Understanding Strokes Gained and Partial Shots

[iacas]

I've written before about how golfers don't seem to understand losing or gaining partial shots. We can't ever hit a shot that counts as only half or three tenths of a shot, after all. A missed five-foot putt counts the same as a drive we pure 285 down the middle.

So, I'd like to take a few minutes here to cover partial shots and work our way toward "strokes gained" or lost as it applies to golfers of all levels - including you.

The simplest way of looking at strokes gained and partial shots is with putting. From one inch away, every golfer in the world is expected to take 1.0 strokes to hole out. Nobody ever two-putts, nobody three-putts, etc. The same is pretty much true from one foot away, as well: virtually everyone takes 1.0 putts (the true number, even on the PGA Tour, is probably something like 1.00000000000000001, but you get the picture…).

From three, the number jumps to something like 1.04 - PGA Tour pros only make about 96% of their three-footers. The other four times, they two-putt. So (96 x 1) + (4 x 2) = 104. 104 strokes for 100 attempts is 1.04 strokes per attempt.

Spoiler

In other words, if you have a three-foot putt, and you make it, you actually gain 0.04 strokes against your standard (if your standard is a PGA Tour player). By the standard, you should have taken 1.04 strokes to get the ball in the hole from three feet. You only took one stroke, so you "saved" the 0.04. If you somehow manage to make 100 three-foot putts in a row, that 0.04 strokes saved each time multiplies out to four strokes saved in total.

Let's back up a bit farther. From eight feet, a PGA Tour player is about 50/50 to make it. They still almost never three-putt from this range, so let's just keep thing simple and consider that they're either going to hole it or two-putt. If they have 100 eight-foot putts, it would take the average PGA Tour player 150 putts to hole out.

So, imagine that this 1.5 is your standard, and you make an eight-foot putt. You've "gained" half a stroke on the average. You were expected to take 1.5 strokes, but you took just one. If you miss an eight-footer on the next hole, you played two eight-footers in three strokes: dead on what you're expected to do.

What if you happen to have six eight-foot putts in a row, on the golf course, and you miss them all? While it may feel as though you've given away six strokes, because all of those putts likely felt "makable," you've only given away about three strokes: 12 putts - 6 attempts * 1.5 putts/attempt = 3 strokes "lost." And that's if your standard of comparison is a PGA Tour player. If you want to compare yourself to a bogey golfer, you've actually lost only half that: 1.5 strokes (a bogey golfer takes about 1.75 strokes from eight feet, so 6 * 0.25 = 1.5).

From 33 feet, the numbers are 2.0 for a PGA Tour player and about 2.2 for a bogey golfer. You're expected to take two strokes if you're a PGA Tour player, and 2.2 if you're a bogey golfer. Now, again, you can't take 2.2 strokes to hole out, but you can take 11 strokes over five attempts from 33 feet, and 11/5 = 2.2. Every five 33-foot putts, the PGA Tour player will gain a full stroke: it will take them 10 and the bogey golfer 11.

Now that this part is understood, let's start putting some pieces together. Consider a golfer putting from B, above, 33 feet away from the hole. If he two-putts, he's going to finish neutral - he won't lose or gain strokes to a PGA Tour player. But let's imagine three scenarios. In the first, he hits his first putt to a foot and then taps in. In the second, he hits it to three feet. He takes his time and makes that. In the third, after horribly judging the speed, he hits his putt eight feet past the hole, but makes it coming back.

In each instance he took two putts, but where he gained and lost strokes changes:

a) 33', 1'
b) 33', 3'
c) 33', 8'

The math on those start the same: from 33', the player is expected to take 2.0 strokes. It "costs" the player 1.0 strokes to hit the first putt, so at each of the second positions he has already expended one putt. If we look at the strokes gained for each of those distances, we find:

a) 2.0, 1.0
b) 2.0, 1.04
c) 2.0, 1.5

In a, the player took one stroke to shave his "expected" strokes from 2.0 to 1.0. He's neither lost nor gained strokes, on either of his two strokes. He was expected to take 2.0 putts from 33', and he put it to a spot from which he's expected to take 1.0 more strokes.

In the b and c, though, the numbers don't work out the same. If a player hits his 33' putt, as he does in b, to about three feet, we already know he's expected to take 1.04 strokes from there. So he was at 2.0 expected strokes, and he "spent" a full stroke to get to a position from which he is expected to take 1.04 strokes. He "lost" 0.04 strokes. That he then holed the three-foot putt is great - he "gained" that 0.04 strokes back. He was expected to take 1.04, but it only took him one stroke.

c is even worse (and then better) for our player: from 33' he's expected to take 2.0 strokes, but he "spends" a stroke to hit his ball to a position from which he's expected to take 1.5 strokes. He's already hit a putt, and still has "1.5 putts" left, by the averages. So, going from 33' to 8' means our player LOST half a stroke on that putt. If he then holes the eight-foot putt, well, he gains it right back. Just as we saw above.

This is how strokes gained (or lost) works: you look at the average number of strokes it takes a certain level of player to hole out from where they were before and after a stroke. If they're 33 feet away on the green (2.0), and they hit it to a position from which they're expected to take 1.2 strokes to hole out, they've lost 0.2 strokes with their first putt.

It's the same thing from the tee, or an approach shot, too: even though a player is unlikely to hole out. Standing on the tee, a player is expected to take perhaps 4.0 strokes, and if they advance their ball with their tee shot to a position from which they're expected to take 3.18 strokes, they've lost 0.18 strokes with their tee shot. If they then hit their ball to 20 feet on the green (from which they might be expected to take 1.87 strokes), they've gained back 0.31 strokes (3.18 expected - 1 stroke taken - 1.87 expected strokes from new position).

I've told this story a few times. @mvmac and I were playing a soggy course with a little wind coming from the south. The 10th and 12th holes on this course are 460 and 480 yards, and he had a hybrid and a 3-wood, while I had two hybrids, into each of the greens. We managed to hit our shots to about 15-25 feet, and we jokingly said to each other "strokes gained!" after each. Why? Because from 200 to 230 yards, hitting the green at all - let alone getting the ball to only 15 or 25 feet - is a substantial gain in strokes for a single shot. Heck, a PGA Tour player is going to average 1.87 strokes from 20 feet, and averages 3.32 from 220 yards out in the fairway, so that one stroke that took @mvmac and I from 220 yards to 20 feet cost us one stroke but saved us almost half a stroke (against a PGA Tour player): 3.32 - (1 + 1.87) = 0.45 strokes gained. Two-putting from there cost only the 0.13 strokes (2.0 - 1.87).

Let's take a look at a hole:

Let's imagine the hole is a certain distance and a hole on which you are likely to average 4.2. (If you're a scratch golfer, maybe the hole is 475 yards long, or if you're an 18 handicaper, maybe it's 355 yards long). Standing on the tee at A, you're expected to hole out in 4.2 strokes, which is of course impossible on any given single playing of the hole. That means that you're going to lose or gain 1.2, 0.2, 0.8, 1.8, or 2.8 strokes almost every time you play this hole. You can't break even on any single playing of the hole.

But anyway, that's the important number: 4.2.

Let's say you hit a good shot from the tee into the fairway to B. Again, to remain somewhat agnostic with respect to various handicaps, let's say you're going to average 3.0 from there. Your tee shot, which "cost" you one stroke, moved you from a spot where you were going to average 4.2 to a spot from which you average 3.0. You've shaved 1.2 strokes by "spending" only one stroke.

Let's say that the rest of the positions work out as follows:

B: 3.0
C: 3.2
D: 2.7
E: 3.6

Strokes gained (and "expected shots") is based primarily on two things (because adding in other factors could complicate things to the point of being ridiculous): the distance remaining to the hole and the lie of the ball. On the putting green, the lie of the ball is obviously "on the putting green." But from 180 yards, players average lower expected shots from the fairway than they do from the trees, or a fairway bunker.

So again, a player expecting to average 4.2 from the tee (A), hits it into B, C, D, and E. If we limit the distances to relative descriptors, we can start to see how these make sense:

B: 3.0 - Fairway, medium distance from the hole
C: 3.3 - Fairway, long distance from the hole
D: 2.7 - Rough, very short distance from the hole
E: 3.6 - Fairway bunker, short-ish distance from the hole

These four examples demonstrate two things that make strokes gained a pretty reasonable way to assess the value of a shot: the farther a shot is from the hole, the more shots you're expected to hole out, and the worse the lie, the same: the more strokes you're expected to take to hole out.

Let's step through a full example. A player standing on the tee at A is going to hit it to C, miss the green in the rough short and right, chip to eight feet, and miss the par putt before tapping in for bogey.

Shot      Expected     Result      Expected       Strokes Gained
----      --------     ------      --------       --------------
1            4.2         C           3.3              -0.1
2            3.3     Grsd Rough      2.6              -0.3
3            2.6      8' Green       1.5              +0.1
4            1.5      3" Green       1.0              -0.5
5            1.0       Holed          0                0.0
                                                  --------------
                                              Total:  -0.8

The tee shot was played from a spot with 4.2 expected shots to a spot with 3.3 expected shots. This cost the player one stroke, but only reduced his expected score by 0.9. Thus, he lost 0.1 strokes.

From there, the player hit a mediocre shot: they were in a position to average 3.3, but advanced the ball into a position from which they're expected to take 2.6. They gained only 0.7 strokes at a cost of another full shot. They lost 0.3 strokes.

The player hit a slightly better than expected chip - they gained 0.1 strokes by hitting it from a 2.6 position to a 1.5 position (for this one position I'm just using the PGA Tour distance) at a cost of just one stroke - but the player is 1.1 strokes closer.

But, then he missed the putt (1.5 expected strokes) and tapped in, losing 0.5 strokes on the two-putt exchange. In total, the player lost 0.8 strokes, but we know that just knowing the expected score from the tee and the score they made: 5 - 4.2 = 0.4 - 0.1 + 0.5.

Though the player hit five shots, only two were "neutral" with respect to strokes gained or lost. The player lost partial strokes on the approach shot (which missed the green) and their putt (which missed the hole), but gained a very small 0.1 on a slightly better than expected chip shot.

Let's do one more example: A to D to 3 feet and holed for a birdie.

Shot      Expected     Result      Expected       Strokes Gained
----      --------     ------      --------       --------------
1            4.2         D           2.7              +0.5
2            2.7      5' Green       1.25             +0.45
3            1.25      Holed         0.0              +0.25
                                                  --------------
                                              Total:  +1.2

This player hit a big tee shot (maybe it hit the cart path a couple of times) to D. He went from 4.2 to 2.7 expected strokes with one stroke, making up 0.5 strokes with his tee shot. Then, from short range, he hit his shot to five feet from where he's expected to take 1.25 strokes (he's expected to make 75% of his five-foot putts), again saving nearly half a stroke: 2.7 to 1.25 with a cost of one stroke is 2.7 - (1 + 1.25) = 0.45. Then, to wrap up the great hole, he holes the five-footer.

These two examples highlight just how many different shots go into making up a score on any given hole: virtually every shot that isn't a tap-in results in an exchange - positive or negative - to the expected strokes. If you play a poorer shot than your comparison standard, you lose strokes. Play a better one than expected and you gain.

The funny thing is, too, how people tend to see these shots. Though the player lost shots in the first example on both the tee shot and the approach shot, they're likely to blame a poor chip and a missed putt for the bogey. Yes, they lost strokes with the putt, but they actually gained a 0.1 strokes with the chip. The drive and the approach shot cost them, and the putt - a 50/50 proposition - simply landed heads up instead of tails up.

In the second example, the players will likely give themselves credit for the approach shot, but overlook that they got a bigger advantage hitting the ball off the cart path and into the rough, where they gained a full half stroke. They'll also credit their clutch putting, but even if they'd two-putted, the strength of their first two shots would still have netted them 0.2 strokes gained for the hole.

---

So that's it in a nutshell: both strokes gained and how partial shots work when playing golf.

The next time you're out there, and you miss a 50/50 putt, take consolation in the fact that you're "owed" one. The next time you hit it to 25 feet from 162 yards, tell yourself that you gained some strokes with that shot (it's better than the PGA Tour average, after all). The next time you hit a good drive, take pride in saving 0.2 strokes or whatever. And, for Pete's sake, if you two-putt from 30 feet, stop kicking yourself for "never making them." Almost nobody does, and for players at your level, that two-putt probably saved you a partial stroke.

[mvmac]

Great post! Important info for golfers to understand.

[DeadMan]

Great post.

One thing to sort of add on, I think it's good for golfers to understand the make %s for various putts. You can really feel like a terrible putter out there when you miss a bunch of 10 footers, but the reality is that those are hard to make. You make a 10 footer, you've done something pretty darn good. PGA Tour players aren't PGA Tour players because they make a bunch of 10 footers.

[b101]

Really useful breakdown and whilst it still takes me a while to get my head around, I can definitely see where you're coming from and why it makes sense. Obviously completely complements the LSW section about safely advancing the ball as far as you can, too 

[iacas]

14 hours ago, DeadMan said:

One thing to sort of add on, I think it's good for golfers to understand the make %s for various putts. You can really feel like a terrible putter out there when you miss a bunch of 10 footers, but the reality is that those are hard to make. You make a 10 footer, you've done something pretty darn good. PGA Tour players aren't PGA Tour players because they make a bunch of 10 footers.

Yes, I like to tell this story.

I had my golf team playing from the forward tees one day (in twosomes, best ball score). The 17th (errr, 8th… they switched the nines a few years ago) hole is still a 460-yard par "five" from the forward tees, and a golfer hit a driver and a 6-iron to about 25 feet. Then he nearly holed his "eagle" putt and walked off shaking his head and muttering "I should have made that putt…"

I stopped him and said "wait, no. Do you realize what the make % even on the PGA Tour is from that range? You shouldn't have made that putt. That you gave it such a great chance - and that you had only a 25-footer on a long hole to begin with - is a credit to your skill on that hole. Stop feeling bad about yourself - you should feel really good about that hole."

So, there's solace to be found in these types of things, too. For example, if I'm in the shit, and I manage to advance my ball to a nGIR position, I tell myself that I gained almost all the strokes I lost with my crappy tee shot right back. That can be a good feeling, and can help you maintain a fairly accurate outlook on your game, too.

[RandallT]

Great post!

As a very minor addendum in case people are interested, I was looking at Broadie's chart compared to the current PGA season putting for 8 and 9 footers recently- just to see how the 50/50 benchmark of 8ft was holding up since he published his numbers way back when.

Take a look at the spoiler below, as I have a sense that the median pro is raising the bar a tad, so that 50/50 mark is moving a bit beyond 8ft. It's still early in the season, but the median player hits about 47% from 9ft, and about 53% from 8ft.

Spoiler

9 FOOTERS

But that's the top players (shown mainly to grab the column headers. Here's the median (of 176 total players listed for 9ft putts):

Link: http://www.pgatour.com/stats/stat.347.html

The median player seems to be hitting over 47% of 9-footers this year! That seems pretty good. The best players have hit 70% or more (10-20 attempts)- that seems superhuman, and will likely drop over the season.

 

8 FOOTERS

The top players:

The median players (183 players listed):

Link: http://www.pgatour.com/stats/stat.346.html

The median player seems to be hitting nearly 53% of 8-footers this year. That seems pretty good. The best players have hit in the high 70s%. Sample sizes still in the 10-20 attempts range, so there's a decent amount of variability.

The worst players for 8ft putts are hitting 30% or so. There are about 20 players listed who hit 1/3 of 8ft putts or fewer. So even pros, when given 10-20 chances can miss 70% from 8ft. And they're on TOUR!

 

Just thought it interesting, that's all. This changes NOTHING from your analysis, but thought I'd post because I was just looking at it the other day. I still use the Broadie numbers personally for any analysis spreadsheets.  Assuming these are all 2-putts (as you also say), I could swap out the 1.50 number for 8ft to 1.47 expected shots, but that likely would make a very small difference in the strokes gained putting numbers. 

 

[iacas]

A few years ago it was 7'10" so it wouldn't surprise me to see it creep upward slowly. That said, it's still relatively early in the year, too, and the number could drop. Look at the shot attempts: 10, 13, 19… relatively low numbers.

[GolfLug]

I don't know if Broadie has a table for the 50/50 tee shot distance (assuming FIR) for different length holes on Par 5s and Par 4s. A table similar to the putting table. 

My driver distance and 17 deg hybrid distance difference is only 20 yards. But if I know that on a particularly long hole (maybe 440+ yard hole) even a perfect fairway split 240 yard drive will still lose me a 0.2 shot then I might as well hit a hybrid and lose another 0.1 (arbitrary low number) with distance lost but increase my odds of minimizing overall loss by increasing fairway hit chance by 50% or saving a 0.5 shot loss. Net gain of 0.4. Not sure if the math adds up exactly like that, but I think it would make general sense. 

Of course I could just practice up the driver to increase FIR to negate the hybrid FIR advantage, but that's a different thread, yes?

[iacas]

1 hour ago, GolfLug said:

I don't know if Broadie has a table for the 50/50 tee shot distance (assuming FIR) for different length holes on Par 5s and Par 4s. A table similar to the putting table. 

My driver distance and 17 deg hybrid distance difference is only 20 yards. But if I know that on a particularly long hole (maybe 440+ yard hole) even a perfect fairway split 240 yard drive will still lose me a 0.2 shot then I might as well hit a hybrid and lose another 0.1 (arbitrary low number) with distance lost but increase my odds of minimizing overall loss by increasing fairway hit chance by 50% or saving a 0.5 shot loss. Net gain of 0.4. Not sure if the math adds up exactly like that, but I think it would make general sense. 

Of course I could just practice up the driver to increase FIR to negate the hybrid FIR advantage, but that's a different thread, yes?

Fairway or rough from that far away is almost never going to be a 0.5 shot difference. Generally speaking remember The Rule. It's really just that simple. Consider Shot Zones, the distance gradient, and the Shades of Grey on that hole.

[Lihu]

This was a really long post to read, and re-read multiple times. Thanks for the post. It was very informative.

[cutchemist42]

So maybe asking the dumb question, and I think I might understand it but just double checking, 2nd shot on a Par 5 when it comes to Strokes Gained is basically...

• Taking where your tee shot ended up
• Taking that distances away from the pin on your 2nd shot
• How much closer your 2nd shot gets you to the pin for your 3rd shot

Love the writeup, thank you.

[iacas]

1 hour ago, cutchemist42 said:

So maybe asking the dumb question, and I think I might understand it but just double checking, 2nd shot on a Par 5 when it comes to Strokes Gained is basically...

• Taking where your tee shot ended up
• Taking that distances away from the pin on your 2nd shot
• How much closer your 2nd shot gets you to the pin for your 3rd shot

Kinda.

Let's say that standing 500 yards away from the hole with your ball teed up, your comparative standard (it may not be a PGA Tour player, and for the sake of round numbers, I'll make up a standard here) averages 5.0 strokes.

So you hit a good tee shot 250 yards.

From 250 yards in the fairway, your comparative standard averages 3.9 strokes. It "cost" you one stroke to get there, so you "gained" 0.1 strokes.

From 250 out, you hit he ball to 20 yards short of the green in the rough. From there, your comparative standard averages 2.6 strokes. It again cost you one stroke to get there, so you "gained" 0.3 strokes.

But from there, it takes three to get down for a par. Because you were expected to (by your comparative standard) get down in 2.6, you "lost" the 0.5 (3.0 - 2.6 = 0.4).

You may have lost them chipping, or putting. I didn't know if needed to continue shot by shot. But you lost them there, just as you gained them earlier.

[Dinoma]

Thanks for all the clear explanations, I really like stats and it's such a great way to break down your round. I'd never thought of thinking of each individual shot in this manner as I played. I think it would help to recalibrate expectations.

On a side note, I hope Game Golf expand their strokes gained section to be a bit more granular.

[cutchemist42]

56 minutes ago, iacas said:

Kinda.

Let's say that standing 500 yards away from the hole with your ball teed up, your comparative standard (it may not be a PGA Tour player, and for the sake of round numbers, I'll make up a standard here) averages 5.0 strokes.

So you hit a good tee shot 250 yards.

From 250 yards in the fairway, your comparative standard averages 3.9 strokes. It "cost" you one stroke to get there, so you "gained" 0.1 strokes.

From 250 out, you hit he ball to 20 yards short of the green in the rough. From there, your comparative standard averages 2.6 strokes. It again cost you one stroke to get there, so you "gained" 0.3 strokes.

But from there, it takes three to get down for a par. Because you were expected to (by your comparative standard) get down in 2.6, you "lost" the 0.5 (3.0 - 2.6 = 0.4).

You may have lost them chipping, or putting. I didn't know if needed to continue shot by shot. But you lost them there, just as you gained them earlier.

Thank you for this, I think I understand but just want to ask another question. When it comes to strokes gained then, not every 2nd shot is the same?

Lets just say there's two drives of 200 yards and 250 on a 500 yard course. There is then equal 2nd shots of 200 yards. There is then differences between those two 2nd shots and the strokes gained or lost?

[iacas]

23 minutes ago, cutchemist42 said:

Thank you for this, I think I understand but just want to ask another question. When it comes to strokes gained then, not every 2nd shot is the same?

Lets just say there's two drives of 200 yards and 250 on a 500 yard course. There is then equal 2nd shots of 200 yards. There is then differences between those two 2nd shots and the strokes gained or lost?

Yes, of course. Ignore the tee shot.

If you have a 130-yard par three and a 180-yard par three, hitting the ball 130 yards and onto the green is a better shot on the first hole than hitting a 130-yard shot on the 180-yard hole.

Strokes gained cares about four things:

• The distance your ball was from the hole before you hit it.
• The distance your ball was from the hole after you hit it.
• The lies of each of the above.
• The expected strokes to be taken by whomever you choose as your "comparative" golfer.

[travish]

Very well said, Knowing the average number of shots it takes a player to complete a hole from a given location is the starting point for strokes gained.

Strokes gained makes use of the Shotlink data provided by the PGA, which keeps track of each player's shots throughout the season with an accuracy of less than one inch. With this information, we can figure out how many shots an average tour player needs to finish a hole from a certain distance.

[pganapathy]

On 3/28/2016 at 1:07 AM, iacas said:

So, there's solace to be found in these types of things, too. For example, if I'm in the shit, and I manage to advance my ball to a nGIR position, I tell myself that I gained almost all the strokes I lost with my crappy tee shot right back. That can be a good feeling, and can help you maintain a fairly accurate outlook on your game, too.

This is actually a problem for most golfers.  Not because they hit the second shot well, but because they expect to hit every shot well, even though they are nowhere close to that level.  So they get upset that because of the bad first shot they couldn't be GIR.  Is this fair. Definitely not.  Is it human nature.  Almost certainly yes for many people.  Most of us are deluded enough to believe we can hit every shot well because we have hit it once before, many moons ago.