Increased Randomness on Putting

[iacas]

11 minutes ago, saevel25 said:

There is no way to wordsmith this in a way to make it that green imperfections (randomized events) would not close the gap between better putters and bad putters. 

The closer putting greens get to resembling Plinko, the less skill matters in determining the outcome.

In plinko, a good putter could three-putt from 3'. 😄

[boogielicious]

2 hours ago, batchvt said:

A putt going at the dead center of the hole that bumps one inch left or right doesn't have a negative outcome 100% of the time.  It has a negative outcome 0% of the time.  It still goes in. 

This is absolutely not a good assumption. Where does it get bumped? A foot from the hole, two inches, five feet? You keep creating scenarios to fit your flawed assumptions ignoring geometry. You also keep focusing on three putts and long putt s and not the basic point of the OP.

PGA Tour players make 50% of their 8 foot putts because they have the correct read, speed and start the ball on the correct line for the amount of break. Add imperfections that can bump the putt off line and they make less than 50% due to the imperfections. A ball going in dead center, getting bumped two feet from the hole will go in less times than it would on a perfect green. This is key.

A bad putter would be missing the hole due to a bad read, bad speed or bad start line and make less than 50% on a good green. If one of their off-line, off-speed, off-read putts gets bumped it has two possibilities. One, it gets bumped on line and goes in (less likely) or two, it gets bumped further off line, more likely. They still miss putts they would normally miss on a good green. So their make percentage goes down less because their putts are less likely to go in anyway.

You need to take a step back and review your assumptions. They are flawed and skewed to what you want the outcome to be.

[batchvt]

35 minutes ago, boogielicious said:

This is absolutely not a good assumption. Where does it get bumped? A foot from the hole, two inches, five feet? You keep creating scenarios to fit your flawed assumptions ignoring geometry. You also keep focusing on three putts and long putt s and not the basic point of the OP.

PGA Tour players make 50% of their 8 foot putts because they have the correct read, speed and start the ball on the correct line for the amount of break. Add imperfections that can bump the putt off line and they make less than 50% due to the imperfections. A ball going in dead center, getting bumped two feet from the hole will go in less times than it would on a perfect green. This is key.

A bad putter would be missing the hole due to a bad read, bad speed or bad start line and make less than 50% on a good green. If one of their off-line, off-speed, off-read putts gets bumped it has two possibilities. One, it gets bumped on line and goes in (less likely) or two, it gets bumped further off line, more likely. They still miss putts they would normally miss on a good green. So their make percentage goes down less because their putts are less likely to go in anyway.

You need to take a step back and review your assumptions. They are flawed and skewed to what you want the outcome to be.

Ask @iacas when it get bumped. I was replying his statement of a putt bumped off the center of the hole. Do you think those putts miss frequently?  Do they have a negative outcome 100% of the time?

Most of my putts that enter the hole 1" from the center go in.  

[iacas]

1 minute ago, batchvt said:

Most of my putts that enter the hole 1" from the center go in.

Most is not all:

3 hours ago, batchvt said:

A putt going at the dead center of the hole that bumps one inch left or right doesn't have a negative outcome 100% of the time.  It has a negative outcome 0% of the time.

Hmmm.

Also, this is disingenuous at best:

3 minutes ago, batchvt said:

Ask @iacas when it get bumped. I was replying his statement of a putt bumped 1" off the center of the hole.

That post by me was in response to YOUR statements about how putts that miss the center of the hole will still always go in. It's not true. In fact, a putt that rolls 2' past the hole won't go in the majority of the time if it's 1" off-center:

 

You keep making assumptions and applying constraints, man. Stop.

[batchvt]

13 minutes ago, iacas said:

Most is not all:

Hmmm.

Also, this is disingenuous at best:

That post by me was in response to YOUR statements about how putts that miss the center of the hole will still always go in. It's not true. In fact, a putt that rolls 2' past the hole won't go in the majority of the time if it's 1" off-center:

 

You keep making assumptions and applying constraints, man. Stop.

The disingenuous part is not necessary.

Most post about putts being negatively affected 100% of the time was in response to your post 2 weeks ago, not your reply today.  You said I didn't read your original post's explanation, and I was showing that your original explanation was flawed. 

2 hours ago, iacas said:

No, it isn't. You made up the constraints: you imagined a bell curve of a certain shape/size, you said that the ball would move 1/2", you didn't seem to account for the increased misses by the higher handicap player bouncing the ball back into the hole…

Ok lets discuss these constraints and assumptions.  Since this conversation is a bit all over the place and people are saying they can't think of a case where the better player would benefit, discussing what happens at 3 ft should make this clearer. 

 

I assumed a bell curve for putt dispersion.  Is this a bad assumption?  Many things in life model well with a a bell curve.  Mark Broadie used this assumption in one of his prior papers, so you can ask him if he thinks that was a bad assumption.  I'd like to know why you don't like this assumption if you have a problem with it.  

I assume Mark Broadie's values on make percentages for professionals and amateurs at 3 ft are correct.  Obviously you can challenge this assumption if you like, but it seems unlikely its very wrong.

I assume that the effective size of the hole is 3.4", since putt near the edge with any speed won't go in.  

With these three assumption, I assume I can determine the standard deviation of the players miss pattern on a typical green.  If you are ok with the first three assumption this assumption should clearly be reasonable.   

I assumed that the balls speed when putted from 3 ft is reasonably hole-able, and will be hit at a speed to go about a foot past the hole.  Most putts from 3 feet don't have a high rate of speed enough to cause major problems with the ball not going it if it hits the hole.  I'm also sure you would agree that the better putter is more likely to have the correct speed, so this assumption is going in your favor, not mine.

I assumed the bounce of exact half inch left or right. Now this assumption certainly depends on how bumpy the greens are.  Half inch feels like a pretty good size bump though from 3 ft away.  The assumption of a binary bounce makes the math simpler, but you can easily make the size of the bounce normally distributed and still see the same result directionally. 

I assumed every putt will be impacted by a bump.  This includes putts that would normally miss the hole bumping half the time back in the hole.  Why would you just assume I didn't include those?  

I assume the random Monte Carlo simulation will accurately how the effect of the bumps. If you don't like this assumption, then it's possible to do the math purely with cumulative distributions functions, but its often easier to understand Monte Carlo replications.  

If I missed an assumption you think I made, please call it out.  I'm trying to be very clear and open here, and not just state "your wrong".  

 

Here is a spreadsheet that shows these calculations (binary bounce and normal bounce).  You can save it to your own account and examine it further if you wish. 

Bumps effect on making putts - Google Sheets

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Sheet1 1 Hole width,4.25 Effective Cup Size,3.4 Simulation of 3 ft putt made out of 10000 with 1/2" bump. good player make % at 3 ft,99.54%,Z score,Standard Deviation,Smooth,Bumpy,Change,% Change bad player...

With these assumptions from three feet, It's clearly possible, even probable, for for the bumps to impact the poor putter more than the better putter.  This isn't a feeling.  Its math.  

Please tell me where this math is wrong or where the assumptions are meaningfully flawed.  Better yet, have your friend Mark tell you where this math is wrong or one of these assumptions are meaningfully flawed.  

 

Now I know that a three foot putt is just part of the picture.  But we hit lots of putts (maybe most) from around this distance.  And if you, or anyone else who reads this sees that bumpy greens will help the better putter from three feet relative to the poor putter, it will open their mind that this entire question of bumpy greens is not at all straight forward and obviously benefiting the bad putter.  

 

 

Edited October 4, 2021 by batchvt

[Vinsk]

[saevel25]

5 minutes ago, batchvt said:

I assumed a bell curve for putt dispersion.  Is this a bad assumption?  Many things in life model well with a a bell curve.  Mark Broadie used this assumption in one of his prior papers, so you can ask him if he thinks that was a bad assumption.  I'd like to know why you don't like this assumption if you have a problem with it.  

Yes I think it is. Bell curves are good when talking about difference in ability between human or animal populations. Example, Human height fit to a bell curve. 

If you are talking about a single person's ability to hit putts. I do not think that this fits a bell curve. It is dependent on distance. At 3-FT, you could see a make % of 95%. There is no bell curve here for a single golfer. 

For the randomness, I would assume equally distributed between bumped from 90 degrees left to 90 degrees right. So, a 180 degree range. You have a 1 and 180 chance of hit being bounced in any of those directions. This could be tightened up a bit with some more assumptions on the type of imperfections, the ball speed, you know physics. In a simplistic model, if we are talking about randomness, then it would not follow a bell curve. 

Flipping a coin does not follow a bell curve. It's a straight line at 50% heads or 50% tailed. Equally distributed. 

I ask, in what application did he use it, and would he use it for randomness of putting greens? You bring this up as some sort of validation, but since you do not know, I do not think you can assume this here. 

 

[batchvt]

1 hour ago, boogielicious said:

PGA Tour players make 50% of their 8 foot putts because they have the correct read, speed and start the ball on the correct line for the amount of break. Add imperfections that can bump the putt off line and they make less than 50% due to the imperfections. A ball going in dead center, getting bumped two feet from the hole will go in less times than it would on a perfect green. This is key.

The reason I'm not looking at 8 ft putts is they don't happen very often.  This is Mark Broadie's stats for the distance of the first putt on the green for amateurs.

Distance	Occurrence of First Putt
2	1.15
3	0.46
4	0.86
5	0.86
6	0.86
7	0.89
8	0.89
9	0.89
10	1.76
15	2.62
20	1.75
25	1.25
30	1.47
40	1.28
50	0.93

 

Notice that 8 ft putts are not common as first putts.  Whats common are longer putts.  And of course there are second putts, about 15 of them, which usually occur near the hole, say around 2 to 3 feet.

So why judge the answer on putts that are rare, the 8 ft putts, and not on the putts that are common?  Instead shouldn't we first look at the 2-3 foot putts and then the 15-40 ft putts?  That seems like the logical path doesn't it?

 

[saevel25]

Just now, batchvt said:

So why judge the answer on putts that are rare, the 8 ft putts, and not on the putts that are common?  Instead shouldn't we first look at the 2-3 foot putts and then the 15-40 ft putts?  That seems like the logical path doesn't it?

No, because imperfections and randomness are governed by the physics. There is nothing changing from a 2-3' putt to a 60' putt. 

[batchvt]

6 minutes ago, saevel25 said:

Yes I think it is. Bell curves are good when talking about difference in ability between human or animal populations. Example, Human height fit to a bell curve. 

If you are talking about a single person's ability to hit putts. I do not think that this fits a bell curve. It is dependent on distance. At 3-FT, you could see a make % of 95%. There is no bell curve here for a single golfer. 

For the randomness, I would assume equally distributed between bumped from 90 degrees left to 90 degrees right. So, a 180 degree range. You have a 1 and 180 chance of hit being bounced in any of those directions. This could be tightened up a bit with some more assumptions on the type of imperfections, the ball speed, you know physics. In a simplistic model, if we are talking about randomness, then it would not follow a bell curve. 

Flipping a coin does not follow a bell curve. It's a straight line at 50% heads or 50% tailed. Equally distributed. 

I ask, in what application did he use it, and would he use it for randomness of putting greens? You bring this up as some sort of validation, but since you do not know, I do not think you can assume this here. 

 

Mark Broadie used a normal distribution for the trajectory of the putt in this paper.   He was trying to figure how how many more putts someone would make on a larger hole.  

(PDF) A simulation model to analyze the impact of hole size on putting in golf

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PDF | We develop a model of golfer putting skill and combine it with physics-based putt trajectory and holeout models to study the impact of doubling... | Find, read and cite all the research you need on ResearchGate

The normal distribution shows up in a lot of places, and it does seem somewhat reasonable to use here.   Plinko, interestingly enough creates a normal distribution, so at a minimum it addresses @iacas plinko quip.  

[iacas]

14 minutes ago, batchvt said:

The disingenuous part is not necessary.

I disagree. I call it like I see it. You're being disingenuous. You didn't bump on "intellectually dishonest" but you bumped on "disingenuous"? Okay.

14 minutes ago, batchvt said:

Most post about putts being negatively affected 100% of the time was in response to your post 2 weeks ago, not your reply today. You said I didn't read your original post's explanation, and I was showing that your original explanation was flawed.

It's not flawed, you misread it, seemingly by ignoring the second paragraph you quoted.

14 minutes ago, batchvt said:

Ok lets discuss these constraints and assumptions.  Since this conversation is a bit all over the place and people are saying they can't think of a case where the better player would benefit, discussing what happens at 3 ft should make this clearer.

It doesn't, no. Most putts on the golf course don't happen at three feet.

14 minutes ago, batchvt said:

I assumed a bell curve for putt dispersion.  Is this a bad assumption?

Yep.

14 minutes ago, batchvt said:

I assume that the effective size of the hole is 3.4", since putt near the edge with any speed won't go in.

Effective hole size is much smaller than you seem to think.

14 minutes ago, batchvt said:

If you are ok with the first three assumption

Well, there goes that…

14 minutes ago, batchvt said:

Most putts from 3 feet don't have a high rate of speed enough to cause major problems with the ball not going it if it hits the hole.

Uhm… no. Another assumption. A lot of people just kinda bang in their three footers. It's one of the reasons guys miss from three feet - they don't appreciate how small the capture size of the hole is if the ball rolls at 2' or 3' past speed.

14 minutes ago, batchvt said:

I assumed the bounce of exact half inch left or right.

Right, because that's exactly what happens.

Look, I'm not interested in these sorts of things. You keep adding constraints on top of faulty assumptions.

14 minutes ago, batchvt said:

I assumed …

I assume …

If I missed an assumption you think I made, please call it out.  I'm trying to be very clear and open here, and not just state "your wrong".  

It's "you're."

14 minutes ago, batchvt said:

You can save it to your own account and examine it further if you wish.

No thanks.

14 minutes ago, batchvt said:

 

It's math.

It's math with a ton of assumptions and constraints. It's not representative of real-world putting.

14 minutes ago, batchvt said:

Please tell me where this math is wrong or where the assumptions are meaningfully flawed.

2+2=4, and the hole is 4.25" wide, ergo, I am correct. Please, show me where this math is wrong.

14 minutes ago, batchvt said:

But we hit lots of putts (maybe most) from around this distance.

Maybe? And you wonder why you can't be taken seriously?

14 minutes ago, batchvt said:

And if you, or anyone else who reads this sees that bumpy greens will help the better putter from three feet relative to the poor putter, it will open their mind that this entire question of bumpy greens is not at all straight forward and obviously benefiting the bad putter.

The gap narrows. The more putting resembles plinko, the more luck plays a role and the narrower the gap gets.

It may not be common sense, but it's statistically accurate.

The better player holes more putts that have a chance of missing due to an increase in randomness, and the poor putter misses more putts that have a chance of being holed due to an increase in randomness.

Putting is already one of the most random parts of golf, which is a big part of the reason the gap in skills is already pretty darn narrow.

Again, with a Perfect Putter on a dead-flat surface, I could probably make 10 out of 10. On a synthetic putting green like the one we have downtown, 3 out of 10, 4 out of 10 are common. If we get 5/10, it stands out.

The increase in randomness drops the make rate from not too far out from 100% to 30% pretty commonly, because while balls can be deflected 1-2" from that distance, they're not often deflected that much from shorter distances. You keep making bad assumptions and piling on your own ridiculous constraints.

19 minutes ago, batchvt said:

The reason I'm not looking at 8 ft putts is they don't happen very often.

Literally tap-ins are the most common, so why not just focus on those?

That you have to ask a question like this shows how poorly you understand the problem.

12 minutes ago, batchvt said:

Plinko, interestingly enough creates a normal distribution, so at a minimum it addresses @iacas plinko quip.

That's only true when you drop it from the center (and the theoretical version of plinko are often triangular, not rectangular like the game show).

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Here's the deal, man: you've yet to show anything compelling. You think you have, but it's all hidden under a facade of made-up stuff. Fabrications of faulty assumptions and crafted constraints.

I'm out. You're not making a solid case here at all.

[batchvt]

20 minutes ago, iacas said:

It's math with a ton of assumptions and constraints. It's not representative of real-world putting.

 

Sounds like the same thing critics of strokes gained say as well.  Funny how when that math agrees with your view, it's correct and representative of the real world, and when it doesn't, then its not representative.  

25 minutes ago, iacas said:

Look, I'm not interested in these sorts of things. 

 

Which sorts of things? Models that describe how golf is played and works and understanding the variables that effect your score?  My bad, that that seemed exactly like the kind of things you were interested in.  I thought you would respond with what would be a better choice for those assumptions if you disagreed, but if trying to understand golf with mathematical models isn't your thing then I'm sorry I asked.  

 

31 minutes ago, iacas said:

It's "you're."

 

I see you are interested in spelling, and good at it too.  You are correct.  Thank you for replying with an answer that states what you think "it is" an not just that I was wrong.   

40 minutes ago, iacas said:

Here's the deal, man: you've yet to show anything compelling. You think you have, but it's all hidden under a facade of made-up stuff. Fabrications of faulty assumptions and crafted constraints.

Compelling to you.  Plenty of other people who's first gut instinct told them that the spread would widen or stay the same now have grounds to know they had a reason to think that way. It was ok and logical to think the spread would widen or stay the same.  When one gets down to it, the real answer is "it depends on how bumpy are the greens and how different are the skills the players ."  You can't universally answer the question of which putter is impacted more from bumps because there are too many variables. Like all complicated problems, adjusting those variables doesn't universally lead to the same answer for any and all sets of variables. 

I'm glad that those people now have seen another side to this debate and that there is math and logic to support their intuition.   

 

[iacas]

9 minutes ago, batchvt said:

Sounds like the same thing critics of strokes gained say as well.

No.

9 minutes ago, batchvt said:

Compelling to you. Plenty of other people who's first gut instinct told them that the spread would widen or stay the same now have grounds to know they had a reason to think that way.

Faulty grounds. Grounds based on assumptions and constraints that don't accurately represent real-world situations.

But you do you. I'm going back to this:

1 hour ago, iacas said:

Here's the deal, man: you've yet to show anything compelling. You think you have, but it's all hidden under a facade of made-up stuff. Fabrications of faulty assumptions and crafted constraints.

I'm out. You're not making a solid case here at all.

[boogielicious]

8 hours ago, batchvt said:

Ask @iacas when it get bumped. I was replying his statement of a putt bumped off the center of the hole. Do you think those putts miss frequently?  Do they have a negative outcome 100% of the time?    

Most of my putts that enter the hole 1" from the center go in.  

First, no where in the above posts did anyone say “they have a negative outcome 100% of the time” without qualifications. Please go back and read the above posts, especially post #40.

If they get bumped 1 inch off line, 1 inch from the hole, they may go in. If that same bump is four feet from the hole, it is deflected off its line and is going greater speed. It is now on a new line and will most likely miss the hole. It’s basic geometry. You’ve deflected an object off its target path. If it was going to go in because you are a dead-on-balls accurate putter, it will now more likely miss. If you were going to miss by two feet because you are a terrible putter, then you will still miss. So the bad putter misses about the same and the good putter misses more than they would have on good greens.

I feel you are vastly over complicating your thought process. 

[iacas]

On 9/20/2021 at 1:54 PM, iacas said:

Let's make an extreme example. You have one putter that makes 80% of his putts, and another that makes 50%. The gap is 30% or 0.3 strokes (1.2 versus 1.5).

You introduce enough randomness that 25% of the putts that were going to go in miss and 5% of the putts that were going to miss go in.

The gap is now:

• 0.8 * .75 + 0.2 * .05 = 61%.
• 0.5 * .75 + 0.5 * .05 = 40%

What was a 30% gap is now a 19% gap. The gap narrows.

This is why you’d have had better luck if you had stuck with three putting talk.

[GolfLug]

2 hours ago, boogielicious said:

I feel you are vastly over complicating your thought process. 

This.

Over millions of putts there could a hundred outlier cases, but it should suffice to stay higher the randomness, shorter and wider the bell curve. Intuitively one would know that taller and narrower the original distribution more they stand to loose. I hadn't thought about it initially. 

The individual distance statistical acrobatics seem to only paralyze. 

[boogielicious]

All good science starts with looking at the problem from the simplest viewpoint. In the OP, we don’t have data to do an analysis. We can look up make percentages from various sources, LSW and Broadie, but we have no actual numbers to determine if results are in a normal distribution or other or length of putt, slope, etc.

It is best to then do a thought experiment. We are on a perfect green with a small slope (the slope doesn’t really matter in the experiment). The world best putter can putt 10 putts perfectly into the hole every time because they have the perfect speed, read and start line and their stroke is perfectly repeatable. Their ball falls into the hole at the same spot every time at the same speed which would only go 4” past the hole if it was not there.

The second putter is not very good. They don’t read puts well, cannot start the ball on line very well and cannot control speed very well. In their 10 putts, 9 miss the hole by a lot, 2-3 feet on a 10 foot putt, and miss left, right, long and short. Only one goes in because it was on the right line but not necessarily the right speed. 

Now we introduce variables into the perfect green in the form of bumps, small indentations and different grass length than can vary speed and redirect the ball to some degree. The perfect putter now, using the exact same stroke, putts again. They use the same stroke because the average variation on the green would give the same read. The perfect putter now will miss some putts due to these variables. For the thought experiment, let’s say they now miss 2/10.

The bad putter, using their bad technique now putts again. They still cannot read very well, have the same variable speed and cannot start the ball on their intended line as before. Would it make sense now with the introduced variables that they would suddenly make more putts? Probably not. They most likely would be affected the same as the good putter in terms of the speed being off and bumps redirecting the putt. But let’s say they now make 2/10 due to some randomness. 

The make percentage between the perfect putter and bad putter would get closer. Even if the bad putter now makes zero putts or 4 putts, the percentage narrows because the variation affects the perfect putter more.

[Wanzo]

17 hours ago, iacas said:

You'd have been better off trying to stick with your "increase in three-putts" thing, because from short range it's almost entirely about make rates versus two-putt rates, and it's easy to show how the gap narrows on those, as I've done above. Your only real chance was to try to show how the small increase in three-putts by the bad putter (who three-putts plenty on his own right now) would have outweighed the advantage they gain on the shorter putts

i didn't read the last two pages in full, but this was my main initial thought.  it could be wrong, but it's why i came to my conclusion.  I'd end with this.  Does the same logic work for 100 yard shots where making it is not statistically relevant, the skill is simply how close can you hit this ball to the hole on average.  A good player versus poor player with perfect conditions.  Then add in random lies and gusts of wind.  I would think it increases the average proximity for the poor player more.  Now in the putting example, it would totally depend on the lengths and types of putts you  are talking about.  shorter putts with a decent chance of making, i get the reasoning why less makes (1-putts) so helps narrow the gap.