The Tom Paul Theorem

[BCrosby]

Rich -

I started to call this thing the "Tom Paul Conjecture," but that abbreviates to TPC, an abbreviation that already has a long history on this site.  

Just to let you know, I have contacted the Committee in Stockholm and indicated that, in lieu of the prize, Tom would much prefer a weekend of golf at Myrtle Beach.  They are considering the request.

Bob

[Richard_Goodale]

Bob

Well done.  Make sure that you get the "European" plan at Myrtle Beach.

George

I do not have a stat program handy but I'll gin one up over the weekend at Barona using the direction, distance and trajectory of my wedge shots as my random number generator.

Rich

PS--I'm now carrying a set which consists of Driver, putter and 12 wedges due to the out of control B&I situation.......

[Dan Kelly]

Note to the Barona crowd:

Someone'd better count those wedges. I've known guys who'd try to sneak a 13th in there.

Good title for a golf murder-mystery: "The 13th Wedge."

To accommodate the B&I problems, my own bag has a putter, 13 drivers (vintages 1948 to 1996), and my private stock of Competition Balls.

God, I need a vacation.

[Tom MacWood (Guest)]

Bob
Do you think 16-Cypress Point and 17-St.Andrews are flawed stategically because there are relatively few 2s and 3s respectively - would you consider them among the great hole's in the world? In match play what difference does a hole's par designation make?

[TEPaul]

Bob;

You seem to be logicizing your way through these mathematical applications and the hows and whys very nicely! I think it makes sense to me mathematically so far but of course I'm very limited by my poor math mind in the nuts and bolts of the math itself.

But in the things I probably understand better, ie, the psychology of a number in golf (par) and what it can do to a golfer's perception and decision making, I have to say your logic seems very elegant to me!

But as I understand you, you are saying that a number (par)--(or par change) does make a difference to a golfer, and consequently a number alone (par), if changed, might make a golfer play a hole differently. I agree. But I believe you also said (in your longish post on page 1 to Tom MacW) that if a par number alone were changed on a hole (#13 for instance) that the scoring results would be identical!

How could that be if the number alone has a real effect on a golfer and consequently he makes different decisions because of it? That would seem to inevitably change the scoring results, in my mind! How and by how much and how it would effect both the decision making and scoring results of various levels of golfers is the question.

I believe that the alteration of par on particular holes is a bit of a phenomenon in how it effects the golfers decision making and also his perception of the difficulty or quality of a hole.

But there are certain holes, and #13 ANGC (or #15) might be the best example because of penal Rae's Creek just in front that will exact penalties most and change scoring results most due to it's razor thin risk/reward margins and the consequences!

So again, how would simply the change of a par number on #13, for instance, effect different levels of golfers' perception of the hole, decision making on the hole and their scoring results? I believe in all levels changing to par 4 would make every level play the hole more aggressively. But I think you would see an enormous difference in degree here between the handicap golfer and the Touring Pro!

The handicap golfer would tend to play it far more aggressively as a 4 than a 5. And the Tour pro might too but to such a slim degree as to be almost indistinguishable between a par 4 or 5. Why would the change to 4 have almost an indistinguishable effect in decision making and scoring to a Touring Pro? Simply because they are extremely sophisticated about these things and their risk/reward consequences! In other words their risks are rewarded far more than a handicapper (on a hole like #13). And as a result of that a 4 to a tour pro, say in contention in a traditional dramatic Masters on the back nine, is in fact a par and a 5 is a bogie in effect (and worst than that is probably losing the tournament).

To almost all amateurs par is taken very seriously as a number alone (maybe net par but in effect the same perception of a number)--and I suppose one of the reasons the number is taken more seriously by the amateur is because basically they are generally looking at the hole and its par in a vacuum (certainly compared to the tour pro).

To a tour pro the par number may not even be of consequence--but what is of consequence to them is what the others they have to deal with are likely and expected (by them) to make--of course always considering what the overall tournament numbers are in relationship to those in contention. The example may be the last nine on Sunday but the real interest is that it's just fascinating to note how Tour pros approach the same hole on different days!!

If you want to see the true effect of the cliche "you can lose a tournament on Thurs, Friday, or Sat but you can't win it", this is it in spades. And when Sunday afternoon rolls around and they have managed to do that one thing that they all talk about and strive all tournament to do, ie, "put themselves in position to win", depending on the relative total tournment numbers in relation to each other is where the real fireworks begin and the drama begins or not!

At either #13 or #15 ANGC the entire spectrum of this kind of sophisticated decision making (almost totally disregarding the actual par of the hole) can be perfectly bracketed by the remarks of Hogan, on the one hand, and Nicklaus in '86 on the other hand. Hogan said, "I didn't need an eagle!" That is a  quite cocky and now humorous way of actually saying he could settle for par (5)! Nicklaus, on the other hand, in his short conversation with his son about going for one of those holes with a 3 iron with the clear intent on making an eagle 3, knew he basically could not settle for less than eagle at that point.

My recollection of Nicklaus's remark to his son was simply fascinating because the way he said it either clearly said or clearly implied not how cool it would be to make an eagle there but what a tremendous effect it would have on his fellow competitors (and probably their decision making!). That seemed to be exactly what he was saying and thinking in his decison making!

Nicklaus's unbelievably prescient career-long ability to calculate what he had to do in relation to his fellow competitors at any particular time and the effect that aura had on his fellow competitors seemed to be quite clear to him and part of his decision making. In other words he was obviously aware that the unbelievable explosion of yelling and screaming through the pines if he made the eagle would probably have a much bigger effect than the eagle itself!

Maybe what I'm saying is completely self evident about the degrees of decision making by different levels in relation to the particular par number of any hole but I thought I would say it anyway, in case it wasn't! I guess, I'm saying that to Hogan and to Nicklaus the par number really was meaningless because each knew what they needed to make although that actually was 2 shots difference on the same hole!

Changing a par number on any hole without changing the hole will make a difference to everyone, but to vastly differing degrees, and that's probably the question and may influence this math too--but as to how or how much, I'll leave to you!

[TEPaul]

Tom MacW;

I could be mistaken but I think Bob is saying that on certain holes a particular par number is just very useful mathematically and possibly valid mathematically and otherwise. And because various golfers and levels of golfers happen to look at a particular par number differently really does not make a particular mathematically useful number less useful or possibly less valid.

[TEPaul]

Mike Cirba:

Jeeesus, don't be in such a rush! Can't you see that Bob is working on mathematizing the functional quality of golf holes from an actual playing standpoint? He's going for the Nobel Prize here on this part alone!

You're already getting way ahead of him and bringing things like aesthetics into the equation! Let him solve this first and then he can launch into mathematizing the aesthetics of any golf hole too!

I admit, to mathematize the aesthetics of golf holes he will be dealing in total subjectivity and he might actually have to tap into "The Nash Equilibrium" itself for that one, but I have faith in him, and you should too.

If he pulls off one and then the other, he will probably go for the "General Theory of All Aspects of Golf Architecture"--mathematize it all in one overall formula, and then he will have actually topped Albert Einstein himself who tried something as mundane as mathematizing God and the entire Universe and failed to do it!

[Mike_Cirba]

Tom,

Far be it for me to stop Bob on such a "Noble" quest!  You go, Bob!    I've seen metrics developed in other pursuits that attempted to subjectively quantify aesthetic and sensual considerations, but those "measuring sticks" are best not mentioned on a family program.

By the way, Tom...any thoughts on how a modern architect might view your use of equilibrium theory on routing?  I would just hate to see your original premise become co-opted and corrupted as I postulated (my, aren't we all becoming scientific!) earlier in this discussion.  I hear a scientifically iron-clad proof of the superiority of modern architects is being appended to Mr. Fazio's book as we speak!  

[Dave O]

I have to chime in here as the resident statistics wonk.  There are several mathematical tools that we use to measure the distribution of values around a mean, or in our case, scores around par.  There are two of interest to us.

The first is the standard deviation, which measures the range values around a mean.  The math is a bit complicated but if you have Excel or a decent calculator you can compute it easily.  The larger the standard deviation, the greater the range of scores.  However, this test assumes that the scores are normally distributed, which we know they are not (you can score 4 over on a par 4 but not 4 under).  So you can get a high standard deviation with, for instance, lots of scores under par and just a few that are over if they're high enough.  So we also need to look at how the scores are distributed.  

However, there's something working in our favor called the Central Limit Theorem, which says that if you get enough data - which we should have plenty in the Masters example - then most populations of data start to behave like normal distributions.  And this seems intuitively true, as you think about the 9 that Vijay scored on (which hole was it?) - that score would weight any statistics heavily if there were only 5 or 10 other scores, but if there are 500 or more then it becomes unimportant.

Which is a rather long way or saying that standard deviation alone should be enough in this case.  I don't have the raw data but it would be interesting to see if the methods worked.  I'm still trying to work through the logic of BCrosby's technique.

[ChipOat]

I hate to (temporarily) throw water on this but a single year's worth of data falls well short of "statistically significant" - the sample isn't large enough (about 380 observations over 4 days??).  Without working through the numbers on my HP, I'n guessing that about 1000 observations per hole (over multiple weather conditions) will give you a meaningful bell curve/normal distribution from which to draw conclusions.

Another thought is that if the samples are limited to golfers of a certain ability (i.e. a tight handicap range), I guarantee we'd find that many holes rank differently depending on the golfer's skill.  That's no surprise, of course, but the TPT would fascinate us by quantifying the differentials.

The Tom Paul Theorem, given its genesis, is surely worthy of further statistical study.

[TEPaul]

Would you look at this stuff!? Dave O's "Central Limit Theorem"! This is very impressive! "Given enough data then most populations of data start to behave like normal distributions. This would seem intutively true and VJ's 9 (given enough data) would be unimportant." How cool is this stuff!?

MikeC:

I must admit my "scoring spectrum" idea on any particular hole as some sort of barometer of architectural quality has been taken over by mathematical geniuses! I don't really even know the end result of someone accurately "mathematizing" something into a "provable" theorem, except it may give us a very effective hammer to pummel anyone who denies our ideas about architecture into submission as someone who "doesn't get it" and resulting in a situation where everyone can be certain "he doesn't get it" including the bloody mess we've just pummeled into submission!

If this "TPT Theorem" looks to Bob and some of these math wizards as a reliable and valid tool I really don't think we should pussyfoot around in testing out it's effectiveness!

I don't know where Pat Mucci is right now but when he gets back I suggest we try it out on him first! If we can get him to sputter through bloody lips the heretofore unbelievably unlikely words; "You're right and I'm Wrong", then I would say this "TPT Theorem" is about as reliable as the fact that the sun will rise tomorrow morning!

As for your idea and fears about Tom Fazio co-opting this into some provable way of advancing the idea that he has created some kind of "equilibrium" in architecture and cast classic/strategic architecture and its priniciples into the trash heap of golf architectural history, then I would say you're too fixated on the meaning of the word "equilibrium"  and you're on a meaningless tangent!

I don't even know if "barometer", "equilibrium" or "theorem" are remotely synonymous, and I don't know if I care, at this point.

I feel though that "randomness" used properly in an architectural sense creates temptations, varying options and decision making and a degree of uncertainty all resuting in a rather wide score spectrum on any hole giving it degrees of architectural quality.

So if Fazio thinks this thing that some call "equilibrium" means any kind of sameness and uniformity, he's dead wrong and you have nothing to fear!

As for your "routing" question and how to apply this kind of thinking, actually I might be scratching the surface of something I'll report on a little later about that!

[TEPaul]

Chip:

Take a look at my 4:17pm (incredibly long) post about how a scoring spectrum on a particular hole might apply differently to different levels of golfers.

[Mike_Cirba]

Tom,

I think you may have missed my earlier post related to your mention of equilibrium theory and how it may be viewed through the eyes and opinions of a modern architect.

For you perusal, I have copied it below.  For everyone else who may have read it already, my apologies.

Tom Paul,

Interesting your mention of Nash's equilibrium theory as relates to course architecture.

However, somewhat ironically, you probably have inadvertedly given credence to the Tom Fazio philosophy of design.

It would seem for equilibrium theory to apply to golf course architecture, in the way you suggest, two things would need to remain static;

1) The amount of land for the routing
2) The topography of that land as fit for golf usage

By way of contrast, a modern architect would try to change those static attributes.  If aquiring additional, more suitable (if much more spread out routing) land for golf wasn't a possibility, they would probably focus on changing number two.

Using your example, Tom Fazio might argue that Nash's barroom revelation was simply short-sighted.  Instead, he would seek to change the five other girls into "10's", as well, probably through massive reshaping, restructuring, and artifice (and silicone, or at least bunker-woll ).  That way, he might argue, everyone wins.

Of course, the debate then becomes to what extent is the cost involved in the "makeover" inevitably good for the game, and more importantly, can the trained eye still detect that the beauty is surface only, without real depth?

With escalating costs, boilerplate design, and often diminished strategy and quirk, does everyone really win?    

Thanks for your thoughts...

Mike

[John_McMillan]

Weighing in on the statistical issues -

The central limit theorem is a neat theorem - but not particularly relevant here.  It is true that "most" statistical populations converge to the normal distribution - but the exceptions include truncated distribitions - which Dave points out is the case in golf data - the only possible scores on the 13'th at Augusta are 2 or higher.  

That said, it's not a problem that the central limit theorem doesn't apply - since one isn't making statistical tests or probabilistic statements about the data.  The standard deviation is a statistic which measures the dispersal of data of all populations and distributions.  One is probably more familiar with its tricky cousin, the variance (variance = standard distribution squared).  It would be interesting to see what these statistics are for holes played in the Masters tournament.  

An addendum to the theorem might be that higher variance of scores is a sufficient, but not necessary, condition for a more interesting golf hole.  As I think previous posts have pointed out, a hole can be severely penal - and have a high variance of scores, without being too interesting.  An example is a putt-putt hole I used to play.  It was an uphill 15 foot putt uphill along a narrow lane.  If you missed a fraction of an inch to the right or left, the ball came back, and you tried it again.  No options for the shot - you either made it or you didn't, and if you didn't, you kept trying until you did.  The hole had a high variance of strokes, because some would hole their first putt, while others might take 7 or 8 putts until they got the shot right.  In the case of the 13'th at Augusta, a variance comes because of the choice to go for the green in 2, with more eagles and double bogeys, or lay up with fewer birdies and more pars.

[TEPaul]

John:

Sounds good to me! We should call that "The Essential MacMillan Addendum". If it's sufficient to you it is to me too!

MikeC:

Yes sir, the Faz could co-opt and try to do those things, but he'd be wrong and all his "10s" would be likely to fail the "TPT" application miserably.

[ChrisB (Guest)]

That sound you heard was my head exploding...and I have 2 degrees in stats (lies, damn lies, and...).

[Mike_Cirba]

ChrisB;

Thanks for the best laugh I've had in weeks!  I literally have tears running down my cheeks as I type from your post!  

Yes, we do tend to get a little deep here, but bear with us.  You know the old saying that what you learn in college is about 1% of what you eventually learn through real world application.  

Whether the theories espoused here actually stand up to the cold, harsh light of scientific research is something for the Nobel Committee to determine.  If this isn't a place for people to think and speculate "outside the box", then I don't know what is.  

If nothing else, it sure beats discussing the fine conditioning of Condo Hills CC, the latest and greatest Palm Springs CCFAD.  

And, if you think your head is exploding right now, you should spend some time with this crew in a bar after a few rounds.  On the other hand, you'll surely also laugh just as hard as your insightful post just made me!

[TEPaul]

ChrisB;

Forget about the stats and the attempts to mathematically prove the quality of golf holes. It should be easier to make your head explode just to consider some of the reasons  people think golf holes have quality without a single attempt on their part to prove it!

[John_McMillan]

TEP -

The value of the number crunching exercise should not be to prove something about the holes at Augusta National.  That course is well enough known that not many insights are going to come into that course - particularly for this group.  The value of the exercise would come in the future when discussing some hole which we might at first blush think is rather boring.  Someone can come up with the statistic that it has a high variance of scoring on the hole, which since we've calibrated the theory and know it works on the holes at Augusta National would lead us to re-think how we evaluate the hole.

For example, if someone discovered that the variance of scoring on holes at Medinah was similar to the holes at August National, I would re-think the (currently low) opinion I have of that design.  I don't think the numbers are going to fall out that way - but that would be the potential of the exercise.

[TEPaul]

John MacM:

I do realize the potential of the exercise, I believe. I'm not very mathematical though, and in some of these posts I've been slightly facetious about the excercise, I suppose, but if some think TPT can work well and display some kind of real consistency to it, heh, I think that's great--maybe it really can and maybe it can more accurately indicate something like quality or even quality in archtiecture.

My feeling about this is and has been simply that a hole that has a wide scoring spectrum is generally an interesting hole and a hole that has a narrow scoring spectrum generally isn't.

But I've never been into ranking and rating at all in golf architecture, and that involves numbers. Whether its the top 100 list, or some course being #5 and another being #17 or even a Doak number of a particular course.

I think it was interesting for Tom Doak to come up with his "Doak" numbers in his book, but that's Tom Doak's valuation, period. For others to use Doak Numbers with apparent certaintly like 5 or 7.5 and speak and even argue about it with apparent certainty is fairly ridiculous to me! What are they actually basing that on? They appear to me to just pull numbers out of the air for reasons of their own that are anything but clear to me. The same with the rankings, in my opinion, despite even the inclusion of all this "criteria", the viewing and evaluation of same which is completely subjective.

But analyzing a scoring spectrum on a golf hole would seem to me to have more of a basis in reality because you're not being completely subjective--you're analyzing the game of golf itself on those holes and the way it's actually played on them--the primary reason the holes exist.

Scoring on holes and even reams of data of scoring on holes may even have a basis in subjectivity too but that's OK to me since the scoring is the game and on any hole is the result of anyone's and everyone's decision making as it relates to how the game is best played by them.

But again, I'm not really into math and formula but I do admire Bob Crosby for attemtping to mathmeticize a particular idea or theory and if he appears to pull it off to the satisfiction and understanding of most, I think that's great. I'll certainly try to understand the hows and whys of the math too if he does that.

But in the meantime, I just feel that a wide scoring band on a hole shows the hole is interesting, probably exciting and fun to play, and a hole with a narrow scoring band probably isn't as it indicates a certain "one dimensionality" to me. That idea just makes commonsense to me.

[BCrosby]

Lots of interesting posts.

Tom Paul -

Not 30 seconds after my post from yesterday afternoon I realized I had said something to Tom MacWood that didn't make sense.  You had the bad manners to point it out almost immediately.  Yes, the par designation of a hole will probably affect the raw scoring data for a hole.  Again, that's because the par of a hole sets the framework for the strategic choices of a hole.   You think differently about a long approach to a green guarded by severe hazards (like no. 13 at ANGC) depending on whether it is a par 4 or a par 5.  On the margin, people will make different shot choices because of the difference in par.  That will result in slightly different raw scores.

John -

I was hoping you would chime in.  I believe that there probably are more mathematically elegant ways to get at the TPT numbers (though given the simple ratios, the TPT numbers are damn easy to derive).  But I do think that par has to be kept as the point from which scoring distribution is measured. Why?  Because the utility of the TPT is not that it tells us just the distribution or mean variation of scores.  That raw number, I think, would be relatively uninteresting.  What the TPT number tells you is the width and depth of the distribution of scores both under and over par.  

That number is interesting, I think, because it gives us a way to measure the success or failure of hole designs where the goal was to encourage a wide band of scoring.  Put differently (and to grossly oversimplify) it measures the success or failure of the design of a hole against a partiuclar theory of good golf course design.  The TPT is not an exercise in number crunching, like, say, a sociological study that measures how many people smoke after sex or don't smoke after sex.  The point of the TPT is to test the success or failure of the design of a hole against architectural standards associated with the Golden Age.  Personally, I think it is worth going through all this stuff because I believe so strongly in that particular architectural standard.  But if you don't believe in that particular architectural standard, none of this will have any interest for you.

I don't think you disagree with any of the foregoing.  I am confident you will let me know if you do.  You raise one question that I've been thinking about too.  Specifically, could the TPT numbers be used to make comparisons not just among par 4's at ANGC, but across courses, say between the par 4's at ANGC and the par 4's at Medinah.  A priori, I can't think why not, assuming each of the following is true:

- you have similarly sized fields;
- you have similalry skilled palyers (comparing the scoring data at the Masters with the scoring data for a Member/Guest at Medinah would make no sense);
- you have a similar number of rounds scored;
- the rounds are played under similar rules and playing conditions.

Seems to me that all those conditions are satisfied at any PGA tour stop, major event or otherwise.  So yes, I think its an experiment worth trying.  The problem is going to be getting the raw scoring data you need to run the ratios.  The PGA doens't typically provide them.  I know, I've asked.  Does the USGA provide them at UA Opens?

You also note the central irony of the TPT which is that to test its value as a predictor of good designs, you must test it against our previously determined, purely subjective rankings. But that's ok.  The TPT is a new theory and as a first order of business it has to come up with plausible results.  They can't be results that have nothing to do with our well developed instincts.  At least at the Masters this year, the TPT numbers for ANGC pass that test.  

Mightn't it be the case, however, that someday after a several of run-throughs where the TPT continues to select holes that confirm our best subjective judgments, mightn't it be possible that someday we could begin to give the TPT number some credence on its own?  We'll see.

Mike Cirba -

The TPT is not intended to foreclose any other standard for golf course architecture.  You want to measure a course based on aesthetics, naturalism, resitance to scoring, hydrology, drainage, or cart girls, all those methods are perfectly legitimate.  The TPT is just another tool in the toolbox.

Chipoat -

Maybe the 2002 Masters is not a big enough field, I don't know.  But early results are interesting and indicate there may be some value in continuing to apply the TPT.  At least for the wingnuts that frequent this site.

Tom Mac -

Damn you ask good questions.  First, let me say I've never played or seen no. 16 at Cypress or no. 17 at TOC other than on TV.  I have played ANGC several times.

My guess is that a major field at Cypress over four days would score on 16 slightly better than they scored at no. 4 at ANGC.  Just a guess.  No. 4 is about the same length but has a much smaller putting surface with more places to tuck pins.  No. 16 will have more wind, but I strongly doubt that it would play as a 3.5 to a field of 100 of the best players in the world.  But I don't know for sure and no one else will either till we have the data.

No. 17 at TOC poses more intersting issues for the TPT.  It probably does play at 4.5 for the best players in the world. My guess would be that no. 17 yields a low TPT number if you use a par of 4.  It probably wouldn't be quite as bad as the numbers we came up with for no. 13 at ANGC, but still pretty bad.  If, however, you run the TPT on no. 17 with a par of 5, I suspect you will come up with a very high TPT number.  Maybe the highest on TOC.

Seems to me all that says is that maybe some serious attention should be paid to playing no. 17 as a par 5.  I think lots of pros do play the hole that way.  I've heard interviews where they say so.  In addition, the hole was once designated as a par 5.

Bottom line is that the TPT argues that no. 17 should be a par 5 (assuming the TPT numbers come out as we are guessing). The TPT says that a par 5 designation would be a closer match to the real playing charactersitics of the hole.  You and others may disagree, but it is not a crazy result.  Lots of normal, reasonable people believe no. 17 really is a par 5.  Thus I don't think the difference in the par4/par 5 results for no. 17 under TPT is a particularly troubling indictment of the TPT.

Bob    



  



  

  

[TEPaul]

Bob:

Taking #17 TOC as an example of what par on the hole should be, why not look at it this way?

All par is on any hole is what an expert player is expected to make (with no flukes or whatever they call it). But that really isn't all that analytical and mainly relies only on length! Extremely dangerous features like the orientation of the green, the close proximity of the road and the penal Road hole bunker are not taken into consideration as to what the par should be as much as length obviously is.

So now they call it a par 4 but again that is not all that analytical. If they were interested in determining what exactly the actual par is (what an expert player is expected to make) they could average all the scores of the Open Championship or championships and determine what the average score is that an expert player is likely to make. Seems to me that would be closer to 5 than 4.

So consequently why worry too much about how the TPT skews the number on a hole like that when using a 4 in your calculations? They can call it a par 4 if they want but raw data should prove year in and year out it's more than a par 4 in reality--at least in the technical sense!

[johnk]

BCrosby,

If you want the raw data, I'd suggest you send
Sal Johnson (golfersal@aol.com) a link to this thread, and ask him for the data.

He's got it, for sure, and this might be interesting to him.

You'd be able to calculate the TPT values for every
hole played on the PGA Tour, which might be fun.

johnk

[BCrosby]

JohnK -

Thanks. I tried to call the PGA offices about three weeks ago to get some scoring data and got the complete run around.

TEP -

I agree, though I would come at it a little differently.  First, I think Tom MacWood was trying to criticize the TPT by saying that it gives a nutty result for holes like 17 at TOC.  So my point was that the higher TPT score for 17 as a par 5 vs. the lower score as a par 4 simply reflects the debate that many have had for a long time about what the best par for that hole should be.  In short, the TPT results are not nutty but merely reflective of that larger debate about the hole.

Second, the TPT number is screaming that 17 should be a played as a par 5.   If we are to judge the hole using Golden Age type standards, the TPT is jumping up and down waving it hands and yelling in our face to make it a par 5.  (On the other hand, if you prefer to judge the hole solely on the basis of its resistance to scoring, then keep it as a par 4.  You know where I come out on those two approaches.)

I'll say this very quietly - and you have to promise not to tell anyone - but maybe, just maybe, the TPT is right and the R&A is wrong about no. 17.

All of which is just another way of saying what you are saying.  I think.

Bob

  

[TEPaul]

Bob:

Whew! Yes indeedee--I promise to be very quiet about that all right! We might need to put a curtain on that last paragraph for a while! The R&A wrong? Whew, perish the thought!