The Paradox of Proportionality

[Jerry Kluger]

Does everything have to be an absolute certainty?  Does it have to be an absolute that a shot more off line than another has to be more penalized? I think we would agree that it is usually the case that the shot more off line will have a more difficult recovery shot but that doesn't mean it has to be certain that it will always be the result.  Even with well struck shots there is no certainty that the result will be the same each time.  A random bounce can put a well struck shot in an unexpected location either off the fairway or perhaps even a difficult stance or slope in the fairway. 

[Kalen Braley]

Based on the courses I've played that TD has built, (with massively undulating fairways and sometimes diabolical greens), you can hit a "perfect" tee shot right down the middle and have an incredibly difficult approach shot left based on a seemingly random basis. The golf gods can give you a tough downhill, sidehill lie...where as if your tee ball had gone 2 yards to the left of that spot it would have rolled into a relatively flat garden spot.  This was no more apparent to me than my recent round at Stone Eagle.

[Kalen Braley]

P.S.  When I first heard this phrase way back as TD stated...I thought it referred to features on and off the course being in proportion with other.

For example when framing a par 4 hole, with some type of mountain or other nice view as a back drop...keeping the framing in proportion with its surroundings so the golf hole looked "natural" and not out of place.

[Tom_Doak]

Based on the courses I've played that TD has built, (with massively undulating fairways and sometimes diabolical greens), you can hit a "perfect" tee shot right down the middle and have an incredibly difficult approach shot left based on a seemingly random basis. The golf gods can give you a tough downhill, sidehill lie...where as if your tee ball had gone 2 yards to the left of that spot it would have rolled into a relatively flat garden spot.  This was no more apparent to me than my recent round at Stone Eagle.

Kalen:


If we made it easy to avoid the downhill, sidehill lies, you'd never have to deal with one.    But you could probably play around them fairly easily if you really knew the course.  John Kirk has played Stone Eagle enough that I'd guess he doesn't leave himself so many of those.

[Kalen Braley]

Based on the courses I've played that TD has built, (with massively undulating fairways and sometimes diabolical greens), you can hit a "perfect" tee shot right down the middle and have an incredibly difficult approach shot left based on a seemingly random basis. The golf gods can give you a tough downhill, sidehill lie...where as if your tee ball had gone 2 yards to the left of that spot it would have rolled into a relatively flat garden spot.  This was no more apparent to me than my recent round at Stone Eagle.

Kalen:


If we made it easy to avoid the downhill, sidehill lies, you'd never have to deal with one.    But you could probably play around them fairly easily if you really knew the course.  John Kirk has played Stone Eagle enough that I'd guess he doesn't leave himself so many of those.

Tom,

Just to clarify, my last post wasn't intended to be critical at all.  I think you very much accomplished the "paradox" in several places including a few greens that were an interesting puzzle to solve when stimping at 11.

As for John, he did give me terrific instructions, but unfortunately in most cases, even though I tried to follow his excellent advice, I clearly lacked the ability!!   

P.S.  On 17, there was a back left pin, seemingly tucked behind the bunker on the left hand side.  It seemed to me, I wanted to play my 2nd shot out to the right to have a better angle to the pin.  But when he told me it was better to miss on the left side, I thought he had a screw loose.  My ball ended up on the right side anyways, and when I got to the green I found out the hard way why he was exactly right!! 

[Joe Hancock]

Tom,

There's a lot of high-falutin' words, terms and theories going on here. If I were to rephrase by saying" hit it where it lies, and don't worry too much about luck, whether it be good or bad." would that be too far off, or too simple?

[Steve Lang]

    How about "3 feet from glory" as a simple description?

[Peter Pallotta]

Tom,

There's a lot of high-falutin' words, terms and theories going on here. If I were to rephrase by saying" hit it where it lies, and don't worry too much about luck, whether it be good or bad." would that be too far off, or too simple?

I'm glad you asked, Joe - it might not seem like it, but I was serious about not quite understanding what Tom (or anyone else on this thread) is actually talking about. The key to the discussion is/should be "solving" the paradox*, and what that might mean fairway by fairway and green by green and rough line by rough line and bunker by bunker. Is that what we're talking about, or are we all just stating the obvious (at least from our own anti-Open-Doctor-and-USGA-set-up perspective)?

Peter
*I may simply be using "paradox" either incorrectly and/or differently from others.

[Kalen Braley]

Peter,

Based on Tom's OP, it seems like the paradox he's trying to solve is:

How do you build a course on a hole by hole, shot by shot basis, that is both playable for the high capper, without unduly punishing them, but yet also challenge the low capper.  He seems to suggest the way to do this is by adding a luck component to several areas of the course.  Whether it be a hump in the fairway where on one side your golden, and the other side you have a tough shot to the green, or a feature behind a green where maybe you have an easy recovery, or maybe it rolls into a hazard and your reloading.

Its this arbitrary luck, which statistically should even out over the several playings that can both make it difficult for a good player to score well, while simultaneously not beating up the high capper every time you play it.

[Joe Lane]

Dear Mr. Doak,

I am absolutely tickled to read your post here today: if I may say so, I think this is exactly the line I have been attempting to describe the past few days. If I am astray at all in what I’ve been writing, please let me know; also, I wondered what you thought of my piece about your renovation at Medinah One.

It’s at djlane.wordpress.com; the piece is called “Eyeless In Medinah.”

Thank you for taking the time to write, it’s very much a pleasure—in part I think because your style is very clear.

Joe

[Joe Lane]

Hi to all,

I think that what Tom is saying is greatly elucidated by reading what Nicolas Taleb has written about the subject of randomness, such as The Black Swan, or by familiarity with the work of the Santa Fe collective, or by Stephen Jay Gould’s idea of “punctuated equilibrium,” or by Benoit Mandelbrot’s work on the history of cotton prices. (The key text here is Mandelbrot’s 1967 “How Long Is The Coastline of Britain?” It’s a harder question to answer than it looks.) The basic point in all of this work is that, even in deterministic systems, which is to say systems in which the main actors are known and their basic actions foreseen—such as, say, when somebody hits a golf ball—small differences in initial conditions can have incredibly disproportionate effects. Crane’s basic argument, so far as I can tell, is that this chaos at the heart of golf ought to be contained as much as possible—what Tom is saying, and correct me if I’m wrong, is that Crane’s quest to conquer chaos is impossible. Chaos is not the enemy, Tom is saying—it is a tool. Crane wants to make golf courses linear; golf however is non-linear: that is, what you put in is not necessarily be proportionate to what comes out.

I hope this is helpful to how people think about this.

Joe

[Bill_McBride]

Based on the courses I've played that TD has built, (with massively undulating fairways and sometimes diabolical greens), you can hit a "perfect" tee shot right down the middle and have an incredibly difficult approach shot left based on a seemingly random basis. The golf gods can give you a tough downhill, sidehill lie...where as if your tee ball had gone 2 yards to the left of that spot it would have rolled into a relatively flat garden spot.  This was no more apparent to me than my recent round at Stone Eagle.

The key there is divining which part of a wide fairway is the best place to play to.  A lot of times it can't be figured out in one play.   


I remember my first round on Bandon Dunes.  The flag on 10 was tucked tight behind the daunting front bunker.  Somehow I divined that the best tee ball would be fifty yards left of the line of instinct.  The grass was short, the 9 iron was fairly simple, easy par.   To refute my strategy, my 3 hdcp brother played down the line of instinct and stuffed a wedge to two feet.  😡

[Greg Holland]

Can't the paradox be boiled down to what the good doctor said repeatedly in the "Spirit of St. Andrews?"  I am paraphrasing but, great courses are made ever more so due to undulations and hummocks in the fairways, as at St. Andrews, which create interest day in and day out in every kind of condition.  However, pro players and green committees inevitably want to "flatten" those out in the name of fairness, only to the detriment of the course --  resulting in boring golf and reduction in club memberships.

[Joe Lane]

Hi Greg,

The answer is no. What Mr. Doak is talking about is something like this passage from Nicolas Taleb’s book, Fooled By Randomness: “The main point of the Gaussian, as I’ve said, is that, as we kept saying, that most observations hover around the mediocre, the average; the odds of a deviation declining faster and faster (“exponentially”) as you move away from the average.” In that sense, we might expect that bad shots might be penalized in accordance with how poorly they are hit: that bad shots should follow a gaussian distribution, so to speak. This is what Taleb calls “Mediocristan.”

But there is another realm, this one called “Extremistan.” In this place, events are scalable: in technical terms, they obey what mathematicians call power laws. In this place, as actions or events or whatever move away from the standard, they do not become as unlikely as they do under a gaussian regime. In other words, crazy shit can happen. This is why billionaires are more common than nine-foot tall people: human height follows a gaussian distribution pattern, while the distribution of money does not.

(As a sidelight, it is Taleb’s argument that it was the failure to allow for extreme events that led to the 2007 financial crash and the 1998 Long Term Capital bankruptcy. So this is a non-trivial subject.)

Does this help anyone?

Joe

[Colin Macqueen]

You betcha Joe!!!

[Niall C]

Agreed Tom, yet the USGA and the PGA continue to boast of their graduated roughs. I think I heard the R&A making the same boast about its Open set-up recently.


Joshua Crane is still with us, more than most appreciate.


Bob

The R&A have likely learned there lesson. I suspect it's been a long time since they situated their car park beside the course 


Niall

[Mark_Fine]

Tom,
I have not read all the posts but just think about this concept as to how one plays The Old Course at St. Andrews?  I have hit wild drives onto The New Course (while playing the Old Course) and ended up in good positions.  Forget fairness - it is Rub of the green   Sometimes the best line is not the straight down the middle line.  As a rule of thumb on the Old Course (miss left if you are going to miss) 

[Tom_Doak]

Hi Greg,

The answer is no. What Mr. Doak is talking about is something like this passage from Nicolas Taleb’s book, Fooled By Randomness: “The main point of the Gaussian, as I’ve said, is that, as we kept saying, that most observations hover around the mediocre, the average; the odds of a deviation declining faster and faster (“exponentially”) as you move away from the average.” In that sense, we might expect that bad shots might be penalized in accordance with how poorly they are hit: that bad shots should follow a gaussian distribution, so to speak. This is what Taleb calls “Mediocristan.”

But there is another realm, this one called “Extremistan.” In this place, events are scalable: in technical terms, they obey what mathematicians call power laws. In this place, as actions or events or whatever move away from the standard, they do not become as unlikely as they do under a gaussian regime. In other words, crazy shit can happen. This is why billionaires are more common than nine-foot tall people: human height follows a gaussian distribution pattern, while the distribution of money does not.

(As a sidelight, it is Taleb’s argument that it was the failure to allow for extreme events that led to the 2007 financial crash and the 1998 Long Term Capital bankruptcy. So this is a non-trivial subject.)

Does this help anyone?

Joe

Joe:


Don't put [big] words in my mouth!  Taleb's last book [Antifragile] is probably the best I've ever read, but I learned much more there about how the world works, and why our "trial-and-error" shaping method works so well instead of plans. 


I've never really tried to apply what he wrote to golf strategy.  I suppose there is something there, about how people's demands for order and security are counter to the real nature of the game -- Nature's "order" is much more complex and has no guarantees of what might be around the next corner.

[Tom_Doak]

I was serious about not quite understanding what Tom (or anyone else on this thread) is actually talking about. The key to the discussion is/should be "solving" the paradox*, and what that might mean fairway by fairway and green by green and rough line by rough line and bunker by bunker. Is that what we're talking about, or are we all just stating the obvious (at least from our own anti-Open-Doctor-and-USGA-set-up perspective)?

Peter
*I may simply be using "paradox" either incorrectly and/or differently from others.

Peter:


SOLVING the paradox is something I've been working on my whole career, one green or bunker or feature or day at a time.  I don't think it can be boiled down into one or two posts on Golf Club Atlas ... or, if it can, I'm pretty sure no one has done so yet.  I didn't think I was going to do it yesterday when I started this post, I was just trying to help everyone understand the complexity of the problem we work on.


As Greg Holland correctly observed, many architects try to make the game more fair by flattening out where they consider the ideal spots to be.  It's not just fairway lies; they're likely to be adamant that the edge of a green just over a bunker be flat and receptive, so if you "correctly" just carry the bunker, you are rewarded. 


To me, there's nothing wrong with having a high lip and a steeper slope there [like the 4th at Pebble Beach that we were analyzing the other day] ... all of which make it harder to get down in two whether you are in the green side bunker, or approaching from 50 or 100 yards back on that line.  The CORRECT play on that hole is not to "just carry the bunker," but to land your ball on the flat of the green and take your medicine, because your last shot put you in the wrong place; but the best players seem to think they should always have a "fair" chance to get the ball close to the hole from any position, even if they butchered the previous shot.


Back to the paradox:  it's one thing to build a course as a whole and say that you believe the good and bad breaks will even out over the course of a round.  But when you try to break it down into its component parts ... to have that be true for every hole, for every player, and for every SHOT ... you are not just going to strip out all the bad bounces from the course, but all the strategy, too.  Leaving inequities in the holes is precisely what makes them interesting.

[Tom_Doak]

Tom,
I have not read all the posts but just think about this concept as to how one plays The Old Course at St. Andrews?  I have hit wild drives onto The New Course (while playing the Old Course) and ended up in good positions.  Forget fairness - it is Rub of the green   Sometimes the best line is not the straight down the middle line.  As a rule of thumb on the Old Course (miss left if you are going to miss) 

Mark:


Yes, forget fairness ... and what is proportionality but fairness?


P.S.  I'll bet your opponent thought it was unfair that one side of The Old Course is out of bounds, and the other isn't.

[MCirba]

Or, why bad things happen to good peop..er...golf shots, and visa versa.

[Jeff_Brauer]

I have mentioned this before in different contexts, but so often Tour Pros admit they can't design, but do feel they have value as "design editors" (Kind of have to wonder how Adam feels about that comparison.....)

One of their most asked questions is, "What if I hit it here?  Can I get it close to the pin?"  It is an odd question from an architects POV.  The whole point of hazard placement, etc. is that there are places that are easier and harder to play from. 

So, basically I agree that this kind of thinking has gone overboard, and willing to assign the blame to pros and better players, who think ALL course features ought to somehow help them lower their score.  But, that kind of thinking defeats any idea of proportional punishment.

Random thought, but it would be funny to carry out to logical conclusion some specific features, not just TD's estimate of all flat courses.  Should rough be longer 200 yards from the green than 100 yards?  Fairway narrower? (Gary Player once suggested this)  Usually, we go the other way, not bothering to punish a shot which has no chance of reaching the green anyway, trying to balance out a course playable by different levels.

[Mike_Young]

Wow...after all of these big words and theories .....doesn't the best golfer still usually win after 4 days ? The real randomness in golf is in the swing...

[Jeff_Brauer]

Mike,

Again, why mention 4 days?  I thought TD and others were talking about real golf in America, not just TV golf. I guess he is right....that TV golf starts to convince us we all need "X" that we see on TV at our courses, damn the expense and damn fun play!

Even in architectural terms, basically the Tour Pros are almost all the same player, armed with distance and uncanny accuracy.  A few (Pavin) survive with less length and greater short games and putting, but overall, top 20 length pretty well parallels the money list.

At the average club, you have a mix of guys with length, with or without accuracy, accuracy, with or without length, and recovery skill.  We aren't concerned with 4 days, we are concerned (or at least I am) with the 4-12 month season, and allowing each of those guys a chance to win at least on some days........

[Mark_Fine]

You simply CAN'T design courses around the super long hitters.  You will screw them up and make them no fun and too expensive for the majority of golfers.  The added real estate, extra tees and maintenance costs will make costs go through the roof. 

I played with a college player last summer in a member guest that carried the ball on average over 320 yards or more in the air.   It was ridiculous the lines he took and how he attacked a quite challenging Nicklaus designed golf course.  There was no way to defend against his length without making the course stupid hard for everyone else.  He flew the ball over one green that was a 375 yard elbow hole around a lake.  I don't think Nicklaus ever envisioned anyone going directly for the green from the tee and making the 320 yard carry to be dry.  The guy hit his tee shot over the green into some high grass and still got it up and down for birdie.  What are you supposed to do???