Increased Randomness on Putting

[batchvt]

36 minutes ago, saevel25 said:

It would be hard to assume this. 

1. Does reading a green follow a normal distribution curve? I highly doubt it.
2. Does hitting putts a certain distance follow a normal distribution curve, maybe. 
3. Does hitting putts on the line you want follow a normal distribution curve, maybe.  
4. Does lining up to the line you want follow a normal distribution curve, not entirely sure. 

Ok, so all these things are things a person can control, are skill based. 

So now, take all of these, put them into an equation, and ask does that create a normal distribution curve. This is the issue I have with this line of thought on normal distribution curves. There is a lot that go into putting, and not all of it is normally distributed. 

THEN! add in green imperfections, which basically throws the normal distribution out the window. 

I agree it's complicated. 

What distribution do you think makes more sense to use than normal.  Or do you only think you can understand the very complicated answer of where ball goes by trying to model each variable of putting independently.  It's perfectly reasonable to think you need that much complexity to model the potential paths of balls on the green.  I would probably agree that my model is likely over simplified.  

[batchvt]

3 hours ago, boogielicious said:

Broadie’s paper is about strike directional errors for capture speed WRT hole size. No where does he state that the ball will end up in a normal distribution from the hole due to green reading errors, speed calculations or technique for good versus bad putters. The directional errors are in a normal distribution, not the resulting end location of the putt. He also does not discuss increase randomness of the putting surface. So it does not apply to this particular discussion. 

You again are missing the point. I was not claiming in any way that what you are stating I said. I did not “try” to create false data. I gave you opposite ends of a particular situation to demonstrate the simple math. You are purposely confounding what others are telling you. You keep making incorrect statements as absolutes and trying to do data analysis where you have no actual data for this scenario.

This is very tiring because you are not discussing, your are just being contrary.

Another great post. Glad to see you recognize how complicated understanding the ball's path on the green is.  Green reading, speed calculations, techniques for both bad and good putters, actual slopes, optimal speed for entering the hole, and then of course bumps.  A wide spectrum of inputs.  It's no wonder Mark Broadie thought he needed 14 variables to understand how a putt travels across the green.

So needless to say, I'm confused how, if Mark Broadie, one of the most respected, if not the most respected golf statistician, felt he need to get to this level of complexity to figure out the impact of a large hole on putting, but my, much less sophisticated method is too complicated, and your extremely simplified opposite ends of the spectrum thought experiment has enough detail to understand the problem?

[saevel25]

11 minutes ago, batchvt said:

I agree it's complicated. 

What distribution do you think makes more sense to use than normal.  Or do you only think you can understand the very complicated answer of where ball goes by trying to model each variable of putting independently.  It's perfectly reasonable to think you need that much complexity to model the potential paths of balls on the green.  I would probably agree that my model is likely over simplified.  

I wouldn't think it matters since something random, like imperfections in a green. In the end, randomness is more towards equally distributed to  a list of possible outcomes. Being equally distributed, it would hurt very skilled person over a not very skilled person. 

 

[batchvt]

1 hour ago, saevel25 said:

I wouldn't think it matters since something random, like imperfections in a green. In the end, randomness is more towards equally distributed to  a list of possible outcomes. Being equally distributed, it would hurt very skilled person over a not very skilled person. 

 

I think you are saying you believe the distribution at the hole will be like a uniform distribution, with the same probability at every point.  Is that correct?

[iacas]

5 hours ago, batchvt said:

You don't think Jordan Spieth was one of the best, if not the best putter in the mid 10's?

That's not what you said. You said "the best putter of the mid 10's." No, Jordan wasn't that.

5 hours ago, batchvt said:

You assumed the pro putter didn't miss the line at all from 10 ft, and had no distribution.

You're embarrassing yourself at this point. And you don't even understand why.

[boogielicious]

1 hour ago, batchvt said:

Another great post. Glad to see you recognize how complicated understanding the ball's path on the green is.  Green reading, speed calculations, techniques for both bad and good putters, actual slopes, optimal speed for entering the hole, and then of course bumps.  A wide spectrum of inputs.  It's no wonder Mark Broadie thought he needed 14 variables to understand how a putt travels across the green.

So needless to say, I'm confused how, if Mark Broadie, one of the most respected, if not the most respected golf statistician, felt he need to get to this level of complexity to figure out the impact of a large hole on putting, but my, much less sophisticated method is too complicated, and your extremely simplified opposite ends of the spectrum thought experiment has enough detail to understand the problem?

Mark Broadie came to the same conclusion. By increasing the hole size, the effect of skill was reduced and the amateurs improved more than the pros and therefore the gap narrowed.

Quote

We developed a model of golfer putting ability and combined it with physics-based putt trajectory and holeout models. The golfer putting model incorporates both physical skill, which reflects the golfer’s ability to putt with a desired target velocity and angle, and green reading skill, which reflects the golfer’s ability to estimate the slope of the green. The model was calibrated to real-world professional and amateur golfer data. Optimal putting strategies were found using stochastic dynamic programming. We analyzed the impact of doubling the hole radius on professional and amateur player putting performance. As expected, doubling the hole radius improves the performance of both professional and amateur golfers. However, the relative performance improvement for amateur golfers is larger.

It’s the same in our scenario. Randomness reduces skill and the gap narrows. Post 40 explains this but you seem to ignore that. 

[batchvt]

7 hours ago, boogielicious said:

In very simple math terms, if a person who has a higher percentage for making putts misses more, their make percent will get closer to a person who has a lower make percent who misses more putts.

 

 

In very simple math terms, you are not defining the second variable of the equation. You are not considering the difference in miss rate due to variability, rather you're assuming that the “misses more” rate of player A will be equal or greater than the “misses more” rate of player B?  This is the biggest factor and it’s not being addressed with your math. 

 Trackman measured the launch direction for the average PGA tour player at +/- 0.5 degrees and the launch direction for the average amateur player at +/-0.8 degrees.  We know that even if the A player and B player were equally skilled at playing break and pace, the A player's misses would be nearer to the hole than the B player.

 Thus it would take a larger bounce to move a typical B player's miss back to the hole than it would for player A.  The relationship between the A player's miss and the B player's miss may stay fairly constant even as the magnitude of bounce direction increases.  In other words, it’s likely going to be easier for player A’s ball to be bounced back into the hole than player B's ball.

This is why you can’t just oversimplify the problem and assume away the complex aspects of how bounces affect putts.  It’s just not a simple one-variable solution. 

[boogielicious]

10 minutes ago, batchvt said:

 

In very simple math terms, you are not defining the second variable of the equation. You are not considering the difference in miss rate due to variability, rather you're assuming that the “misses more” rate of player A will be equal or greater than the “misses more” rate of player B?  This is the biggest factor and it’s not being addressed with your math. 

 Trackman measured the launch direction for the average PGA tour player at +/- 0.5 degrees and the launch direction for the average amateur player at +/-0.8 degrees.  We know that even if the A player and B player were equally skilled at playing break and pace, the A player's misses would be nearer to the hole than the B player.

 Thus it would take a larger bounce to move a typical B player's miss back to the hole than it would for player A.  The relationship between the A player's miss and the B player's miss may stay fairly constant even as the magnitude of bounce direction increases.  In other words, it’s likely going to be easier for player A’s ball to be bounced back into the hole than player B's ball.

This is why you can’t just oversimplify the problem and assume away the complex aspects of how bounces affect putts.  It’s just not a simple one-variable solution. 

If you want to create a multi-variable designed experiment, go right ahead. You will come to the same conclusion. From post 40:

Quote

To the majority of you getting this one wrong…

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.

   Reveal hidden contents

The good putter is punished, even though he's punished at the same "rates" as the bad putter, at a higher "value" because he hits more putts that would have gone in, while the bad putter hits more putts that could potentially only be directed in.

To put it another way, there's a larger possible "negative" adjustment or change for the good putter and a larger possible "positive" adjustment or change for the bad putter.

This is true in pretty much* all cases: the more luck plays a role, the less skill plays a role.

* I'm a "never say never or always" kinda guy. I can't think of a time when an increase in randomness or luck also increases or at least doesn't reduce skill, but again… see the first sentence here in this asterisk.

 

[saevel25]

57 minutes ago, batchvt said:

I think you are saying you believe the distribution at the hole will be like a uniform distribution, with the same probability at every point.  Is that correct?

I am talking about how when ball impacts an imperfection, it will produce a random outcome. The list of possible outcomes is most likely equally distributed. 

1. Ball bounces right
2. Ball bounces left
3. Ball bounces forward
5. Ball bounces somewhere between right and forward
6. Ball bounces somewhere between left and forward

If you break it down into degrees, there is 1/180 degree chance the ball is deflected from left all the way around to right. I exclude the ball bouncing backward, because there would be no imperfection to cause the ball to bounce back. 

The outcome on a perfect surface might be predictable based on some sort of probability curve that includes variability in putter speed, face angle, putter path, angle of attack. 

When you throw in imperfections, then the outcome becomes less predictable AKA random. 

If things are random, there is less skill required to achieve a preferred outcome. 

 

[Bonvivant]

2 hours ago, saevel25 said:

I exclude the ball bouncing backward, because there would be no imperfection to cause the ball to bounce back.

This isn't particularly important to your point, but have you never had a ball get slowed down by something? I would call that "back", as in a deceleration greater than that of a "perfect" surface. All of your points are valid, but I was imagining this surface as somewhat uniformly imperfect. There is the chance that a good putter's perfect putt that would go in the heart or stop 6-18" past the hole would hit equal left and right bumps, but more "back" bumps than forwards ones and never even makes it to the hole.

Edited October 5, 2021 by Bonvivant

[saevel25]

4 minutes ago, Bonvivant said:

This isn't particularly important to your point, but have you never had a ball get slowed down by something? I would call that "back", as in a deceleration greater than that of a "perfect" surface.

No

We are not talking about deceleration, but direction the ball gets deflected from it's original path. Meaning, the imperfection would need to be so bad that it causes it to hop backwards. 

 

[batchvt]

Ok lets actually run through this in detail.I’m going to show that the OP may be correct when it comes to how bumpy greens effect individual putt make rates, but wrong about how it effects the putters performance overall.

I’ve already discussed how I’m modeling the putts.You can see it here here.

Make rates have been captured for professionals and amateurs on todays greens.I’ve previously referenced a paper by Mark Broadie that has a set of those make rates which will be used here.

Distance (ft)	Pro Make Rate	Average Make Rate
2	99.87%	93.20%
3	95.40%	76.30%
4	84.80%	60.40%
5	73.00%	48.10%
6	62.30%	39.40%
7	53.80%	33.20%
8	46.80%	28.20%
9	41.00%	24.30%
10	36.40%	21.10%
15	22.00%	12.30%
20	14.60%	8.10%
25	10.30%	5.80%
30	7.60%	4.60%
40	4.70%	3.00%
50	3.30%	2.20%

These are the make rates I set my model to match.After running each distance though my Monte Carlo model these are the make rates I get:

Distance	Pro Make Rate	Average Make Rate	Simulated Pro Make Rate	Simulated Amateur Make Rate
2	99.87%	93.20%	99.88%	93.14%
3	95.40%	76.30%	95.35%	76.02%
4	84.80%	60.40%	84.89%	60.52%
5	73.00%	48.10%	73.65%	48.24%
6	62.30%	39.40%	62.92%	39.65%
7	53.80%	33.20%	53.52%	33.12%
8	46.80%	28.20%	46.35%	29.11%
9	41.00%	24.30%	41.33%	24.31%
10	36.40%	21.10%	35.49%	21.85%
15	22.00%	12.30%	23.25%	12.05%
20	14.60%	8.10%	14.96%	8.80%
25	10.30%	5.80%	10.16%	5.32%
30	7.60%	4.60%	7.45%	4.75%
40	4.70%	3.00%	4.62%	2.90%
50	3.30%	2.20%	3.18%	2.32%

 

The models fit to real life in terms of make rates is reasonable.Now we add a ½ bump random bump in either direction to the distribution and the make rates become this.

Distance	Pro Make Rate	Average Make Rate	Simulated Pro Make Rate With Bump	Simulated Amateur Make Rate With Bump	Gap Change
2	99.87%	93.20%	98.16%	88.10%	Widens
3	95.40%	76.30%	89.80%	73.37%	Narrows
4	84.80%	60.40%	79.80%	58.59%	Narrows
5	73.00%	48.10%	68.99%	47.54%	Narrows
6	62.30%	39.40%	60.20%	38.71%	Narrows
7	53.80%	33.20%	51.56%	32.27%	Narrows
8	46.80%	28.20%	46.81%	28.31%	Narrows
9	41.00%	24.30%	40.64%	23.93%	Widens
10	36.40%	21.10%	34.87%	21.16%	Narrows
15	22.00%	12.30%	21.48%	12.21%	Narrows
20	14.60%	8.10%	14.63%	7.84%	Widens
25	10.30%	5.80%	10.30%	5.67%	Widens
30	7.60%	4.60%	7.59%	4.67%	Narrows
40	4.70%	3.00%	4.37%	2.89%	Narrows
50	3.30%	2.20%	3.30%	2.06%	Widens

 

Now, notice, most of the gaps in terms of make rate have narrowed, just as the OP said they would. Others have said that from 8 feet the better putter gets harmed more. I’m not ignoring that and I agree with you that from 8 ft the better putter very likely gets harmed more. And yes, at this point, it looks like the OP is correct, but not all shots have been examined yet.

Now, data for frequency of first putt at a given distance was also published by Broadie:

Distance (ft)	Number of First Putts
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

 

Since we know typical first putting distance, we can apply both sets of make rates for both players before the bumps and after to see what effect they have on make rate.

 

Distance	Number of First Putts	Pro Make Rate	Amateur Make Rate	Pro # of putts made	Am # of putts made
2	1.15	0.9987	0.932	1.148505	1.0718
3	0.46	0.954	0.763	0.43884	0.35098
4	0.86	0.848	0.604	0.72928	0.51944
5	0.86	0.73	0.481	0.6278	0.41366
6	0.86	0.623	0.394	0.53578	0.33884
7	0.89	0.538	0.332	0.47882	0.29548
8	0.89	0.468	0.282	0.41652	0.25098
9	0.89	0.41	0.243	0.3649	0.21627
10	1.76	0.364	0.211	0.64064	0.37136
15	2.62	0.22	0.123	0.5764	0.32226
20	1.75	0.146	0.081	0.2555	0.14175
25	1.25	0.103	0.058	0.12875	0.0725
30	1.47	0.076	0.046	0.11172	0.06762
40	1.28	0.047	0.03	0.06016	0.0384
50	0.93	0.033	0.022	0.03069	0.02046
Total	17.92		Total	6.544305	4.4918

 

 

Distance	Number of First Putts	Pro Make % Bumped	Amateur Make % Bumped	Pro # of putts made	Am # of putts made
2	1.15	0.9816	0.881	1.12884	1.01315
3	0.46	0.898	0.7337	0.41308	0.337502
4	0.86	0.798	0.5859	0.68628	0.503874
5	0.86	0.6899	0.4754	0.593314	0.408844
6	0.86	0.602	0.3871	0.51772	0.332906
7	0.89	0.5156	0.3227	0.458884	0.287203
8	0.89	0.4681	0.2831	0.416609	0.251959
9	0.89	0.4064	0.2393	0.361696	0.212977
10	1.76	0.3487	0.2116	0.613712	0.372416
15	2.62	0.2148	0.1221	0.562776	0.319902
20	1.75	0.1463	0.0784	0.256025	0.1372
25	1.25	0.103	0.0567	0.12875	0.070875
30	1.47	0.0759	0.0467	0.111573	0.068649
40	1.28	0.0437	0.0289	0.055936	0.036992
50	0.93	0.033	0.0206	0.03069	0.019158
Total	17.92		Total	6.335885	4.373607

 

 

And guess what, the OP is again correct that relatively speaking, the poor putter makes 0.1 fewer putts per round and the better putter makes 0.22 fewer putts per round. The gap on one putts does narrow. People have said I don’t understand the OP’s math.But I hope you see, I do understand it, and this math isn’t that much different directionally when it comes to make rates of longer putts.

But for some reason they stop here, without examining what happens to the 12 and 14 other putts that still need to be holed.

Let’s assume that half of these remaining putts are hit from 2 ft, and half from 3 ft.For all putts after the second, we will assume they are from 2 ft.Now I’m assuming both players putt from the same distance for their following putts, which is clearly a bad assumption. Since good putter has more skill they will be typically be closer for their following putts. So please remember this assumption I’m making here HURTS my case, but I’m doing it anyway.

When you calculate what happens to the two players having them hole out from 2 and 3 ft after a miss, on a green without bumps you get this:

		No Bump						With Bump
		Second putt						Second putt	Second putt
distance (Ft)	Pro # of putts	Amateur # of putts	pro make	am make		distance	Pro # of putts	Amateur # of putts	pro make	am make
2	5.688	6.714	5.680	6.258		2	5.792	6.773	5.685	5.967
3	5.688	6.714	5.426	5.123		3	5.792	6.773	5.201	4.969
		total	0.269	2.048				total	0.697	2.610
		Third putt						Third putt
	Pro # of putts	Amateur # of putts	pro make	am make			Pro # of putts	Amateur # of putts	pro make	am make
2	0.269	2.048	0.269	1.909		2	0.697	2.610	0.685	2.299
		total	0.000	0.139				total	0.013	0.311
		fourth putt						fourth putt
	Pro # of putts	Amateur # of putts	pro make	am make			Pro # of putts	Amateur # of putts	pro make	am make
2	0.015	0.299	0.015	0.265		2	0.015	0.299	0.015	0.265
		total	0.000	0.034				total	0.000	0.034

 

All the data summarizes as follows

		No Bump
	Pro	Amateur	Pro Total Putts	Am Total Putts
one putt	36.4%	25.0%	6.544	4.492
two putt	61.7%	63.2%	22.213	22.761
three putt	1.5%	10.6%	0.806	5.726
four putt	0.0%	0.7%	0.001	0.519
		Total	29.565	33.497
		With bump
	Pro	Amateur	Pro Total Putts	Am Total Putts
one putt	35.2%	24.3%	6.336	4.374
two putt	60.5%	60.8%	21.774	21.873
three putt	3.8%	12.8%	2.054	6.897
four putt	0.1%	1.5%	0.050	1.094
		Total	30.213	34.239
		Difference	0.648	0.741

 

Notice, including the second and third putts makes the total putts per round go up MORE for the bad player than the good player.This is because the bad putter must hit MORE short putts than the good player, and the bumps are going to affect the short putts too. The bumps affect the bad player’s total strokes in aggregate more in the second and third putts, making the gap in TOTAL putts widen.

Now you don't have to agree with my assumptions here.  What I want people to see is that even if make rates do narrow in the poor putters favor from mid and long distances, the overall question of who is more effected requires considering every shot, not just the first one.When you do consider every putt, it’s perfectly reasonable to believe that the good putter ends up better off than the poor putter.

In golf the lowest score wins. The lowest score includes all putts, not just the first putt.

Edited October 5, 2021 by batchvt

[batchvt]

Also apologies for the poorly formatted tables.  

Edited October 5, 2021 by batchvt

[Phil McGleno]

I am not a math guy—just ask the people I pay to do my taxes every year, and my wife with the checkbook— but even I can see the really obvious issues with your post there.

[boogielicious]

1 hour ago, batchvt said:

I’ve already discussed how I’m modeling the putts.  You can see it here. 

Listen @batchvt, you’ve spent a lot of time considering this as a putt modeling problem. But it’s not a putt modeling problem. The OP is almost a trick question and many folks, like you, started down the path of making it more complicated. The thread was started from discussion in the thread below. It’s a simple math problem that just happened to use the make percentages of a good and poor putter as the start points. We don’t even need to call them that.

Player A makes X% of putts and player B makes Y% of putts. X > Y. If both are affected the same amount by a randomness, Z%, that hurts their make percentage, then both X and Y will decrease by Z%. Because they decrease by the same percentage, the difference between player A’s new make percentage, and play B’s make percentage will get smaller. It narrows the gap. 

Example: Player A makes 80% and Player B 50%, the gap is 30%. Randomness reduces their make by 25%, the now only make 75% of their original putts.

0.8 x .75 = 0.6

0.5 x .75 = 0.37

The gap is now 27%. It narrows. It has too mathematically.

Plug in whatever numbers you want and you will see it to be true. The randomness affect both players equally because skill cannot control the randomness.

 

[saevel25]

46 minutes ago, batchvt said:

Now you don't have to agree with my assumptions here.  What I want people to see is that even if make rates do narrow in the poor putters favor from mid and long distances, the overall question of who is more effected requires considering every shot, not just the first one.When you do consider every putt, it’s perfectly reasonable to believe that the good putter ends up better off than the poor putter.

Yea, I am going to question your methods, but I do not really want to because I do not care about going into the weeds on this. 

Honestly, I don't trust you to come up with a method that doesn't try to prove your opinion on this. My major concern is how you model the outcome of an imperfection. Do not answer, because I don't care. In the end, I do not take much stock in your results. Go publish a peered review paper, co-signed by Mark Brodie and I might read it. 

[batchvt]

Really simplified version of the spirit of this post.

Lets say make rates fall 10% on average for the good putter and fall 9% on average for the bad putter.

This is in agreement that the bumps narrow the range of make rates.

Now apply this to the # of putts each player typically hits per round:

10% * 29.5 = 2.95 more putts for the good putter each round.

9% * 33.5 =  3.015 more putts for the bad putter each round.

You can't just evaluate this problem through make rates.  The make rates can narrow, and still hurt the bad putter more than the good putter in total score.

[batchvt]

36 minutes ago, boogielicious said:

Listen @batchvt, you’ve spent a lot of time considering this as a putt modeling problem. But it’s not a putt modeling problem. The OP is almost a trick question and many folks, like you, started down the path of making it more complicated. The thread was started from discussion in the thread below. It’s a simple math problem that just happened to use the make percentages of a good and poor putter as the start points. We don’t even need to call them that.

Player A makes X% of putts and player B makes Y% of putts. X > Y. If both are affected the same amount by a randomness, Z%, that hurts their make percentage, then both X and Y will decrease by Z%. Because they decrease by the same percentage, the difference between player A’s new make percentage, and play B’s make percentage will get smaller. It narrows the gap. 

Example: Player A makes 80% and Player B 50%, the gap is 30%. Randomness reduces their make by 25%, the now only make 75% of their original putts.

0.8 x .75 = 0.6

0.5 x .75 = 0.37

The gap is now 27%. It narrows. It has too mathematically.

Plug in whatever numbers you want and you will see it to be true. The randomness affect both players equally because skill cannot control the randomness.

 

Golf is about how many strokes it takes to make the ball 18 times.  

To keep this really simple, lets say that the stats you just provided are the stats for ever putt the good player and the bad player face. 

So to make the ball 18 times, the good putter will have to putt:

18/80% = 22.5 putts on average.  

the bad putter will have to putt:

18/50% = 36 putts on average.

Now after the bumps, here's what happens:

Good putter

18/60% = 30 putts on average

Bad putter

18/37% = 48.6 putts on average.

The good player increased by 7.5 putts to hole the ball 18 times.  The bad putter increased by 12.6 putts to hole the ball 18 times.

The bad putter was impacted more by the bumpy greens than the good player.  

The problem is too complicated to just compare make rates.  You have to apply those rates.

Edited October 5, 2021 by batchvt