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Ben Sims

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Re: Length Realllllly Matters
« Reply #25 on: April 24, 2009, 02:04:25 AM »
Jim,

I guess my question is this. Aren't the mechanisms in place (at least at the majors) for this argument to dissolve?  Augusta, US Open, Open Championship (to an extent), PGA Champ, all place a huge amount of emphasis on accuracy in the fairway.  Kenny Perry readily admits he's given up 5-7 yards with his new R9 in order to hit more fairways.  Isn't 5-7 yards just about a half to a full club for him? Is length the answer, or greens more akin to Dove Mountain at the match play earlier this year where the pros were dumbfounded?  I just don't see this thread as unique and earth-shattering enough to stir the pot in any new direction.  It's the age old argument about golf courses really...

Jim_Kennedy

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Re: Length Realllllly Matters
« Reply #26 on: April 24, 2009, 02:35:25 AM »
Ben,
There is no getting around the fact that hitting fairways is a good thing, and Kenny Perry knows this, but the longest players find a scoring advantage on the shorter holes by bombing it close and having a wedge approach vs. the longer approach faced by the shorter hitter.

I'm probably in the minority, but I don't believe that highly contoured greens will do much else than raise the scoring average of the field a bit. It won't change who wins.

There really is no stopping Tour players from scoring well unless you make the course silly.

   

"I never beat a well man in my life" - Harry Vardon

Ben Sims

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Re: Length Realllllly Matters
« Reply #27 on: April 24, 2009, 02:51:51 AM »
Jim,

And there you go.  Just like the commercials say, "These guys are good."  Funhouse mirror courses will only detract from overall enjoyment of the game.  For me really, 5 inch overwatered rough and 13' stimped greens are not the answer.  Jack's onto something with the tournament ball, but it'll never happen.  Too much money.  USGA made a phenomenal move in regulating wedge spin.  But it won't change the winners too much really.  Distance and putting prowess combined. It's what has separated the good players from great for eons.  It will continue to be so.

Again though.  I don't think extraordinary length was ever the deciding factor.  It has definitely helped.  But didn't Daly have to be accurate a little bit to win those two majors?  And didn't Tiger dismantle Pebble in 2000 with irons off a lot of tees?  Just a thought.

Brent Hutto

Re: Length Realllllly Matters
« Reply #28 on: April 24, 2009, 10:47:47 AM »
First problem...the "problem" as stated makes a claim concerning Accuracy backed up by an idiotic measure Percentage of Fairways Hit. A simple yes/no tally of on the fairway versus off the fairway, especially on tricked up Tour courses, has a very tenuous relationship to any meaningful definition of Accuracy as a desirable skill.

Low correlations can arise in two ways with very different implications. There can be a genuine lack of causal association between the things you're making claims about. Or there can be a moderate to high degree of association between the actual things but low correlations between the actual thing and the measure chosen to represent it. It is obvious in this case that the latter applies w.r.t. Percentage of Fairways Hit as a measure of Accuracy. In the presence of massive attenuation due to measurement error/bias you can make no assessment whatsoever as to the strength of association between the things you're actually interested in.

Second problem...the USGA is engaged in a protracted campaign to gain acceptance for "reining in" what they view as an evil and unmerited advantage gained by elite players who can spin the living shit out of the ball from the rough using (legal) high-lofted wedges with (currently legal) highly efficient grooves. Whenever someone makes a self-serving claim using laughably invalid measures for support the most plausible explanation is they're blowing smoke up your arse.

The USGA has more resources than God and is perfectly capable of a) hiring people who understand they are really not talking about Accuracy per se and b) collecting and analyzing data that represents some realistically meaningful concept of Accuracy. This is not based on an "analysis" in the sense of someone looking for answers to a question of interest. This is finding some bullshit numbers that appear to support an a priori conclusion that was arrived at for political, emotional or commercial reasons.

Brent Hutto

Re: Length Realllllly Matters
« Reply #29 on: April 24, 2009, 10:51:07 AM »
Mr. McBride,

As a 14 handicap that has length off the tee, I can assure you I would rather be in a match against a shorter competitor on a 7000+ layout.  I'd rather hit 9 iron from rough than 4 iron from fairway any day.

But the question of V grooves from rough is intriguing in it's simplicity.  Studies are showing almost no change in spin from short grass, but spin rates from rough seem to decrease almost 40%.  I think the field better adapt.

But driving accuracy--sorry to blast this thread--will ALWAYS be a function of winning. 

ONLY if PENAL golf features greet those who are inaccurate.

Altering the grooves won't have that much affect on the greatest golfers in the world.  They'll learn how to compensate for it by adjusting their technique and shots.



 Total Driving may have replaced that from years past.

Let me take this opportunity to say to Pat Mucci...

Exactly right, sir. Thank you.

P.S. But the green ink is still kinda weird even when you're making a good point! :-*

Tom_Doak

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Re: Length Realllllly Matters
« Reply #30 on: April 24, 2009, 11:01:23 AM »
If you want shorter, accurate hitters to have a better chance of competing, all you have to do is play SHORTER courses.  Anybody can see those courses produce a different set of winners, and that Tiger is not as dominant in such conditions.

On the other hand, since Tiger is clearly the best player, why would you want to prevent him from winning?

The USGA seems more interested in protecting par than in finding a worthy winner.  They've altogether forgotten about keeping the game fun.  They seem to agree with the golf writers who are shills for the equipment companies on that score ... that better equipment makes the game more fun for average golfers ... forgetting that the same equipment is also promoting difficult architecture, and the USGA's role as the most visible champion of making courses tougher.

JESII

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Re: Length Realllllly Matters
« Reply #31 on: April 24, 2009, 11:10:09 AM »
Does anyone else on this thread think that one of the main reasons players have adopted the "Bomb and Gauge" approach is that 6 - 8 foot putts are just not that difficult for them anymore?

I'd bet there is less "bomb and gauge" on the courses with tougher greens...

Jason Topp

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Re: Length Realllllly Matters
« Reply #32 on: April 24, 2009, 11:12:37 AM »

The USGA seems more interested in protecting par than in finding a worthy winner.  They've altogether forgotten about keeping the game fun.  They seem to agree with the golf writers who are shills for the equipment companies on that score ... that better equipment makes the game more fun for average golfers ... forgetting that the same equipment is also promoting difficult architecture, and the USGA's role as the most visible champion of making courses tougher.

Historically, I would agree with this view, but I think the current USGA set up guy has really made a difference on this front.



Jim_Kennedy

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Re: Length Realllllly Matters
« Reply #33 on: April 24, 2009, 11:13:36 AM »
Ben,
Tiger also dismantled Pebble by having the ability to hit par 5s in two from  200+ yard out, in 6" of rough, and with a 7 iron.
There are at least 50 players on Tour whose par is 68, not 72, when they step on the first tee. Length isn't the only factor, but it helps.

As far as statistics go, they are fun to look at and useful but they are not reliable predictors of future performance.
"I never beat a well man in my life" - Harry Vardon

Gary Slatter

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Re: Length Realllllly Matters
« Reply #34 on: April 24, 2009, 11:15:23 AM »
In his (auto)biography "The Education of a Golfer," Sam Snead said something to the effect that he would rather have an 8-iron out of the rough than a 5-iron from the fairway. 

Now Snead is one of the greatest golfers of all time and he employed this tactic on a somewhat regular basis, no different than some guys today.  He clearly possessed the length, and the control he had with the shorter club to hit the green in regulation (even from the rough) seemed to often outweigh the peril of hitting tee shots accurately.  This concept made sense years ago, and it often still does.

...But then again, Snead also tanked the 1939 US Open on account of his lack of course management, so perhaps he's not the leading theorist on the subject.


I think Sam cleaned the grooves of his 8 iron with a file.
Gary Slatter
gary.slatter@raffles.com

Brent Hutto

Re: Length Realllllly Matters
« Reply #35 on: April 24, 2009, 11:40:36 AM »
Does anyone else on this thread think that one of the main reasons players have adopted the "Bomb and Gauge" approach is that 6 - 8 foot putts are just not that difficult for them anymore?

I'd bet there is less "bomb and gauge" on the courses with tougher greens...

That idea had never occurred to me but it seems very likely true. It is indisputable that pros today make more 8-footers than they did in Nicklaus's heyday and probably make immensely more of them than they did in Snead's. And I find it convincing to think that laying back to 170 yards or more by hitting an iron off the tee really lengthens the odds of hitting in to 6-8 feet even from a perfect lie.

So if I understand your theory, it's that in the past they payoff for getting inside, say, 10 feet was such-and-such fraction of a stroke. Now on perfect greens the payoff is maybe twice as great because they make twice as many 8-footers. But at an Oakmont Open setup of Augusta Masters setup that's less true.

I like it...

JESII

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Re: Length Realllllly Matters
« Reply #36 on: April 24, 2009, 11:50:12 AM »
true Brent, but I was thinking of par putts.

I see these guys blast away from the tee with the seeming comfort in knowing that the worst a drive can do is force as low running shot up next to the green from where they chip insode of 10 feet and make it for par...but the good drives are now 30 yards closer to the hole than the smoother swing...

Jerry Kluger

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Re: Length Realllllly Matters
« Reply #37 on: April 24, 2009, 12:03:01 PM »
Brent: For a guy with a scientific mind you seem so eager to accept a statement as fact without any evidence to support it.  I do not accept as a fact that players today make more 6 to 8 foot putts.  Sure, the guy who is leading makes more of them but we all know from our own experience that we are human beings and sometimes we perform better than other times. 

Another fact which should be taken into account is today's drivers.  How much accuracy does a player give up with a 460cc driver and 45 inch shaft versus a 190cc 3 wood with a 43.5 inch shaft - I don't know the answer but I would guess it isn't much. 

Limiting fairways to a maximum of 25 yards combined with 6 inch primary rough makes for a premium on accuracy.  Does it make for better golf or more interesting golf - Cabrera won at Oakmont and ANGC and he surely is a bomber.  Personally, I think that his play at ANGC was more interesting to watch and required more types of shots. 

JESII

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Re: Length Realllllly Matters
« Reply #38 on: April 24, 2009, 12:06:41 PM »
Jerry,

You must think one of two things; either the maintenance of greens on the PGA Tour is worse today than 20 years ago, or the players putting mechanics have deteriorated in these 20 years...otherwise, more 6 - 8 foot putts are going in the hole!

Brent Hutto

Re: Length Realllllly Matters
« Reply #39 on: April 24, 2009, 12:10:40 PM »
The made-putts-by-distance numbers from ShotLink in that range are quite significantly higher than the same numbers gathered by Dave Pelz 15-20 years ago. I trust the ShotLink number completely and the Pelz numbers unless someone has evidence his methods were flawed. I don't have the comparison at hand but they have come close to doubling their percentage made in the 6, 8, 10 foot range over just a couple decades.

Chuck Brown

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Re: Length Realllllly Matters
« Reply #40 on: April 24, 2009, 12:32:18 PM »
It would have been nice to ask Jim Vernon (a very nice man, by all accounts, and a good man for the USGA as far as I know) some questions:

1.  "Jim, are we to understand that the USGA has mixed motives in enacting the groove regulations; that one goal is to reward the player that hits more fairways, but also to encourage players to 'throttle back' off the tee, in order to hit those fairways?"

2.  "Does the USGA anticipate that tour players will demand, from their ball sponsors, balls that spin more, to make up for lost spin due to groove re-formations?"

3.  "Is it the hope of the USGA that with tour players feeling that they need more spin, and putting higher-spin balls into play, that the USGA will have effectively encouraged a kind of voluntary rollback among the players affected by the groove rules?"

4.  "Does the USGA fear that tour players will not respond to the groove rules as anticipated (per the above questions and answers), but will instead elect to put higher-lofted wedges, of 62-64 degrees or more, and thereby generate spin [or at least, ball-stopping loft], while using low-spin balls that they can bomb off the tee?"  This leads to other questions:  "Will the USGA ban high-lofted clubs of more than 60 degrees, and how would you expect average tournament committees to police lofts, since a 60-degree wedge can quite easily be bent to 63 or more"?

5.  "The USGA has always maintained the position (laudable, in my own view) that any 'bifurcation' of the rules was a big negative.  Why should anyone consider the groove rules as antything other than a 'bifurcation'?"

6.  "Under the Joint Statement of Principles, the USGA pronounced in 2002 that any further gains in golf ball distance due to technology would be undesirable.  Then, there were more gains, and now, with technology itself apparently somewhat 'flat', distance gains themselves have flattened.  Doesn't the USGA and PGA Tour data pretty conclusively prove that in the last 20 years, golf ball distances have jumped markedly in association with technology, and flattened when technology is static?  Doesn't it all prove that player size, player fitness, player training and coaching, etc., are all red-herrings in the debate of golf ball distance?"

7.  "Will the USGA publish its golf ball study data?"

[Edit., to add one more question for Mr. Vernon...]

8.   "Are you able to tell us, has the USGA been threatened by any equipment manufacturer with litigation if the USGA were to roll back the fail-point in the Overall Distance Standard, as many of golf's most prominent players, course architects and writers have suggested should be done?"
« Last Edit: April 24, 2009, 05:14:29 PM by Chuck Brown »

Jerry Kluger

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Re: Length Realllllly Matters
« Reply #41 on: April 24, 2009, 01:01:11 PM »
I agree that today's greens are probably smoother than they were in Nicklaus' or Snead's day, but aren't they a heck of a lot faster as well. 

JESII

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Re: Length Realllllly Matters
« Reply #42 on: April 24, 2009, 04:14:08 PM »
Sure, but from inside 10 feet on generally flat greens (most Tour greens) faster is better/easier.

Garland Bayley

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Re: Length Realllllly Matters
« Reply #43 on: April 24, 2009, 04:31:17 PM »
Garland,
Grooves on a driver, or any club less than 20*s of loft,  lessen the backspin. The reverse is true when lofts get over 40*.

I guess many of the long drive championship competitors didn't get the memo, because they use grooveless drivers.
"I enjoy a course where the challenges are contained WITHIN it, and recovery is part of the game  not a course where the challenge is to stay ON it." Jeff Warne

Jason Topp

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Re: Length Realllllly Matters
« Reply #44 on: April 24, 2009, 04:47:36 PM »
Does anyone else on this thread think that one of the main reasons players have adopted the "Bomb and Gauge" approach is that 6 - 8 foot putts are just not that difficult for them anymore?

I'd bet there is less "bomb and gauge" on the courses with tougher greens...

Jim:

Interesting question.  I've been reading a Bill James baseball statistics book recently so forgive this analysis which I will break into three posts:

History of Bomb and Gouge -

Statistics and results show that top players changed strategies in the the early 2000's - increasing their focus on length and worrying less about accuracy.

Vijay Singh and Tiger Woods show this well.

2000

Tiger hit the ball 20 yards farther than Singh off the tee (298 to 279) and hit more fairways (71.2 (ranked 54th) to 67.9 (ranked 112th)  Woods won $9 million and Singh $2.5.  Woods won 9 out of 20 tournaments.  Singh won 1 out of 26.

2004

The driving distance difference shrunk to nothing and Singh was slightly more accurate than Woods (60% to 56%) but 4% less accurate than the year before and 12% less accurate than in 2000.  In other words, Singh decided to sacrifice accuracy to make up his distance gap 8behind Woods.

Singh won 9 tournaments and $10.5 million and Woods won 1 tournament and $5.3 million. 

2005 

Woods cranked up his driving again - adding 15 yards and taking a 15 yard advantage over Singh (316 - 301) and a little hit in accuracy, now behind Singh by 6% (60-54).  Woods won $10.5 and Singh won $8.5 million that year.  Woods won 6 out of 19 tournaments.  Singh won 4 out of 30.


Since 2005, Woods has won 20 more tournaments.  Singh has won 6. 

Jason Topp

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Re: Length Realllllly Matters
« Reply #45 on: April 24, 2009, 04:48:04 PM »
Possible explanations as to why it works:

1.  Easier short putts

As to your theory that an improvement in ability to make short putts explain why players adopted bomb and gouge, I doubt it for two reasons: 

One - I believe 6-8 foot putts have gotten easier but not by a ton.  Pelz's studies showed 6 feet as the 50/50 point for a tour pro back in the 80's.  It is impossible to tell for sure from the PGA Tour statistics but it looks to me like that distance may have increased a foot or maybe a foot and 1/2 at most.

Two - If easier putting is the cause, one would expect bomb and gouge to be increasing on tour even after driving distance jumped.  I do not think the statistics support such a view.

2.  Courses are too long

   Tom Doak opined longer hitters do better than shorter hitters on longer courses.  That statement is inconsistent with recent Masters history in which shorter hitters have done much better after the course was lengthened. 

   As I will spell out below, I think shorter courses negate the advantages enjoyed by long hitters if they are really short or something about the course takes driver out of a long hitters hands (e.g.  a bunch of doglegs bordered by trees so tall that a long hitter is prevented from cutting corners (Harbour Town) or a course so riddled with punitive bunkers that are a full stroke penalty that a player can decide to layup on every hole (Hoylake)).  Absent those conditions, I think a short hitter benefits from having par fours that it can reach in two with a reasonable approach but long enough that a long hitter does not have a wedge in his hands.  A short hitter benefits from par fives that either everyone can reach or (almost never) no one can reach.  I’m guessing that length makes little difference in the advantage enjoyed by long hitters on most par threes.



3.  Bomb and Gouge Sweet Spot Theory

Geoff Shackelford has argued bomb and gouge is particularly effective when the player has a wedge in his hand.  Because of the increased loft, if a player hit a wedge, he is better off getting as close as possible to the green even if it means he is in the rough.  He has argued it is not possible to grow rough thick enough to counteract this effect. .

I think the the statistics support Shackelford's view – at least within reasonable limits.  Adding my own spin, I think bomb and gouge provides a double advantage to long hitters for holes of distances that are short enough that the player can leave himself a full wedge or less into the green.  This advantage is at its greatest when a course features many holes that are long enough that short hitters cannot employ such a strategy but short enough that long hitters can.  I call that distance the “Bomb and Gouge Sweet Spot.”

Between 1998 and when players took full advantage of technology improvements driving distance increased 20 yards for pretty much all classes of PGA tour player.  (Woods went from 296 in 1998 to 316 in 2005)(Singh went from 284 to 303 in 2003)(#180 in driving stats went from 258 to 278).  In other words, in terms of actual length, long hitters had no greater advantage over shorter hitters than they did in 1998.

   I think the reason bomb and gouge began to work was because singificantly more holes were short enough that the player could get within wedge distance off the tee. 

I would also guess that, because courses had not yet been lengthened to compensate, that many holes fell within distances that rewarded a long hitter with a wedge approach but was outside a wedge approach for a short hitter. 

In 2004, when he went to bomb and gouge, Singh could get to partial wedge distance by whaling away with driver on all holes of 430 yards or less (assumung average weather and ground conditions and that 130 yards is the cutoff for a full wedge shot).  Even though he hit fairways 6% less often, being 20 yards closer to the hole more than offset that disadvantage.

Woods responded by whaling away with a driver in 2005.  Now,  Woods could get within wedge distance on all holes of 446 yards or less and  the loss in accuracy was more than offset by shorter approaches.

Both of these guys were long compared to tour average.   Fred Funk averaged 270 off the tee in 2005.  If he employed bomb and gouge, he could only do so on holes of 400 yards or less to make it pay off (270 plus 130).  In other words, Funk was double penalized on holes between 400 and 446 yards.  He not only had to make up for the distance he had always lost to Woods, now his accuracy provided him no significant advantage compared to Woods on par fours less than 446 yards.

In 1998, this advantage would have existed for a gap between 388 and 426.(296 off tee plus 130 yard wedge for Woods, 258/130 for the 180th rated driver).  In other words, bomb and gouge provided a double advantage to Woods over Player 180 on holes between 388 and 426 yards.

   Under my theory, one would expect bomb and gouge to be less effective for par fours between 446 and 490 (using 2005 distances, which have held pretty steady).  It would be very effective for holes between 400 and 446 and less effective on holes of 400 and less.


« Last Edit: April 24, 2009, 04:50:36 PM by Jason Topp »

Jason Topp

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Re: Length Realllllly Matters
« Reply #46 on: April 24, 2009, 04:48:31 PM »
Bomb and Gouge Sweet Spot Theory Applied to the Masters

   The Masters is not the best place to judge my theory because there is little rough, but it is the easiest for which to obtain records on the internet.  It appears to fit very neatly with my theory.

Prior to 2006, the Masters generally rewarded long hitters.  For example, Mickelson and Woods won 4 of 5 events between 2001 and 2005. 

During the time period between 2006 and 2008 2 of the 3 winners were relatively short off the tee – Trevor Immelman, Zach Johnson.  Furthermore , a bunch of other short hitters were in contention .

In 2009 – the Masters moved tees up on many of the holes and bombers returned to dominate the tournament.  The five people with the best chances on Sunday were all long off the tee – Cabrera, Perry, Campbell, Woods and Mickelson.

These differences could simply be due to random chance.  Nonetheless, if they are not, my Bomb and Gouge Sweet Spot Theory predicts that the course would provide the smallest advantage to long hitters between 2006 and 2008

In fact, the lengths of the holes at Augusta are interesting.  At the length it played between 2006 and 2008 every single par four was longer or shorter than the Bomb and Gouge Sweet Spot with the exception of the 3rd, which was shorter.  None fit within the range:

1 455 (uphill)
3 350
5 455
7 450
9 460
10 495 (way downhill)
11 505 (way downhill)
14 440 (uphill)
17 445 (uphill I think)
18 465 (uphill)

   
With the exception of the 3rd, nearly every hole had an effective length somewhere near 450-460 yards – or just longer than the Bomb and Gouge Sweet Spot.

That would not have been the case before 2006.  Prior to 2006, 1, 7 and 17 would have been in the sweet spot.  Prior to 2002 – 1, 7, 9, 11, 17 and 18 would have all been in the sweet spot.

In 2009, several holes were played from the front of the tee box.  Doing so would most likely put the holes just on the long portion of the Bomb and Gouge Sweet Spot, therreby giving long hitters back the double advantage they traditionally have enjoyed at the Masters.
   

George Pazin

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Re: Length Realllllly Matters
« Reply #47 on: April 24, 2009, 04:54:06 PM »
Jason, I believe the real reason bomb and gouge works is simply that occasionally the bombers will have a week where they hit 70& of the fairways and make a bunch of putts. One great week and a few good weeks will keep you on Tour for awhile, as long as you can stand it mentally (the off weeks, that is).

I believe the biggest differences in technology from the 70s are:

1) Mishits are MUCH MUCH MUCH better.

2) Perfect hits go crazy distances (as Shiv said, 350 is the new 300).
Big drivers and hot balls are the product of golf course design that rewards the hit one far then hit one high strategy.  Shinny showed everyone how to take care of this whole technology dilemma. - Pat Brockwell, 6/24/04

Jason Topp

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Re: Length Realllllly Matters
« Reply #48 on: April 24, 2009, 05:03:58 PM »
Jason, I believe the real reason bomb and gouge works is simply that occasionally the bombers will have a week where they hit 70& of the fairways and make a bunch of putts. One great week and a few good weeks will keep you on Tour for awhile, as long as you can stand it mentally (the off weeks, that is).


George:

Woudln't that have been true in the 70's as well? 

I came up with the general outlines of this tought process at Hazeltine in 2002 when Tiger Woods, Rich Beem, Chris Riley, Justin Leonard and Fred Funk were trying to win a tournament on a long golf course.  My impression was that the added length of the course gave the shorter hitters a better chance to win which seemed counter-intuitive.  This year, the course could play near 7700 yards.

My guess is that the PGA Tour has now generally lengthened courses sufficiently to catch up with technology.  If my theory is correct, we should see the dominance of the top players diminish over the next ten years because this double advantage will probably disappear due to longer courses and equipment restrictions. 

Jason Topp

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Re: Length Realllllly Matters
« Reply #49 on: April 24, 2009, 05:11:33 PM »
The made-putts-by-distance numbers from ShotLink in that range are quite significantly higher than the same numbers gathered by Dave Pelz 15-20 years ago. I trust the ShotLink number completely and the Pelz numbers unless someone has evidence his methods were flawed. I don't have the comparison at hand but they have come close to doubling their percentage made in the 6, 8, 10 foot range over just a couple decades.

Brett - when I looked at that, I do not agree.  Shotlink gives percentages in ranges, say less than 3 feet, between  5' and 10' etc. 

It is impossible, however, to convert that to the Pelz measurements because you do not know how putt lengths are distibuted within that range.  For example the stats showing a player makes 99% of putts of 3 feet or less is misleading because the vast majority of those putts will be tap ins.  If 99% of the putts are tap ins and 1% are three footers, the statistic would show the guy was a lousy putter, not a good putter.

Shotlink stats generally show players making more than 50% of putts between 5 and 10 feet.  If players have a lot more 5 footers than 10 footers, Pelz 6 foot 50/50 range may still be accurate. 

I suspect the Pelz number has changed but do not have enough information to be sure by how much.  12-18" was my best guess, but I cannot recall how I came up with it.

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