR statistics
- Mark Broadie, Columbia Business School (Wikidata entity)
- How PinFlag calculates strokes gained
Every figure on this page is computed from the published baselines, the same ones PinFlag prices your shots with. The scope of the figures: Every value is the published tour baseline on the same baselines as the calculators; the worked hole is the identity check, shot values summing to expected strokes from the tee minus strokes taken.
Get PinFlag for iPhone
PinFlag shows you this number on the course, for the shot in front of you, before you swing: any target priced with your own dispersion and the lie read from the course map, your real shots drawn on the hole, and two taps to log. Golfer is $14.99 a month or $99.99 a year, with a 14-day trial on the annual plan through the App Store.