Putting Capture Speed

[iacas]

You may recall hearing Dave Pelz tell you that the optimal distance a putt has to roll past the hole is 17 inches.

How big might you guess the hole is at 17 inches? 4 inches wide? 3 ½?

What if I told you that the hole, at 17 inches, was only about 2¼ inches wide? What? Am I crazy? No - it's just math.

Consider a well cut hole, and what's required for the putt to go in. For a putt to be holed, it has to have enough time for the ball - 1.68 inches in diameter - to fall half that distance, or 0.84 inches, or more.

Gravity is a constant force (9.8 m/s ² ) and 0.84 inches is about 0.021336 meters. Given that distance (d) = 0.5at ² we can solve for t time:

0.021336m = 0.5 * 9.8 m/s ² * t ² .

0.021336m = 4.9 m/s ² * t ² .

0.021336m / 4.9m/s ² = t ² .

0.004354s ² = t ² .

t = 0.065987 seconds.

In other words, a golf ball needs approximately 0.066 seconds to fall 0.84 inches, striking some part of the back of the cup at the equator for the ball to be holed.

As you all know, d=rt. Distance equals rate times time. For example, in two hours going 60 MPH you'll travel 120 miles. 120 miles = 2 hours * 60 miles/hour. Simple stuff.

I don't know what the "rate" of a ball rolling 17" past the hole is, but smart people do and they've plugged that in to the equation. t is always going to be 0.066 seconds, and thus they can solve for d. That "d" is effectively the amount of air a ball needs to have under it's path in order to fall into the cup by dropping 0.84 inches (or more). A putt that rolls over the very very outside edge of the hole might only have a quarter of an inch of "air during which it can fall. If the putt is barely rolling at any speed, that'll take 0.66 seconds or longer and the putt will drop. If the ball is rolling really fast, it'll cross that 1/4 inch in no time at all, and not fall in.

Here are the numbers, in graphical form:

In other words, a putt that rolls six inches past the hole (0.5 feet, or 0.5') is effectively 3.8 inches wide. We lose 0.45 inches off the sides of the cup (0.225 off each side, the left and the right) and are effectively putting to a hole that's 3.8 inches wide.

If this graphic shows you anything, it's that the cup gets really small, really quickly. The hole is less than an inch wide for a putt that rolls four feet past the hole. Heck, even a putt that rolls only three feet beyond the hole - leaving what would amount to a tap-in for most people - is only 1.4 inches wide.

Here's that same graphic in a form that makes the distance a bit more obvious. Notice how at "A" the distance the ball needs to travel is much shorter than the distance needed in "B".

Putt a ball about eight feet past the hole and there's almost no chance of it going in the hole - the target is virtually 0 inches wide. These are the putts that hit the back of the hole, fall 0.7 inches instead of 0.84, and pop up and sit behind the hole.

(These numbers are for a flat green at about 8 on the stimp. On faster greens, these holes are a little larger because a ball can be rolling more slowly and still roll six inches past the hole, or two feet past the hole. On downhill putts, the hole can be a little larger too for the same reason - the ball is rolling more slowly - but this is often offset by the fact that the far edge of the cup is a little lower, so the ball has to fall more than 0.84 inches. On an uphill putt, a similar thing occurs - the ball will be traveling faster to roll out three feet past the hole (or whatever distance), but the back of the cup is a little higher so the ball only has to fall perhaps 0.8 inches.)

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So, what's the point of all of this?

If you like putting to large targets, strive to hit your ball about six to twelve inches past the cup.

17 inches, two feet... three feet... they're all too firm. The ball will be rolling too fast at the hole and it will be rolling too fast to have a very large target - 2.25 inches, 1.9 inches, and 1.4 inches respectively.

Okay, so why not strive for "dead at the hole" capture speed? After all, the hole becomes 4.25 inches wide then, right? Well, three reasons.

1. If you're off by an inch in terms of your speed, or two inches, you're virtually 100% certain not to make the putt. Never up, never in.
2. The lumpy donut. It's not a huge effect, but it can play a small role when the ball is moving that slowly.
3. Wobble. As a ball comes to a stop, the last six inches of its roll are really, really affected by small imperfections in the green. The ball will sharply break left and right on these small things (spike marks, a tuft of grass, a heel print) and nobody wants to see their putts swerve half an inch right because of a tiny little bump and miss the hole.

6-12 inches gives you a pretty darn big hole to putt into and it avoids the "wobble" problem.

You've probably heard about golfers hitting the ball "firmly" and "taking out the break." Well, guess what? You know all those putts that lip out? Capture speed problems. The hole was too small, the ball didn't have enough time to drop, and it hit the far side of the hole with most of the ball still above the edge of the hole, veered hard sideways off the back of the cup, and climbed out.

Give yourselves the biggest hole to putt to: strive to roll the ball six to twelve inches past the hole. You might leave one short now and then, but I guarantee you'll make more than enough additional putts to offset the occasional ones left short.

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Update 2017-11-09: Here are the numbers for other stimp speeds:

Effective Capture Width at Various Roll Speeds and Stimps

Speed	Stimp 8	Stimp 10	Stimp 12
Die	4.2"	4.2"	4.2"
6"	3.8"	3.9"	3.9"
1'	2.6"	2.7"	2.8"
2'	1.9"	2.1"	2.3"
3'	1.4"	1.7"	1.9"
4'	0.9"	1.3"	1.5"
5'	0.5"	0.9"	1.2"

Edited November 9, 2017 by iacas
Added Updated Numbers

[Shindig]

I took AimPoint on Saturday and the instructor discussed this.  A few people were shocked at that 17" isn't still true.  Among other problems with using Pelz's measurements today is that tour greens when he came up with the 17" rule were about as slow as a muni green these days.

[Beau F]

Great post iacas!  The physics behind the theory really explained what you were saying to me.  I'll keep this in mind the next time I go out.

[Stretch]

An additional nugget that can help with visualization -- a golf ball travels roughly five and a half inches (actually 5.2752) each time it fully revolves. So another way to think about it is that you want one to two rolls past the hole, no more.

[Ron Stewart]

wow! that gave me a headache, but was a great read. Thanks for posting that, I'm going to impress my friends with all that knowledge this weekend lol

[CalBoomer]

Before you throw Dave Pelz under the bus, here are a few other things to consider. Pelz, although a NASA engineer in a former life, did not not use theoretical calculations to come up with his "17 inch" rule. He used his mechanical robot putter at different settings. That was also how he determined that a putt is more likely to go in with the pin in left rather than taken out. There is an old saying that goes: "One of the tragedies of science is the slaying of a beautiful theory by ugly facts." As noted above, the lumpy donut, ball wobble, and never up never in are also factors to be accounted for. Since any physical act, like putt distance, follows Gaussian distribution and has a standard deviation (both plus and minus), one might expect that some distance must be added to the theoretical "falling" distance to increase the likelihood that the ball gets to the hole (ie, never up never in). So, if you take this theoretical consideration into account, and add some distance to that predicted above, Pelz's experimental data may not be so far off.

[Chicago Lefty]

This was some of the best info I came out of the Aimpoint seminar with.  Great visualization of the concept.

[Harmonious]

Pelz does get credit for the 17" number, but it is not a definite for all cases.  To quote him, from the "Putting Bible" (page 191):

"Understand that 17 inches is an average.  The actual optimum distance past varies a little (an inch or two) with almost every putt on every green, depending in its surface conditions.  Uphill and downhill putts have slightly different optimum speeds, although not by as much as you might expect.  Because downhill putts have gravity helping them stay on-line as they roll through the lumpy donut, their optimum speeds tend to be a little lower as they reach the hole, so they still roll close to 17 inches past (when they miss the hole) before they stop...

"Larger variations in the 17-inch distance occur on different grasses. On seaside greens, where the grain of Bermuda grass is very strong, I have seen optimum putting speeds roll balls as much as 36 inches past the back edge of the hole.  Compare this to U.S. Open greens, which I've measured with optimum speeds that roll balls only five inches past the cup..."

What he says about Bermuda greens is very true.  There is nothing like hitting a "perfect" putt dead at the hole, only to see the grain grab the ball at the last minute and curve it away.

[imtomtomim]

I love when people go and disprove Pelz.  He's such a big figurehead in golf instruction and I keep hearing left and right about how wrong concept x and y is.  hilarious

[Clambake]

Good stuff - I like when science is used in golf.    But I agree with CalBoomer that the math shown here isn't disproving Pelz's experimental conclusion of 17 inches.

First, the math you're showing assumes that it is necessary for the equator of the ball to strike below the rim of the hole in order for the ball to deflect downward into the cup, but I think two factors make this not quite so absolute.   First, the collision of the ball against the back of the cup is not an inelastic collision in that the earth rim is pliable and distorted briefly during the collision, absorbing some of the forward energy of the ball.    Also, even if the collision was completely inelastic, it is theoretically possible that the equator can strike above the rim deflecting the ball upwards but also killing enough of the forward velocity such that the ball can still land back on the hole side of the rim and fall in.     Both of these would add some additional velocity margin to the calculations you've shown.    Science shows us that if the equator of the ball strikes below the rim then it is physically impossible for the ball to not go in, but it doesn't prove that if the equator strikes above it must stay out.

Second, as CalBoomer pointed out the lumpy donut was a key factor in Pelz's hypothesis and conclusions - the ball is more likely to be deflected off path by that donut the slower it is rolling, so his theory was that it needed a greater velocity to counteract this effect but not so great that the ball would skate over the hole.     This is not factored into the capture speed analysis you've done.

I imagine someone really smart could model all of the real physical parameters with some pretty complex math and be able to show more definitive results.    However, it seems that perhaps in a way the capture speed and relative hole size analysis you've shown may actually help prove Pelz's theory more than disprove it.     Take the 6-12 inches metric you recommend, add in the inelastic collision with the back of the hole, and also factor in the lumpy donut factor and speed necessary to minimize its effect, and I suspect you'll come closer to Pelz's experimentally derived 17 inches.

[saevel25]

Its interesting math, and math is very precise, while real world is not. To me putting is an art form as well. Take a right to left banana putt that you need to aim almost horizontal to the hole. Now, i would contend that you might just be looking for the point were the ball will just go towards the hole. Its quite hard to say, i am going to hit this 6 inches past the hole. So really, it depends on the putt. I do say that make sure its going on the the far side of 6", give your putt a chance to get into the hole.

[The Recreational Golfer]

Originally Posted by Clambake

Good stuff - I like when science is used in golf.    But I agree with CalBoomer that the math shown here isn't disproving Pelz's experimental conclusion of 17 inches.

First, the math you're showing assumes that it is necessary for the equator of the ball to strike below the rim of the hole in order for the ball to deflect downward into the cup, but I think two factors make this not quite so absolute.   First, the collision of the ball against the back of the cup is not an inelastic collision in that the earth rim is pliable and distorted briefly during the collision, absorbing some of the forward energy of the ball.    Also, even if the collision was completely inelastic, it is theoretically possible that the equator can strike above the rim deflecting the ball upwards but also killing enough of the forward velocity such that the ball can still land back on the hole side of the rim and fall in.     Both of these would add some additional velocity margin to the calculations you've shown.    Science shows us that if the equator of the ball strikes below the rim then it is physically impossible for the ball to not go in, but it doesn't prove that if the equator strikes above it must stay out.

This, to me, suggests the putt that does a 180 and "lips in." For lengths of putts that I feel I can truly control the speed at which the ball approaches the hole, that's how hard I try to hit the putt--so it approaches the hole no faster than lip-in speed.

That qualifier is important if I want to put the Pelz or the AimPoint analysis, or even the perfect model, into practice. The farther the ball gets from the hole, the harder it is for me to have the ball approaching the hole at 17" speed, or whatever speed you name.

Think of the maximum distance you could putt a ball consistently to within a plus/minus 3 inch error, which is the error built into the AimPoint recommendation.

In practice, up to about 8 feet, I'm in control of speed to this degree. From 15 feet, not so much. From 30 feet, plus/minus 2 feet would be good.

The analysis is easy. Applying it is tough.

[iacas]

Originally Posted by CalBoomer

He used his mechanical robot putter at different settings.

The thing with the 17" rule is that Dave Pelz knows that it was bunk shortly after he published his data, but he never decided to qualify the information. The 17" figure he came up with was way too dependent on certain conditions - at Oakmont where the greens might stimp at 13, the ball can roll four feet past the hole and still have an effective capture width of over 3.6 inches because the ball is rolling so slowly it can still "catch an edge" and fall in. The faster the greens, the more likely the ball is to "catch an edge" at the same relative roll-out, because the roll-out is at a slower pace the faster the green.

As I said above, the information is legitimate and valid for a stimp 8 green that's relatively flat. You can extrapolate from there: the faster the green, or the more downhill the putt, the larger the "roll out distance" can be to stay at any particular "effective hole size." That's simply because the ball is moving more slowly. Uphill, the opposite - a ball that rolls two feet by might have an effective hole size closer to that of the 3 foot hole size above (1.4 inches) because it's traveling FASTER than a putt which will roll two feet by on a flat green stimping exactly the same. It's all about the time it takes the ball to fall 0.84 inches.

Originally Posted by CalBoomer

As noted above, the lumpy donut, ball wobble, and never up never in are also factors to be accounted for.

Sure, but that's why the optimal putting distance is not 0-6".

Originally Posted by CalBoomer

Since any physical act, like putt distance, follows Gaussian distribution and has a standard deviation (both plus and minus), one might expect that some distance must be added to the theoretical "falling" distance to increase the likelihood that the ball gets to the hole (ie, never up never in). So, if you take this theoretical consideration into account, and add some distance to that predicted above, Pelz's experimental data may not be so far off.

No, not at all. Pelz was testing balls that ROLLED that distance past the hole, he wasn't factoring in some sort of standard distribution from a human performing the act.

I'll try to make this very simple. Your ball needs enough speed (six inches past or so) not to wobble or veer from the lumpy donut, but not so much speed that you make the hole really small. If you want to keep putting to smaller targets, be my guest! :-) But I suspect this information will change the way some people putt.

And I'm not picking on Pelz just to pick on Pelz... he's just been about the only person to really put a number out there. I will point out that in your quote he only allows for a variation of "an inch or two." That's not enough of a variation in reality.

The take-away from this? The slower the putt is moving, the bigger the hole. Trying to ram putts in from short range might seem like a good idea, but consider how small you're effectively making the hole when you do that. (And Pelz wasn't that far off, but again, even those five to eleven inches greatly reduce the hole size...).

That's all.

P.S. I do think he gets the optimal distance bit wrong too. The effective hole size of a downhill putt that goes four feet past the hole might be exactly the same as the effective hole size of an uphill putt that goes only a foot past the hole. They might have exactly the same "effective hole size" because the speed the ball is traveling might be the same.

Originally Posted by Harmonious

What he says about Bermuda greens is very true.  There is nothing like hitting a "perfect" putt dead at the hole, only to see the grain grab the ball at the last minute and curve it away.

The worst grain can only affect the break of a putt about an inch or so over ten feet.

Grain has a tremendous effect on the effective STIMP (or speed) of the putt. Down-grain putts can roll more slowly along the tops of the grass than into-the-grain putts that are, well, into the grain and need speed.

That's how grain affects the break - by affecting the speed of the ball. It doesn't actually affect the raw curvature very much at all. You might call it semantics, but that's why AimPoint works regardless of the grain - if you get the speed right, the actual amount of break barely differs at all from a completely grainless green.

Originally Posted by Clambake

Good stuff - I like when science is used in golf.    But I agree with CalBoomer that the math shown here isn't disproving Pelz's experimental conclusion of 17 inches.

I didn't say it did. But Pelz did miss several things (or choose not to publish them).

And Pelz aside, too many people think that "firming the ball in the back of the cup" is the best strategy. It's not... or rather, it is if you like putting to really small targets. ;-)

Originally Posted by Clambake

Also, even if the collision was completely inelastic, it is theoretically possible that the equator can strike above the rim deflecting the ball upwards but also killing enough of the forward velocity such that the ball can still land back on the hole side of the rim and fall in.

What you're forgetting in that instance is that you're hitting the SIDE of the hole, you're not hitting the "smaller" effective hole size and thus more of the "back" of the hole. So the ball won't be deflected simply upwards - it'll be deflected upwards and to the side.

Yes, if you can hit the ball dead into the back of the cup with 2 feet of "speed" then you'll make them all day. But if you venture outside of, what, 1.9 inches or whatever the number was for 24", then you're going to lip out a lot of putts.

These numbers are't just theoretical math... They've been tested as well. Extensively.

Quote:

Originally Posted by Clambake

Science shows us that if the equator of the ball strikes below the rim then it is physically impossible for the ball to not go in, but it doesn't prove that if the equator strikes above it must stay out.

If you want to rely on about 1/20th of an inch, which only gives you about a 5% chance of "lipping in" the putt, be my guest. :-). The fact remains that the slower the ball is traveling at the hole, the larger the effective hole size, and the effective hole size shrinks a lot faster than you might normally think .

Originally Posted by Clambake

Second, as CalBoomer pointed out the lumpy donut was a key factor in Pelz's hypothesis and conclusions - the ball is more likely to be deflected off path by that donut the slower it is rolling, so his theory was that it needed a greater velocity to counteract this effect but not so great that the ball would skate over the hole. This is not factored into the capture speed analysis you've done.

Yes, it is. And I didn't come up with these numbers, as is clear from the one chart. AimPoint did this - both theoretically and mathematically. Their science is every bit as good, and is in fact better by a good margin - than any of the research Pelz did, what, 15-20 years ago? If their science wasn't good, they wouldn't predict the exact path of 80-foot triple-breaking putts like you see on TV.

Their science is good... I was just explaining more of the math behind it. From what they've told me they've accounted for the ball not quite falling 0.84 inches and the equator striking just a little above the hole. I was trying to keep the examples simple and just say "half the ball" and so on.

Originally Posted by saevel25

So really, it depends on the putt. I do say that make sure its going on the the far side of 6", give your putt a chance to get into the hole.

Silly counter-example aside (why wouldn't you want the ball to roll six inches to a foot past the hole in your example, anyway?), the point I'm making is that "firming a ball in the back of the cup" is giving it a reduced chance or even literally almost no chance of going in. The hole shrinks faster than you'd probably think.

[LankyLefty]

I really don't think their is on definitive number 6-12 is probably a lot better then 17 because it got wiggle room. Even if 17 inches is off how many people set up from 20 feet out and said "OK i need this putt to go 21 feet and 5 inches"? I think the biggest lesson from 17 inches was that you need to hit the ball through the hole not for it to stop on top of the hole. I also think greens are far to different from each other to say that any finite number would work and saying that you should hit it somewhere between 4 and 17 inches behind the hole doesn't mean a whole lot. In my mind the big lesson is that putts that stop at the whole don't go in much. You need to hit it a small distance past the hole to have the best chance weather that distance is optimally 12 inches or 17 is merely semantics to me.

[The Recreational Golfer]

I'm reminded on Nikki on one of the early Big Breaks (remember her? the one who hit a good shot on one of the shows and thought it was a life-changing event and couldn't figure out why the rest of the contestants were sniggering?).

Well, on the show where she faced elimination, she had to make a 20-foot foot putt, or something like that, and she ran it about 12 feet by, that part I do remember, and she said, "At least I gave it a chance." Egad. Even my wife, who doesn't play golf, couldn't believe it.

Last roll, in the hole, does it for me. I have had more slow-moving putts topple in the side (that would have stayed out if hit harder) than get knocked away in the last few inches by a bump in the green (than would have gone in if hit harder).

[CalBoomer]

Originally Posted by iacas

The slower the putt is moving, the bigger the hole. Trying to ram putts in from short range might seem like a good idea, but consider how small you're effectively making the hole when you do that. (And Pelz wasn't that far off, but again, even those five to eleven inches greatly reduce the hole size...).

Originally Posted by The Recreational Golfer

I'm reminded on Nikki on one of the early Big Breaks (remember her? the one who hit a good shot on one of the shows and thought it was a life-changing event and couldn't figure out why the rest of the contestants were sniggering?).

Well, on the show where she faced elimination, she had to make a 20-foot foot putt, or something like that, and she ran it about 12 feet by, that part I do remember, and she said, "At least I gave it a chance." Egad. Even my wife, who doesn't play golf, couldn't believe it.

Last roll, in the hole, does it for me. I have had more slow-moving putts topple in the side (that would have stayed out if hit harder) than get knocked away in the last few inches by a bump in the green (than would have gone in if hit harder).

Absolutely no argument that the putt that dies at the hole sees the biggest hole and has the greatest chance of going in. However, if my 10 foot putt has a standard deviation of +/- 1 foot from the 10 foot range and I am trying for 10 feet exactly, then approximately half of my putts will fall short of the hole, whatever its theoretical "size."  So, irrespective of "hole size" at various speeds, I should be aiming for 11 feet, just to make sure all my putts at least have a chance of going in. And I suspect it would require a reasonably good amateur to be able to meet the +/- 1 foot standard at 10 feet, especially if it were tested on sequentially different greens with no chance to "groove" the stroke.This is a purely statistical analysis of the "never up, never in" adage. Having said all that, I certainly agree that it makes no sense to try to ram in short putts.

[allin]

I think the real issue is whether you should try to hit putts firmly to control line or die them in to the hole.  On better faster greens I vote dying it into the hole.  But when green conditions are poor, I play public and muni courses, the risk of going by is worth it to compensate for the bumpiness. Either way if your distance control is such that you are 18 inches or less past the hole you are going to make a lot of putts and rarely 3 putt.  That is darn good putting/

[iacas]

Originally Posted by The Recreational Golfer

Well, on the show where she faced elimination, she had to make a 20-foot foot putt, or something like that, and she ran it about 12 feet by, that part I do remember, and she said, "At least I gave it a chance." Egad. Even my wife, who doesn't play golf, couldn't believe it.

Last roll, in the hole, does it for me. I have had more slow-moving putts topple in the side (that would have stayed out if hit harder) than get knocked away in the last few inches by a bump in the green (than would have gone in if hit harder).

First paragraph: you're right, I remember thinking the same thing. I love how in match play people "ram" the must-make putts too. Yes, you definitely want to get the putt to the hole, but goodness, just go for three feet past, not six!

Originally Posted by CalBoomer

Absolutely no argument that the putt that dies at the hole sees the biggest hole and has the greatest chance of going in. However, if my 10 foot putt has a standard deviation of +/- 1 foot from the 10 foot range and I am trying for 10 feet exactly, then approximately half of my putts will fall short of the hole, whatever its theoretical "size."

Nobody's suggesting you shoot for "die it at the hole" speed. If you shoot for 12 inches then every putt gets to the hole without the hole getting "too small."

Take a guy who never wants to be short. His range is +/- 3 feet. So he tries to get everything 3 feet past the hole.

The thing is that guy might be better off aiming for two feet, and leaving the occasional putt short, because the putts six feet by the hole are so unlikely to go in it's effectively the same as leaving the putt short. THEN you have to consider the fact that the distribution over that six feet is highly unlikely to be even - it may follow a bell curve or it may be weighted towards the guy always leaving putts short or long, and so that must be taken into account too.

What about the guy who, from 40 feet, is +/- 5 feet? Ten feet past has basically zero chance of going in, so that guy should probably still stick with about a foot past, because even the ones that go six feet by have almost no chance of going in... and then that guy should work on his distance control, because now we're being silly and he's a really bad putter. :-)

Originally Posted by CalBoomer

And I suspect it would require a reasonably good amateur to be able to meet the +/- 1 foot standard at 10 feet, especially if it were tested on sequentially different greens with no chance to "groove" the stroke.

Well that's a bit of a weird test. Warm up on the green beforehand. I don't think +/- 1 foot is very difficult.

Originally Posted by allin

I think the real issue is whether you should try to hit putts firmly to control line or die them in to the hole.  On better faster greens I vote dying it into the hole.  But when green conditions are poor, I play public and muni courses, the risk of going by is worth it to compensate for the bumpiness. Either way if your distance control is such that you are 18 inches or less past the hole you are going to make a lot of putts and rarely 3 putt.  That is darn good putting/

Agreed, to an extent. People tend to over-rate how "speed" can cancel out "bumps." We've all seen putts get deflected early on by a spike mark despite the ball having plenty of speed.