Increased Randomness on Putting

[Double Mocha Man]

On 9/19/2021 at 8:02 PM, Keep It Simple said:

...and player B who never makes a putt on a perfectly smooth putting surface.

Hopefully you weren't using me as your inspiration for player B.

[Wanzo]

10 hours ago, saevel25 said:

It doesn't change the fact that near the hole, a certain amount of made putts would miss and missed putts would be made

agree, but my question is....if there is not a hole, putt to a dot, does the gap between a good and bad putter increase (larger dispersion)....the initial question ( with my tweak of "no hole" 🙃.)

 

[ChetlovesMer]

22 minutes ago, Wanzo said:

agree, but my question is....if there is not a hole, putt to a dot, does the gap between a good and bad putter increase (larger dispersion)....the initial question ( with my tweak of "no hole" 🙃.)

 

I got this.

If there's no hole than neither the good putter nor the bad putter will make any putts. 

Did I get that right? 

[iacas]

38 minutes ago, Wanzo said:

agree, but my question is....if there is not a hole, putt to a dot, does the gap between a good and bad putter increase (larger dispersion)....the initial question ( with my tweak of "no hole" 🙃.)

Thing is… there is a hole.

Increased randomness decreases the skill.

It's that simple, Matt.

[Wanzo]

2 hours ago, iacas said:

Thing is… there is a hole.

The thing is, there's not in my question back.  The initial question makes more sense if it's about holed putts.  I guess that was the intent since that's how you did the math on the answer.  I don't think your answer takes into account strokes to hole out from longer distances, increased dispersion on those, three putts.  But whatever, I'll move on since you keep saying it's simple.

[saevel25]

4 minutes ago, Wanzo said:

I don't think your answer takes into account strokes to hole out from longer distances, increased dispersion on those, three putts.  But whatever, I'll move on since you keep saying it's simple.

It is simple... 

Lets say a bad golfer hits a putt on a line that would leave it 5-FT to the left of the hole. If there is some randomness on the green, each time he hits this putt, there is a chance it would end up 5'-6" from the hole, or maybe 4'-6" from the hole. The randomness doesn't necessarily cause ever putt to end up worse. Yes, the dispersion would increase if you map the putts.

Lets say this golfer hits 100 putts. If his perfect green shot zone is a 5-FT circle, then maybe the randomness shot zone is 5'-6" circle. Some of those 100 putts would end up further away, but with enough putts, and if it is equally random to end up further away or closer to the hole, then an equal number would end up closer. 

In reality, it will even its self out to not causing significant strokes lost (SGP). What matters more is just the putts that end up missed or made. 

[iacas]

15 minutes ago, Wanzo said:

The thing is, there's not in my question back.

Matt did a pretty good job of answering you with regards to three putting. It’s not factored into my math because it’s not particularly relevant. As discussed a ball that’s going to miss has a 50-50 shot of ending up closer or farther from the hole if it hits a bump.

[batchvt]

Mixing logic and statistics, without actually doing any statistics, can be misleading. For years people assumed that the short game was more important than the long game because 60% of the shots for most players came within 100 yards.  This is logical.  Mark Broadie blew this idea up with actual numbers by thinking about the consequences of the next shot's location on scoring.

I believe Wanzo is thinking about the effect of the next shot and he his correct that three putts will increase more for the poor putter than the better putter.

The reason Wanzo is correct is the statistics of the second putt are not symmetrical. From Broadie's stats, the make rate for and amateur at 2 ft is 93.2%. The make rate at 3 ft is 76.3%.  The make rate at 1 ft is going to be very very close to 100%. 

Notice the impact of moving from 1 ft to 2 fts is much smaller than moving from 2 ft to 3 ft.  It’s not a symmetrical affect. 

Every golfer intuitively know this. Do you worry when a put rolls out just a bit more than you thought, trickling  a foot by the hole?  No.  What about when the put keeps rolling out to 3 ft or 4 ft.  You're probably yelling at it to stop because you know each and every inch here hurts your chances of making the next putt more and more.

Since we have clean statistics for short putt make rates, lest just assume for now the second putt doesn't have bumps.

Say a putt would end up at 2 ft on pure greens.  If the bumps move a long putt that would have been at 2 ft to 3 ft half the time and to 1 ft the other half the time (randomness), the poor putters’s three putt rate goes up from 6.8% to 11.9%.  A 5.1% increase in three putt rate.

But a professional’s (better putter)’s stats look like this: 100% at 1 ft, 99.8% at 2 ft, 95.4% at 3 ft.  So if they get the same bumps- half to 1 ft, half to 3 ft- the better putters 3 putt rate goes from 0.2% to 1.3%, a 1.1% increase.

The randomness on where the first putt causes the worse player’s 3 putt rate it increase by 5 times more than the better player. 

Now maybe you think the plus/minus 1 ft is too wide, and it probably is.  But this doesn’t matter directionally because the outperformance by the better putter comes from the non-symmetric consequences of putting from different distances.  This effect still exists even if you think the puts only get bounced offline by a couple inches either way. 

Statistically the better putter doesn’t really care that much if they putt from 1 ft 6” or 2 ft 6”.  The bad player does care about that difference.

So in closing, Wanzo is correct, and it's Mark Broadie’s strokes gains that shows us why he is correct.  The bumpy green makes the poor putter three putt a much higher rate than the better putter. 

Edited October 3, 2021 by batchvt

[boogielicious]

35 minutes ago, batchvt said:

Mixing logic and statistics, without actually doing any statistics, can be misleading. For years people assumed that the short game was more important than the long game because 60% of the shots for most players came within 100 yards.  This is logical.  Mark Broadie blew this idea up with actual numbers by thinking about the consequences of the next shot's location on scoring.

I believe Wanzo is thinking about the effect of the next shot and he his correct that three putts will increase more for the poor putter than the better putter.

The reason Wanzo is correct is the statistics of the second putt are not symmetrical. From Broadie's stats, the make rate for and amateur at 2 ft is 93.2%. The make rate at 3 ft is 76.3%.  The make rate at 1 ft is going to be very very close to 100%. 

Notice the impact of moving from 1 ft to 2 fts is much smaller than moving from 2 ft to 3 ft.  It’s not a symmetrical affect. 

Every golfer intuitively know this. Do you worry when a put rolls out just a bit more than you thought, trickling  a foot by the hole?  No.  What about when the put keeps rolling out to 3 ft or 4 ft.  You're probably yelling at it to stop because you know each and every inch here hurts your chances of making the next putt more and more.

Since we have clean statistics for short putt make rates, lest just assume for now the second putt doesn't have bumps.

Say a putt would end up at 2 ft on pure greens.  If the bumps move a long putt that would have been at 2 ft to 3 ft half the time and to 1 ft the other half the time (randomness), the poor putters’s three putt rate goes up from 6.8% to 11.9%.  A 5.1% increase in three putt rate.

But a professional’s (better putter)’s stats look like this: 100% at 1 ft, 99.8% at 2 ft, 95.4% at 3 ft.  So if they get the same bumps- half to 1 ft, half to 3 ft- the better putters 3 putt rate goes from 0.2% to 1.3%, a 1.1% increase.

The randomness on where the first putt causes the worse player’s 3 putt rate it increase by 5 times more than the better player. 

Now maybe you think the plus/minus 1 ft is too wide, and it probably is.  But this doesn’t matter directionally because the outperformance by the better putter comes from the non-symmetric consequences of putting from different distances.  This effect still exists even if you think the puts only get bounced offline by a couple inches either way. 

Statistically the better putter doesn’t really care that much if they putt from 1 ft 6” or 2 ft 6”.  The bad player does care about that difference.

So in closing, Wanzo is correct, and it's Mark Broadie’s strokes gains that shows us why he is correct.  The bumpy green makes the poor putter three putt a much higher rate than the better putter. 

Welcome to The Sand Trap. Thanks for posting. Most of us know all about strokes gained to this book below. There are also quite a few threads on this is the Swing Thoughts section. When you have a chance, please pick an avatar.

Lowest Score Wins - Shoot Lower Scores on the Golf Course NOW

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Shoot lower scores on the golf course… NOW!

Also, the gap will narrow in the OP scenario.

Edited October 3, 2021 by boogielicious

[iacas]

1 hour ago, batchvt said:

I believe Wanzo is thinking about the effect of the next shot and he his correct that three putts will increase more for the poor putter than the better putter.

I'm considering that too. And yes, the bad player will three-putt at a slightly higher increase than the good player three-putts at an increased rate.

Where you (and @Wanzo) go wrong is that you're over-rating how often those three-putts will increase relatively. (Randomness also affects longer putts less so during the high-speed part of the putt, so you're likely also expanding your "putt distribution" model more than you'd find in the real world, but that's almost beside the point: the same bump that might deflect a ball 1° or slow it down an inch when it's rolling 0.5 MPH will deflect the ball substantially less rolling at 5 MPH).

There's also the distribution of the average distance putters face, the steep ramp of putts made from shorter distances, etc.

1 hour ago, batchvt said:

The reason Wanzo is correct

He's not correct, though. 🙂 Not overall. Will the poor putter three-putt more? Yep. Will they three-putt a bit more often than the better putter three-putts? Yes. But the better putter is going to two-putt more instead of making more so than the poorer putter two-putts instead of one-putting.

1 hour ago, batchvt said:

Every golfer intuitively know this.

These kinds of things aren't necessarily intuitive.

Intuitively people think that putting on faster greens is more difficult. And yet, studies have shown golfers of all ability levels putt better on faster greens. Good putters putt "more better," but even bad putters putt better. They make more three-putts due to poorer distance control, but they make more one-putts than they add three-putts, so the net gain is positive.

1 hour ago, batchvt said:

Say a putt would end up at 2 ft on pure greens.

The greens aren't pure! Your analysis falls down here in two ways: Both the good and bad putter are affected by that resulting putt, too.

We're talking about a relative change, and yet you've ignored the distance of the original putt.

A more likely scenario is this:

From 30' a scratch golfer averages 2.03 and a bogey golfers averages 2.16 putts (roughly). Here's how:

Golfer	1-putt	2-putt	3-putt	Total
Scratch	6%	85%	9%	2.03
Bogey	2%	80%	18%	2.16

The bogey golfer was already going to three-putt twice as often. 9% more often. And one-putt one-third as often.

You're failing to account for this built-in disparity. If we assume randomness helps and hurts evenly, as you did, then the bad putter has a 9% chance of helping them three putt less often while the good player has only a 4.5% chance of helping them avoid the three-putt. Additionally, the good player has a 3% chance that the ball that would go in the hole will be diverted away, while the poor player has only a 1% chance.

You've made the same error you're claiming we've made, but you've ignored the other end of the putt: where it starts. You're putting everyone at two feet, and ignoring where they started.

I understand what you're saying. But you're not considering where the shots originate just as you're saying that we're not considering the next putt. And I'm saying that I have considered the next putt, and it doesn't have as large an effect as the first putt does. Nor are you apparently considering the distribution of putts faced.

1 hour ago, batchvt said:

Now maybe you think the plus/minus 1 ft is too wide, and it probably is.

It probably is, yeah. But anyway…

1 hour ago, batchvt said:

So in closing, Wanzo is correct, and it's Mark Broadie’s strokes gains that shows us why he is correct.  The bumpy green makes the poor putter three putt a much higher rate than the better putter. 

He's not correct. FWIW I had this conversation with Mark a few years ago, about ball rollback stuff and "lighter" golf balls.

And I know a thing or two about this area… 😉

[batchvt]

4 hours ago, batchvt said:

Since we have clean statistics for short putt make rates, lest just assume for now the second putt doesn't have bumps.

Let's address this assumption as well. 

Mark Broadie wrote a paper that simulated the possible effect of hole size on scoring.  To do it, he modeled putting variables as normal distributions and then ran thousands of simulations so see how make rates changed.  So let’s do that with these short putts instead of just assuming the stats are the same.

At 3 ft pros make a 3 ft put 99.5% of the time and amateurs make those puts 76% of the time.  So the model is a normal distribution with a standard deviation of .75 inch so that the pro’s puts fall inside the 2.125 radius hole 99.5% of the time, and the amateur has a standard deviation where their puts fall within the hole’s radius 76% of the time. 

Now let’s assume every put gets bumped by a half inch either left or right with equal likelihood.  Run that model through 10,000 simulations and you get this.

Simulation of 3 ft putt made out of 10000 with 1/2" bump.
	Smooth	Bumpy	Change	% Change
Good Putter	9955	9865	90	0.9%
Bad Putter	7660	7458	202	2.0%

 

Now this is just simulated data, but it follows a thought process Mark Broadie used for a similar challenge.  The smooth make amounts are right where we would expect them to be.  So the model fit’s the base case. 

For the bumpy greens, the model the good putter makes 0.9% putts less per round, and the bad putter makes 2% less puts per round. 

The bad putter is negatively effected more by the bumps on the green than the good putter is. 

So using Mark Broadie’s modeling method the idea that bumps always mean the better player is hurt more than the bad putter in terms of make percentage is wrong.

On short putts, the bad putter’s make percentage will be affected more by the bumps. 

Back to the three putt example I gave earlier.  Not only will the bad putter have more three putts because they get bumped to further way for their second putt, even when they have that second cleanup put, the bumps will effect them more.  So this the effect of the bumps is going to be meaningful. @Wanzo is correct on this.

2 hours ago, iacas said:

From 30' a scratch golfer averages 2.03 and a bogey golfers averages 2.16 putts (roughly). Here's how:

Golfer	1-putt	2-putt	3-putt	Total
Scratch	6%	85%	9%	2.03
Bogey	2%	80%	18%	2.16

 

This is a good table.  And it highlights the key point.

With bumpy greens, both the bad putter and the good putter will three putt more.  But the bad putter will three put relatively more.  To explain what I’m saying, the good putter may now 3 putt 12% of the time, and the bad putter may now 3 putt 23% of the time.  This is because the bad putter will end up further from the hole after the first put at times due to the bumps, and on bumpy greens they will miss relatively more of their second short putts than the good player too as shown above.

The gap between the bad putter 3 putt % and the good putter 3 putt % grew from 9% to 11% in my made up example. What I’m saying is this gap will grow and it seems like you agree with this directionally.

2 hours ago, iacas said:

I'm considering that too. And yes, the bad player will three-putt at a slightly higher increase than the good player three-putts at an increased rate.

The question then is, does the gap in 1 putt percentage shrink between the bad player and the good player on one putts?  Two things to consider here:

1-I’ve shown it doesn’t shrink for short putts, it grows.  So an assumption that it will shrink much, if at all for longer putts, may not be well founded

2-Even if it does shrink, the relative benefit here is limited.  It can only shrink to zero, meaning the gains to the bad player are capped.  The relative difference is not capped when it comes to the relative benefits for the good player in 3 putts. 

To summarize.  It’s been stated that a good putter will be hurt relatively to a bad putter on bumpy greens in terms of make percentage, but I hope people see now, this isn’t true on short putts.  Bad putters are impacted more on short putts on bumpy greens. 

I’ve also shown that a bad putter is affected more by a random alternation between 1 ft second putts and 3 ft second putts, and shown that this is because the make rates at these distance are not symmetrical around the middle 2 ft putt.  Therefore, bad putter’s make rates for the second putt are going to fall relatively because the are putting from further away, and because they don’t make as many putts on bumpy greens when close to the hole relatively to a good putter.

Now I haven’t seen anyone say how the make rates are going to change between the good putter and the bad putter a distance, and this seems to be a the key point of your position.  How many fewer putts do you think the good putter will make, and how many fewer putts do you think the bad putter will make?

Edited October 3, 2021 by batchvt

[iacas]

7 minutes ago, batchvt said:

Let's address this assumption as well.

Oy.

Look, there's a simpler application here: any time you increase the randomness in something, you decrease the role skill plays.

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.

And let's bear in mind something else, here, too: we're talking about fractions of a percentage at the end of the day. A slightly lighter ball is probably not going to be going five feet offline even from 100' away.

And again…

3 hours ago, iacas said:

FWIW I had this conversation with Mark a few years ago, about ball rollback stuff and "lighter" golf balls.

8 minutes ago, batchvt said:

So the model is a normal distribution with a standard deviation of .75 inch so that the pro’s puts fall inside the 2.125 radius hole 99.5% of the time, and the amateur has a standard deviation where their puts fall within the hole’s radius 76% of the time.

Now let’s assume every put gets bumped by a half inch either left or right with equal likelihood.  Run that model through 10,000 simulations and you get this.

Simulation of 3 ft putt made out of 10000 with 1/2" bump.
	Smooth	Bumpy	Change	% Change
Good Putter	9955	9865	90	0.9%
Bad Putter	7660	7458	202	2.0%

 

So many bad assumptions here.

12 minutes ago, batchvt said:

For the bumpy greens, the model the good putter makes 0.9% putts less per round, and the bad putter makes 2% less puts per round.

The bad putter is negatively effected more by the bumps on the green than the good putter is.

You've not demonstrated that. You've made bad assumptions, injected your own constraints about the distance a ball is moved, the odds at which it's moved, and the distance from which it's hit. You've only demonstrated that if you make something up, you can make it seem to fit your assumed conclusion.

12 minutes ago, batchvt said:

So using Mark Broadie’s modeling method the idea that bumps always mean the better player is hurt more than the bad putter in terms of make percentage is wrong.

I'm unaware of anyone saying "from any distance with any injected constraint, the gap always narrows."

12 minutes ago, batchvt said:

@Wanzo is correct on this.

Still no. You're taking a very stunted view here.

18 minutes ago, batchvt said:

But the bad putter will three put relatively more.

You haven't demonstrated that, and even if you did, you'd also have to demonstrate that they'll two-putt instead of one-putting more often than the scratch golfer, etc.

12 minutes ago, batchvt said:

To explain what I’m saying, the good putter may now 3 putt 12% of the time, and the bad putter may now 3 putt 23% of the time.

I love when we just get to make shit up!

12 minutes ago, batchvt said:

1-I’ve shown it doesn’t shrink for short putts, it grows.  So an assumption that it will shrink much, if at all for longer putts, may not be well founded.

No you haven't. You did no such thing. You showed that a putt if randomly moved 6" closer or 6" (or one foot, or whatever the distance was) farther from the hole favors the better putter, you didn't show that given the same 5' putt which would be affected more.

12 minutes ago, batchvt said:

To summarize.  It’s been stated that a good putter will be hurt relatively to a bad putter on bumpy greens in terms of make percentage, but I hope people see now, this isn’t true on short putts.  Bad putters are impacted more on short putts on bumpy greens.

They aren't.

---

Look, I realize that what you're saying sounds like it's right to you, but dude, it's not.

[batchvt]

1 hour ago, iacas said:

And let's bear in mind something else, here, too: we're talking about fractions of a percentage at the end of the day. A slightly lighter ball is probably not going to be going five feet offline even from 100' away.

 

Why mention a lighter ball? I thought this question was about bumpy greens. 

[batchvt]

2 hours ago, iacas said:

 

Look, I realize that what you're saying sounds like it's right to you, but dude, it's not.

Thank you for saying that what I've written sound right.  I probably sounds right to other people too.

You did a very thorough job of saying I was wrong and had bad assumptions, but dude, you left out the reasons why. 

2 hours ago, iacas said:

Oy.

Look, there's a simpler application here: any time you increase the randomness in something, you decrease the role skill plays.

If I had to guess, this belief is the key reason many have argued that randomness decreases the gap between good putters and bad.  I understand this seem like it would be correct, but this is just a feeling and there is no settled fact or law of games that states this.

On the contrary, there are lots of debates on this topic when it comes to game design and how randomness effects outcome in terms of skill.  Just google “how does randomness affect skill” to see that this not a new topic, or a shallow one.

And most of those discussion end up at “it depends”.

You can’t say that anytime you increase randomness you decrease the role skill plays.  Sometimes this is true, and sometimes it’s not. 

As an example, wind adds an element of randomness to golf.  Does wind decrease the role skill plays?  I feel like many people would say that wind helps to identify skill in golf. 

My putt from 3 feet on bumpy greens is another example.  The reason the better player is not affected much in that model is most of their putts go into the hole in the middle of the cup. So a bump sill leads to a made putt nearly all the time.  But the poorer player has more putts go in on the edge of the hole, so the randomness changes the outcome of more of their putts.  Importantly the number of putts they barely  make to those they barely miss isn’t equal.  The randomness therefore effects the skilled putter less, while affecting the poor putter more. 

Now even if you don't like my assumptions for putting, many events in life model to a normal distribution, and it's not hard to see why this same logic applies to other games like archery, or darts, etc.  Once again, you can't just assume randomness reduces the effect of skill for every skill.  

Now, yes, these are just two examples.  But the key to understanding why the bad putter doesn’t benefit from the bumps is to realize “anytime” is not a correct statement.  Sometimes randomness reduces the impact of skill, sometimes it enhances it.  You have to study the consequences of the randomness to understand when each case is applies.

[batchvt]

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

Bumps (if large enough to deflect a ball that would go in out of the hole or large enough for a near miss to become a make) have a negative outcome 100% of the time when the ball is going in, and a positive outcome 50% of the time when the ball is going to be a near miss.

Or to put it in different terms, every bump on a ball that would be going in the middle has a negative outcome - it steers the ball farther away from the center of the hole, and every bump that steers the ball on a putt that's missing has a 50% chance of "helping" by steering it in the right direction.

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.  You need to get up to 2" bumps before you need to think about negative consequences of a ball heading hitting a bump when  at the dead center.  

[Piz]

Good putters would still be good putters; but the average putts per round would increase.

[iacas]

1 hour ago, batchvt said:

Why mention a lighter ball? I thought this question was about bumpy greens. 

Because that's the genesis of the discussion.

There's a lot you don't know, man.

1 hour ago, batchvt said:

Thank you for saying that what I've written sound right.  I probably sounds right to other people too.

"Sounds right to you" isn't the same as "is right."

1 hour ago, batchvt said:

You did a very thorough job of saying I was wrong and had bad assumptions, but dude, you left out the reasons why.

I disagree. Both my previous posts and that one up there have plenty of reasons why.

I'm really not big into meta discussions, either, so… let's keep this short, since you're not actually saying much.

1 hour ago, batchvt said:

If I had to guess, this belief is the key reason many have argued that randomness decreases the gap between good putters and bad.

You know who agrees with that? Mark Broadie. I talked about this briefly with him today and he agrees: increased randomness would narrow the skill gap in putting.

1 hour ago, batchvt said:

I understand this seem like it would be correct, but this is just a feeling and there is no settled fact or law of games that states this.

Sure there is. To pretend otherwise is to be intellectually dishonest. It's a bit muddy in some things where the line between skill and luck itself is blurry, but if you have a game of pure skill, the introduction of more and more luck just reduces the gap between the more skilled and the lesser skilled player.

1 hour ago, batchvt said:

On the contrary, there are lots of debates on this topic when it comes to game design and how randomness effects outcome in terms of skill.  Just google “how does randomness affect skill” to see that this not a new topic, or a shallow one.

Again, a lot of those articles are dealing with gambling, and stuff where skill and luck are more difficult to distinguish. And yet, one of the first articles I found, also said:

Quote

Rando-Chess is the same as normal Chess, except after the game is over, the players roll a die and if it comes up “1”, the winner becomes the loser and vice-versa. Though Rando-Chess has more randomness than Regular Chess, it has equal skill, since you can apply all your Chess knowledge to improve your chances of winning Rando-Chess. This seems to demonstrate randomness doesn’t limit skill.

Assuming it's a six-sided die, then it absolutely narrows the gap in skill in determining the outcome. Sure, you can still "apply" your skill to "improve your chances of winning," but any game where a guy who would lose on straight skill 100% of the time wins 17% of the time is displaying a narrowed gap. Assume between two players one wins 90% based on skill:

Regular Chess (almost pure skill^): 90% winning rate.
Rando-Chess (17% luck?): .9*.83 + .1*.17 = 76.4% winning rate.

^ Chess has a tiny bit of randomness in determining who goes first.

54 minutes ago, batchvt said:

You can’t say that anytime you increase randomness you decrease the role skill plays.  Sometimes this is true, and sometimes it’s not.

It's true far more often than it's not.

54 minutes ago, batchvt said:

As an example, wind adds an element of randomness to golf. Does wind decrease the role skill plays?  I feel like many people would say that wind helps to identify skill in golf.

Knowing how to play in the wind is a skill. It's not all that random. Though the wind will gust a little bit, it generally blows at roughly the same intensity and in the same direction. Given a large enough sample size, players all average higher in the wind, which means it's more difficult, but playing in the wind is a skill, not "random."

54 minutes ago, batchvt said:

My putt from 3 feet on bumpy greens is another example.

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…

54 minutes ago, batchvt said:

So a bump sill leads to a made putt nearly all the time.

Because you constrained it to such!

54 minutes ago, batchvt said:

The randomness therefore effects the skilled putter less, while affecting the poor putter more.

Precisely backward.

Putting has one of the narrowest gaps in skill difference in golf (a scratch golfer is going to out-putt a PGA Tour player far more often than they'll out-ball-strike them from 200 yards), and the randomness inherent in putting now is one of the big reasons why. Increase that randomness and the gap gets even narrower.

Have you ever rolled putts on a Perfect Putter? Give me a perfectly flat, uniform surface and I can probably make 95 or so out of 100 putts from 15'. Make the surface random but the same speed (maybe a Lego surface or something), and the more random, the more I'm going to miss.

54 minutes ago, batchvt said:

Now even if you don't like my assumptions for putting, many events in life model to a normal distribution, and it's not hard to see why this same logic applies to other games like archery, or darts, etc.

You can't make the assumptions you've made. You've made stuff up. You've said "oh, even if a bump from this distance moves the ball 0.5" the good putter is still going to make way more." You've made stuff up.

54 minutes ago, batchvt said:

Once again, you can't just assume randomness reduces the effect of skill for every skill.

No, man. I've not assumed this.

54 minutes ago, batchvt said:

Now, yes, these are just two examples.  But the key to understanding why the bad putter doesn’t benefit from the bumps is to realize “anytime” is not a correct statement.

It's true in golf. And by saying "anytime" I'm talking about over the long haul, not over any one specific time with made up constraints. I'm talking about thousands of putts hit by thousands of golfers. A large sample size.

55 minutes 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.

Yes it does! It's less likely to go in. It may still go in, but it requires a narrower window of ball speed due to the decreased capture width of the hole. Thus, the odds of the putt going in are decreased.

If you can't grasp that, if you make statements like that, I'm not sure you're equipped to have this kind of conversation, because you're clearly picturing some very narrow made-up constraints to "putting" to make a statement like that.

1 hour ago, batchvt said:

It has a negative outcome 0% of the time.

You're wrong. You're assuming the ball will have a pretty low speed so that it can still go in 100% of the time off-center. A non-zero number of putts that would go in if hit at the dead center of the hole will lip out or otherwise miss if hit 1" off-center.

1 hour ago, batchvt said:

You need to get up to 2" bumps before you need to think about negative consequences of a ball heading hitting a bump when  at the dead center.  

Nope.

[saevel25]

Every scenario you can think of, in terms of putting randomness, just makes it so better putters end up making less putts than they would on perfect greens. 

Go putt on a perfectly flat hardwood floor. A great putter would make a stupidly high percentage of putts. Now, go have him putt on bumpy carpet. In the end he would make less putts because the imperfections make a more random interaction between the ball and the carpet. 

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.