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Mark Pearce

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Re: “Angles Don’t Matter”
« Reply #125 on: February 16, 2023, 05:35:03 PM »
You understand that you just contradicted yourself in that answer?  I'm not arguing with your principle, just your grasp of English.
I did not. Fairway bunker (or OB) left… playing to get the "better angle" to the green down the left side is almost surely the bad play.

That's just avoiding trouble, period, regardless of the "angle" with which you're left.
You did and I suspect you actually know that you did.


"The angle it gives you into the green is great" cannot, however you construe it, not mean that the angle into the green matters.  There is simply no possible way of interpreting that sentence that means angles don't matter.  What you mean, and what I said before, is that the benefit of that great angle into the green, is so significantly outweighed by the statistical disadvantage of playing for that great angle that it makes no sense to play for that great angle.


Jason's first sentence very concisely summarises your argument, and I am happy to accept that the statistics overwhelmingly prove that.  I'm disappointed, the strategic romantic in me wants to believe differently but I'm very willing to believe it.  But that summary and the statement that "angles don't matter" are not the same.  It might well be accurate to say that angles are far less important than we think, and that avoiding hazards is so much more important to scoring that angles should be ignored for scoring purposes, but that's, again, not the same as "angles don't matter". 

In June I will be riding the first three stages of this year's Tour de France route for charity.  630km (394 miles) in three days, with 7800m (25,600 feet) of climbing for the William Wates Memorial Trust (https://rideleloop.org/the-charity/) which supports underprivileged young people.

Erik J. Barzeski

  • Karma: +1/-0
Re: “Angles Don’t Matter”
« Reply #126 on: February 16, 2023, 07:44:12 PM »
You did and I suspect you actually know that you did.
Perhaps if I had put words like "angle" and "great" in quotes you'd read it the way I "said" it in my mind when I wrote it. I don't see situations where angles matter except:
  • When the ball is rolling. I've been consistent about that.
  • Exceptions. These are rare.
Exceptions exist. I generally talk in generalities. Finding one situation (and the original bit that I replied to was a hypothetical) where an angle might matter doesn't "disprove" the general statement because I have not said "angles always matter and there are no exceptions, even when the ball isn't rolling."

But that summary and the statement that "angles don't matter" are not the same.
Do you want a disclaimer attached to every post about how there are some rare exceptions, or can we assume that the fine folks with whom we're talking here are smart enough to assume that people are generally not stating that things are 100% true 100% of the time with no exceptions?

Angles don't matter unless the ball is rolling*.

* (And the incredibly rare exceptions that almost certainly exist.)
« Last Edit: February 16, 2023, 07:46:41 PM by Erik J. Barzeski »
Erik J. Barzeski @iacas
Author, Lowest Score Wins, Instructor/Coach, and Lifetime Student of the Game.

I generally ignore Rob, Tim, Garland, and Chris.

Sean_A

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #127 on: February 17, 2023, 12:51:45 AM »
You did and I suspect you actually know that you did.
Perhaps if I had put words like "angle" and "great" in quotes you'd read it the way I "said" it in my mind when I wrote it. I don't see situations where angles matter except:
  • When the ball is rolling. I've been consistent about that.
  • Exceptions. These are rare.
Exceptions exist. I generally talk in generalities. Finding one situation (and the original bit that I replied to was a hypothetical) where an angle might matter doesn't "disprove" the general statement because I have not said "angles always matter and there are no exceptions, even when the ball isn't rolling."

But that summary and the statement that "angles don't matter" are not the same.
Do you want a disclaimer attached to every post about how there are some rare exceptions, or can we assume that the fine folks with whom we're talking here are smart enough to assume that people are generally not stating that things are 100% true 100% of the time with no exceptions?

Angles don't matter unless the ball is rolling*.

* (And the incredibly rare exceptions that almost certainly exist.)

How about "angles often don't matter"? Is there any need for false hyperbole when making statements? I fail to see the point in claiming to use millions of data points only to use easily avoidable sloppy language when drawing conclusions.

Ciao
New plays planned for 2024: Nothing

Ally Mcintosh

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #128 on: February 17, 2023, 03:34:27 AM »
Lads, lads, lads,


It’s a general hypothesis. Angles don’t matter because there’s not conclusive data that show they do matter.


It’s like those GCA Mythbusters threads I started: If I put forward the hypothesis that “Angles matter”, it would have been busted! It’s not an absolute.


(Incidentally it’s not even Erik’s thread or choice of words).

Kyle Harris

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #129 on: February 17, 2023, 07:04:15 AM »
Lads, lads, lads,


It’s a general hypothesis. Angles don’t matter because there’s not conclusive data that show they do matter.


It’s like those GCA Mythbusters threads I started: If I put forward the hypothesis that “Angles matter”, it would have been busted! It’s not an absolute.


(Incidentally it’s not even Erik’s thread or choice of words).


This.

And from a coaching/teaching/caddying perspective suppose a player misses it to the so-called "wrong angle."

Do you want that player feeling like they missed and now have a bad choice in front of them? No chance?


Or do you want that player to know that the stats and data show they really are not at a disadvantage?

Which mindset is better for success? I know which one I'm choosing.
http://kylewharris.com

Constantly blamed by 8-handicaps for their 7 missed 12-footers each round.

Thank you for changing the font of your posts. It makes them easier to scroll past.

Kalen Braley

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #130 on: February 17, 2023, 11:08:33 AM »
Lads, lads, lads,

It’s a general hypothesis. Angles don’t matter because there’s not conclusive data that show they do matter.

It’s like those GCA Mythbusters threads I started: If I put forward the hypothesis that “Angles matter”, it would have been busted! It’s not an absolute.

(Incidentally it’s not even Erik’s thread or choice of words).

This is the crux of the beef.

Its clearly just a hypothesis, but being asserted as immutable fact.

Like Sean I'm also perfectly fine if the messaging had been "Angles matter a lot less than you think" or something along the lines.

Ally Mcintosh

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #131 on: February 17, 2023, 11:23:42 AM »
Lads, lads, lads,

It’s a general hypothesis. Angles don’t matter because there’s not conclusive data that show they do matter.

It’s like those GCA Mythbusters threads I started: If I put forward the hypothesis that “Angles matter”, it would have been busted! It’s not an absolute.

(Incidentally it’s not even Erik’s thread or choice of words).

This is the crux of the beef.

Its clearly just a hypothesis, but being asserted as immutable fact.

Like Sean I'm also perfectly fine if the messaging had been "Angles matter a lot less than you think" or something along the lines.


But that’s exactly what people are saying. They matter so much less than you think that it’s not entirely clear how much they matter at all….


But that won’t stop me designing angles / strategy in to as many holes as possible. In fact, in some ways it just encourages me to exaggerate and maximise the angles in any way possible, just so that they can matter more than not much!

Jeff_Brauer

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #132 on: February 17, 2023, 11:57:07 AM »
The fact that Lou put an eye catching newspaper headline on the article doesn't detract from its content.


Another way to look at it is that good golfers have learned (and now measured more precisely) that playing conservatively over a long season results in better scores.  I compare it to football coaches who become more averse to gadget plays as they progress in their career.  Sure, a Super Bowl winning play is exciting, but for every one of those there are 25+ plays that fail, and they know it.

According to Fawcette, widening fairways makes playing for an edge to get the open front angle is even more lunacy.  The biggest statistical difference in scoring comes from being in the fw vs being in light rough with spinners, but I think most of us intuitively knew that, so most should play tee shots to hit the fw in whatever fashion we can.


Another more depressing way to look at it is that all of us have devoted our time over the years to a website pushing a myth.  Ouch, that hurts!


Either way, the stats guys seem to be taking over the strategic thinking of the top young players.  I am not sure how architecture should adapt, but have been thinking about it.  Worth a thread maybe.
« Last Edit: February 17, 2023, 12:12:02 PM by Jeff_Brauer »
Jeff Brauer, ASGCA Director of Outreach

Kalen Braley

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #133 on: February 17, 2023, 12:02:34 PM »
Lads, lads, lads,

It’s a general hypothesis. Angles don’t matter because there’s not conclusive data that show they do matter.

It’s like those GCA Mythbusters threads I started: If I put forward the hypothesis that “Angles matter”, it would have been busted! It’s not an absolute.

(Incidentally it’s not even Erik’s thread or choice of words).

This is the crux of the beef.

Its clearly just a hypothesis, but being asserted as immutable fact.

Like Sean I'm also perfectly fine if the messaging had been "Angles matter a lot less than you think" or something along the lines.

But that’s exactly what people are saying. They matter so much less than you think that it’s not entirely clear how much they matter at all….



Not to belabor the point but when something is "not entirely clear", I would think its self-evident that all encompassing statements like "Angles don't matter" border on the absurd.

P.S. I don't think the varying sides are that far apart at this point.  I think nearly everyone would agree that on many or even most holes, they probably don't matter, but overall just looking for a bit more conciseness.  ;)

Mark Pearce

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #134 on: February 17, 2023, 12:56:27 PM »
It's like modern politics.  People feel the need to express themselves in simple soundbites and defend them absolutely, rather than recognising nuance and finding language that more accurately reflects their meaning.  Like Kalen, I don't think anyone actually disagrees much, if at all, with the basic premise, it's just that some won't permit an expression that departs from the absolute.  As someone who works every day with language and its exact meaning, I find it very frustrating but guess I should just accept that in the real world, clarity of language is as old fashioned as real ale.
In June I will be riding the first three stages of this year's Tour de France route for charity.  630km (394 miles) in three days, with 7800m (25,600 feet) of climbing for the William Wates Memorial Trust (https://rideleloop.org/the-charity/) which supports underprivileged young people.

Adam Lawrence

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #135 on: February 17, 2023, 12:58:56 PM »
It's like modern politics.  People feel the need to express themselves in simple soundbites and defend them absolutely, rather than recognising nuance and finding language that more accurately reflects their meaning.  Like Kalen, I don't think anyone actually disagrees much, if at all, with the basic premise, it's just that some won't permit an expression that departs from the absolute.  As someone who works every day with language and its exact meaning, I find it very frustrating but guess I should just accept that in the real world, clarity of language is as old fashioned as real ale.


But some of us like real ale, and...
Adam Lawrence

Editor, Golf Course Architecture
www.golfcoursearchitecture.net

Principal, Oxford Golf Consulting
www.oxfordgolfconsulting.com

Author, 'More Enduring Than Brass: a biography of Harry Colt' (forthcoming).

Short words are best, and the old words, when short, are the best of all.

Ally Mcintosh

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #136 on: February 17, 2023, 01:08:03 PM »
You guys are getting completely caught up in language rather than meaning.


The general consensus of those that follow GCA is that angles matter a great deal. Hence the title “angles don’t matter” is a way of showing that this is not entirely true. It is - of course - not an absolute. It wouldn’t work the other way round because the general consensus isn’t that way round. In that case, the headline would read “Angles actually do matter”.


That aside, I think that GCA connoisseurs don’t want to give up on this point because it’s one tangible aspect that can be easily understood and talked about. No-one wants to concede that “strategy” isn’t really the most important priority in an architect’s toolbox.

Joe_Tucholski

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Re: “Angles Don’t Matter”
« Reply #137 on: February 17, 2023, 01:25:42 PM »
No-one wants to concede that “strategy” isn’t really the most important priority in an architect’s toolbox.


Deceiving the golfer into thinking strategy matters is pretty darn important.

Ally Mcintosh

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #138 on: February 17, 2023, 01:31:35 PM »
No-one wants to concede that “strategy” isn’t really the most important priority in an architect’s toolbox.


Deceiving the golfer into thinking strategy matters is pretty darn important.


Only to those that think strategy is more important than it is and hence are deceived. That’s a pretty small sub-set:


Golfers who know how to score generally disregard it (or at least the angles part of it). The vast majority of other golfers (save for those who are into architecture) don’t even consider the strategy of a golf course as part of their vocabulary.

Kalen Braley

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #139 on: February 17, 2023, 01:41:32 PM »
No-one wants to concede that “strategy” isn’t really the most important priority in an architect’s toolbox.


Deceiving the golfer into thinking strategy matters is pretty darn important.

Only to those that think strategy is more important than it is and hence are deceived. That’s a pretty small sub-set:

Golfers who know how to score generally disregard it (or at least the angles part of it). The vast majority of other golfers (save for those who are into architecture) don’t even consider the strategy of a golf course as part of their vocabulary.


Ally,

I have a much harder time believing this last statement that strategy doesn't matter.

The best golfers in the world, (who are also the best scorers) talk a lot about how they develop a strategy before majors and other big tournaments.  They do site visits on their own dime, spend hours putting together a hole by hole game plan, practice shots they will need to win, etc.  And they talk about things like coming in from the right side of the fairway on 11 at Augusta or how the pin location on 2 leads them to decisions back on the tee.

Is all this just sound byte bullocks?

Ally Mcintosh

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #140 on: February 17, 2023, 02:24:37 PM »
I’m not sure, Kalen. Hopefully Erik will chime in because he’s much closer to how the pro’s think than I am.


As I said, it isn’t an absolute. I always knew that angles mattered less than people thought but was not aware that scoring from the “wrong” side of the fairway might be as good as from the “right” side of the fairway. At my home course (where I have firmly believed that there is a right and wrong side), I still play away from trouble first and foremost. Being on the fairway outweighs playing from the “right” angle…. But I figure that most courses don’t really have a right and wrong side that are actually meaningful.

Ira Fishman

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #141 on: February 17, 2023, 02:41:51 PM »
Erik acknowledged two important exceptions: when the ball is rolling and off the tee on doglegs. I mentioned centerline bunkers. Don’t they requiring playing the correct angle? I think Kyle mentioned SS Blue 8 (one great golf hole) as an example of another exception. But are centerline bunkers a general exception? You need to pick one side or another or take the risk of flying them.


Ira


PS Any stats from recent Opens regarding Hogan’s Alley?

Max Prokopy

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #142 on: February 17, 2023, 03:43:54 PM »

But that won’t stop me designing angles / strategy in to as many holes as possible. In fact, in some ways it just encourages me to exaggerate and maximise the angles in any way possible, just so that they can matter more than not much!


I very much appreciate this sentiment.  The statistics are what they are, and they are important.  However, your intent to include this aspect of design is still welcome from my point of view.  There are things other than scoring when considering a golf course.  I do think visuals matter and angles affect visuals, so please carry on as you were. 

Erik J. Barzeski

  • Karma: +1/-0
Re: “Angles Rarely Matter”
« Reply #143 on: February 17, 2023, 07:38:10 PM »
How about "angles often don't matter"? Is there any need for false hyperbole when making statements?
Angles rarely matter. Angles almost never matter. Angles don't matter except in a few situations… whatever. It's all the same thing, and no different than what I've been saying. This isn't my topic: I didn't choose the title.

(Incidentally it’s not even Erik’s thread or choice of words).
Correct, thank you.

It's clearly just a hypothesis, but being asserted as immutable fact.
"Angles matter" is no less a hypothesis, except that the available data supports "rarely matter" far more than "often matter."

Another more depressing way to look at it is that all of us have devoted our time over the years to a website pushing a myth.  Ouch, that hurts!
Indeed.  :)  But again, the context in which they rarely matter is scoring.

Either way, the stats guys seem to be taking over the strategic thinking of the top young players.  I am not sure how architecture should adapt, but have been thinking about it.  Worth a thread maybe.
I think we have a few threads on it.

The best golfers in the world, (who are also the best scorers) talk a lot about how they develop a strategy before majors and other big tournaments.  They do site visits on their own dime, spend hours putting together a hole by hole game plan, practice shots they will need to win, etc.  And they talk about things like coming in from the right side of the fairway on 11 at Augusta or how the pin location on 2 leads them to decisions back on the tee.
There are some old-school people out there who haven't quite adapted, and a lot of the site visits are to find start lines (i.e. can I carry the bunker on this line, how much will the fairway slant kick a ball to the left, etc.), to figure out where you can miss it around greens, that sort of thing. A lot of their "strategy" is determined from an overhead view, like Google Earth or something similar, before they're ever on-site.

As I said, it isn’t an absolute. I always knew that angles mattered less than people thought but was not aware that scoring from the “wrong” side of the fairway might be as good as from the “right” side of the fairway. At my home course (where I have firmly believed that there is a right and wrong side), I still play away from trouble first and foremost. Being on the fairway outweighs playing from the “right” angle…. But I figure that most courses don’t really have a right and wrong side that are actually meaningful.
Just about bang on.

Erik acknowledged two important exceptions: when the ball is rolling and off the tee on doglegs.
They can be if the dogleg happens in such a way that you almost have to shape the ball to hold the fairway. That's more about the angle of your ball flight, and the curve on it, than what we're traditionally talking about here with "angles."

Don’t they requiring playing the correct angle?
Uhhhh… quite often, no. If they're penal enough, you're often treating it like it's on the side of the wider part of the fairway. Or if it's penal enough, you're hitting a 3W to stay just short of it. The fairway bunker on that hole at Kapalua or whatever is interesting… because it's next to a cliff or whatever, and there is an incentive to get it to the green in two.

And I've also said that I'm talking only about scoring. If angles matter to you for artistry/beauty, or for "interest," or any other reasons, cool. They "matter" for those contexts. I've talked only about scoring.
Erik J. Barzeski @iacas
Author, Lowest Score Wins, Instructor/Coach, and Lifetime Student of the Game.

I generally ignore Rob, Tim, Garland, and Chris.

Mark_Fine

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #144 on: February 18, 2023, 11:20:12 AM »
Trust this might have been stated already as I have not read all six pages of posts:

Obviously course conditions are paramount but ALL golfers, outside of maybe the highest handicappers and pure beginners, realize that angles can matter.  That said, the better the player the more important they are because they can do something about it.  When your primary focus is to make solid contact and finish the hole with the same ball, you are not really worried too much about angles.   


Same as saying don’t be above the hole on really fast sloping greens or leave your approach shot short sided behind a bunker.  Higher handicappers surely understand this but their ability limits what they can do about it.  The better the golfer the more they can control their outcome. 


Also play a course with aerial hazards like Harbour Town or Valderrama and then decide if angles really matter. 

One more clue to determine if angles really matter to a particular golfer - watch what they do on the tee.  If they tee up their ball on one side or the other rather than right in the middle, you will have your answer. 
« Last Edit: February 18, 2023, 11:46:14 AM by Mark_Fine »

Jeff_Brauer

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #145 on: February 19, 2023, 09:19:33 PM »
My son, a good golfer, has an interesting take on this.  Basically, when he comes in from the "wrong" side of the fw he does play for the fat part of the green, thus basically incorporating the Decade Strategy of playing safe, and probably his overall score goes down as a result.  When he has the better angle to the flag, he attacks and gets in trouble more often, raising his average score, and it all averages out.


I guess the term "sucker pin" is rooted in reality somehow.
Jeff Brauer, ASGCA Director of Outreach

Kyle Harris

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #146 on: February 20, 2023, 06:08:58 AM »
Nobody here really knows how to improve, do they?


One of the premises here is that angles don't matter because the amount of time to acquire the skill such that you're overcoming the variance in your golf swing to have such command over the ball to take advantage of every angle that may give you an advantage (assuming you're aware of it in the first place) is legion.


Take Iron Byron out there and angles matter.

You are not Iron Byron.


In almost every case where the angle matters there is sufficient width within and distance between the two options that you're making the choice between being within reach of the green in regulation and not. Yes, your ability to hit the ball far enough matters here but that's if, and only if, you can subsequently take advantage without putting the penalty shot in play.

Put another way: Old Man Par never chases angles.
http://kylewharris.com

Constantly blamed by 8-handicaps for their 7 missed 12-footers each round.

Thank you for changing the font of your posts. It makes them easier to scroll past.

Niall C

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #147 on: February 20, 2023, 08:18:55 AM »
Jeff


That's interesting comment from your son but it seems to assume a binary choice of going for the pin or playing completely safe. From the correct angle he can choose to play somewhere in between. His chances of success of sinking a 15 ft putt are surely better than sinking a 30 ft putt ?


Maybe by playing in between he would slightly increase his chances of going in the hazard but then there might be a fair chance of getting up and down if he's a good player and let's also not forget that there is a much better chance of 3 putting from 30 ft than from 15 ft. There is such a thing as playing too safe.


Niall

David Cronan

  • Karma: +0/-0
Re: “Angles Don’t Matter”
« Reply #148 on: February 20, 2023, 08:42:32 AM »
My son, a good golfer, has an interesting take on this.  Basically, when he comes in from the "wrong" side of the fw he does play for the fat part of the green, thus basically incorporating the Decade Strategy of playing safe, and probably his overall score goes down as a result.  When he has the better angle to the flag, he attacks and gets in trouble more often, raising his average score, and it all averages out.


I guess the term "sucker pin" is rooted in reality somehow.


Your son is wise, Jeff. One summer I was entered to play in the Michigan Mid-Am. Per usual, I was trying to cram a year's worth of practice into 2 weeks. The pro a the club where I was a member, Lochenheath, asked if I wanted to play a quick 18 holes that evening. We'd be the last 2 players on the course and could probably zip around (in a cart) in 1.5 - 2 hours. Sounded good to me so at around 7 pm we took off to the 1st tee, teed off and chased after our drives. As I got out to the cart, I was surprised to find there was no pin/flag on the 1st green and asked our pro what we should do. He said, "Well, we're out here, let's get some practice in and just hit to the center of the greens."


I was actually surprised at the end of the round that my score was not much worse. In fact, it was right around par. It was then that he told me he had the greens crew remove all of the flags before our round and that unless I had a wedge in my hands, it'd be wise to hit to the center of the greens during the tournament.


Somehow, during the 1st round of the tournament, I was -3 thru 5 holes and that was enough to convince me that I was in the zone and started taking "Dead Aim" at all flags.


Suffice to say, I flamed out on the front 9, but that didn't stop me from "Flag Hunting." I shot a million but eventually learned the lesson.

Erik J. Barzeski

  • Karma: +1/-0
Re: “Angles Don’t Matter”
« Reply #149 on: February 20, 2023, 10:06:10 AM »
That's interesting comment from your son but it seems to assume a binary choice of going for the pin or playing completely safe. From the correct angle he can choose to play somewhere in between. His chances of success of sinking a 15 ft putt are surely better than sinking a 30 ft putt ?
It's not really Jeff's son's take: that's what Lou has said all along as well: people play more conservatively when they have the "wrong" angle, which is actually roughly where they SHOULD play from any angle, but they'll typically aim closer from the "right" angle and short-side themselves or whatnot.

I'm surprised that nobody has tried to show that "angles matter" by looking at the stats and showing something like this… Let's say that from 150 yards in the fairway a class of player averages 3.12 shots from the "bad" angle and 3.15 shots from the "good" angle (so, a pretty good player). Those are so close it's basically a wash, but how they get those averages might be something like this, out of 1000 times played:

"Bad" Angle (4.12): 1 eagle, 111 birdies, 667 pars, 218 bogeys, and 3 doubles.
"Good" Angle (4.15): 3 eagles, 129 birdies, 592 pars, 265 bogeys, and 11 doubles.

That might show "angles matter" a little… because the scoring spread changes. One location results in more under-par scores but also more over-par scores with fewer pars. But then I'd counter to point out that these stats are derived only from shots hit from the fairway,  so if the "better" side of the fairway also has a fairway bunker over there, then that is going to massively affect the scoring, and that you shouldn't play for that angle you should play for safety first… and so on. Which is what Kyle and I have been talking about, ultimately.

That's why the ultimate target is often still basically the same on the green (or should be) regardless of where you're playing from… (as long as the ball isn't rolling, and any other rare exceptions).

But you would have at least shown that even though the numbers can work out the same, the actual resulting angle might matter in that sense. It'd be looking at it a little too closely, and not seeing the bigger picture, but it'd still speak to the point a bit.
« Last Edit: February 20, 2023, 10:09:31 AM by Erik J. Barzeski »
Erik J. Barzeski @iacas
Author, Lowest Score Wins, Instructor/Coach, and Lifetime Student of the Game.

I generally ignore Rob, Tim, Garland, and Chris.