The misperception of the short game.

[George Pazin]

I'm going to have to break down and buy Mr. Broadie's book, but for those who've read it, please answer this:

- Is there any accounting for position? In other words, comparisons on different sides of the fairway, different sides of the green, etc. Or is straight up distance from the hole?

- Is there any accounting for the context of the shot? In other words, did it happen on Thursday morning? Sunday afternoon?

The one "stat" - it's a picture, really - that I tend to like during broadcasts is when they show a pictorial representation of where shots hit and what the result is (birdie, par, bogey, other).

[Michael Felton]

Michael,

I understand what you re getting at but in the end the only true reflection of how they played the hole is they both shot 4. Using Brent's analogy then Corey is the better player as he hit the green from distance where as Bubba missed from closer. What if Corey's first putt was a long 100' putt with a large swing that was not possible to stop closer than 8'? But that is the problem isn't it, too little info to draw a conclusion as to who played the hole better. By drawing attention to the extra factors it also shows up the greatest flaw. In such matters maybe the 'KISS' principal is the best method

Jon

Jon,

Yes they both shot 4 and we are not trying to say who played the hole better. Clearly they both played the hole overall at the same level, because they both took the same score. What the stats are trying to do is determine where each player's strengths were.

Given the example, which player had the better long game and which one was the better putter? Traditional stats say Corey had the better long game and Bubba was the better putter. The new ones say Bubba had the better long game and Corey was the better putter. Which one do you think is more representative of the facts?

[Michael Felton]

I'm going to have to break down and buy Mr. Broadie's book, but for those who've read it, please answer this:

- Is there any accounting for position? In other words, comparisons on different sides of the fairway, different sides of the green, etc. Or is straight up distance from the hole?

- Is there any accounting for the context of the shot? In other words, did it happen on Thursday morning? Sunday afternoon?

The one "stat" - it's a picture, really - that I tend to like during broadcasts is when they show a pictorial representation of where shots hit and what the result is (birdie, par, bogey, other).

I haven't finished reading the whole thing yet, but no there is no accounting for context or sides of the fairway or sides of the green. That's really beyond the scope of what they're trying to do. The goal is to see where a player gains their shots or loses them. Over the period of a season (or even a tournament), the things like which side of the hole are they on will even out and what you are left with is the average performance from each player at each distance (or at least range of distances). The only differentiation is between tee, fairway, rough, sand, recovery and on the green.

[Brent Hutto]

George,

He has sections of the book based on some data (not ShotLink) that he collected during his own research predating the ShotLink era. But it is a very, very limited dataset. He also does simulation studies of various scenarios.

But no, the ShotLink dataset that is the basis for the core of the book does not encode any of the things you mention. Some of that is probably there in the raw data when it's collected. But it would be virtually impossible to do any useful accumulated stats if the data were broken out into thousands or permutations.

So you can't make any conclusions about Bermuda versus Kikuyu grass or Thursday rounds versus Sunday or those who made the cut vs. those who miss the cut or windy days versus calm or any of a hundred other What Ifs we could sit here and name. It's not that the raw data couldn't be gathered like that, it's that once you got so particular then every single shot is unique in some way or another. As someone pointed out earlier in the thread, there are only so many times in the history of the Tour that someone has hit a shot from 185 yards with the ball sitting nestled down in 2-1/2" Bluegrass rough, situated three inches below his feet with a bunker between him and the hole and the wind out of the southwest at 12 gusting 17 on a Friday in the last group of the day needing a birdie to make the cut and keep his Tour card for next season, watched by 26 people in the gallery but not on television.

The question is not whether everything conceivable has been taken into account. The question is whether knowing how many strokes it takes a Tour player to hole out from a particular distance and broad category of lie (tee, fairway, rough, sand, obstructed...plus putts) is sufficient to gain useful information about the game. If you don't think anything useful can come of it, then I suspect you'd be out of luck because with a few minor additions here or there it's hard to imagine a more elaborate dataset coming about any time soon.

But it sure as heck beats:

Driving distance (two holes per day)
Fairways Hit
Greens in Regulation
Up-and-down percentage
Number of putts
Sand save percentage

Which not only fail to encode even a fraction of the information in the ShotLink data, more importantly THEY DON'T EVEN ADDRESS THE RESULTING NUMBER OF STROKES AT ALL.

That's the part that makes it unbelievable we're even having this so-called "discussion". The old garbage stats HAVE NOTHING WHATSOEVER TO DO WITH SCORING. Why on earth should we give a shit about anything that's totally divorced from the strokes taken in actual play?

[Brent Hutto]

While I'm an repeating myself like an idiot I'll once again give the most basic illustration possible of the kind of thing you can do with this dataset.

We can probably all agree (Jon excepted of course) that being 40 yards from the green and in the fairway will require fewer strokes to hole out on average than being 400 yards from the green and in a bunker. Not that a Tour player couldn't take five strokes from 40 yards and not that a Tour player couldn't hole out in two strokes from 400 yards. But the averages say that 40 yards is closer to the hole than 400 and fairway is better than sand.

Here's a question we might think is much less obvious. How about being 40 yards from the hole in the fairway versus 10 yards from the hole in the rough? On one hand 10 yards is closer than 40 but being in the fairway is better than being in the rough.

With the ShotLink data we can know with a fairly high degree of confidence and precision how many strokes it will take ON AVERAGE for a Tour player to hole out from 40 yards in the fairway. And likewise how many strokes they average from 10 yards away in sand. The answers are about 2.6 strokes versus about 2.5 strokes, respectively. So almost a wash but the typical Tour player would be slightly better off 10 yards in sand than 40 yards in fairway.

What we can't do is answer any question about what kind of sand, how much green to work with or how receptive the green might be to various shots. But for the basic question, the answer is sitting there ready to be looked up.

[JMEvensky]

Brent,thanks for responses 279 and 280--apparently it took you repeating yourself like an idiot for an idiot like me to understand it.Thanks for translating into a language I can speak.

[George Pazin]

Brent, I certainly agree that more information is better than less. And I certainly get what you're saying about refining the stats too much; in a game where misses are often measured in inches, it could get silly to find comparison points.

However, the one modification I would like to see in Mr. Broadie's data analysis would be some sort of adjustment for preferred side of fairway miss or preferred side of green miss. This wouldn't seem to be that difficult to add on - merely measuring, on any given hole, how golfers fared from one side versus the other, fairway/rough or green - the difference could be statistically significant, I'd think. Heck, missing the 18th fairway left this week is a much greater penalty than missing the fairway right!

It could well be that on most holes, it evens out, but I'd like to think on the best courses (the ones we all prefer on here!), the more important factor may not be distance or fairway vs. rough vs. bunker, but simply which side did a golfer favor. I recall in Pete Dye's autobiography that he mentioned in certain instances on his courses, a golfer may be better off missing a green and ending up in the bunker, as opposed to a long putt from the incorrect side. This could be very important, I think, in analyzing the game, and certainly in analyzing golf courses.

[Brent Hutto]

I think as soon as "preferred side" is mentioned to a Tour player, his response will start with "what's the hole location". It turns out, at least in my opinion, that as soon as you get beyond a very simple rubric you'd immediately have to choose among multiple, equally meaningful additional attributes.

Because keep in mind, there is no representation in Strokes Gained for "fairway versus rough". If there were, then maybe "fairway versus right rough versus left rough" would be practical. Or even "fairway versus right rough hole on right versus right rough hole on left..." and so forth.

But the table is by distance AND situation. So it is 20 yards in the fairway versus 40 yards in the fairway versus 60 yards....versus 480 yards in the rough versus 500 yards in the rough... for every combination of the five situations and all the possible distance categories. Plus putting which is a separate table.

Now it may well be possible that there's a ShotLink dataset out there which encodes side of fairway and/or hole location and/or other elements. If so, the basic distance/situation versus strokes tables could be use to evaluate only a subset of a player's shots from a given season or whatever. I did not notice any mention of that being available in the book.

[Phil McDade]

However, the one modification I would like to see in Mr. Broadie's data analysis would be some sort of adjustment for preferred side of fairway miss or preferred side of green miss. This wouldn't seem to be that difficult to add on - merely measuring, on any given hole, how golfers fared from one side versus the other, fairway/rough or green - the difference could be statistically significant, I'd think. Heck, missing the 18th fairway left this week is a much greater penalty than missing the fairway right!

George:

Isn't that a fairly subjective thing? Preferred for whom, and in what situations? Brent's basic point -- I think -- is that large data sets can yield observations and conclusions from broad categories of conditions/outcomes -- length, fairway, rough, sand, and such. Isn't a preferred landing area highly dependent on the given player's approach to the hole, his particular swing, and specific round/match conditions (of the kind he mentions)? Mickelson's preferred landing area for the fairway on PGA Tour Stop X may be very different than the preferred landing area for Stricker. Some golfers maybe prefer to always hit fades into greens, which could impact where they choose to play off the tee. Length (or lack of it) may have a tremendous role in how a player approaches a hole, and how they prefer to tack their way toward the final tap-in.

I see what you're getting at; I'm just not sure collecting that much additional data would yield more understanding, given the incredibly wide variance with how players approach each particular hole (sure, they all want to avoid water/traps/he's-got-no-shot situation; but having said that, a Furyk likely approaches a reachable par 5 in a very different manner than a Mickelson.)

[A.G._Crockett]

Broadie's work, like the Shotlink data itself, is not meant to be predictive for any one player, any one shot, any one hole, etc.  It is an examination of a mountain of data to analyze trends for the entire Tour over a period of years on all courses.

As such, talking about sides of the fairway, or why certain players do or do not play well at the US Open, or anything about Tom Watson, or the "mental" side of golf, are either misuses, misunderstandings, or irrelevancies to the data and the analysis of it.

The data shows conclusively that quality ball-striking is more important to scoring and winning money on the PGA Tour over a period of time than the short game or putting is.  You don't have to LIKE the data or the analysis of it, much less agree with it, but that doesn't change it!  Nobody alive consistently makes a high percentage of putts outside 10', even on the perfect greens of the PGA Tour.  So the question becomes how best to get inside 10' in as few strokes as possible. 

The answers are pretty obvious and really seem intuitive as well; hit it a long way off the tee with at least reasonable accuracy, hit a lot of greens in regulation, and when you miss the green, have enough control of your golf ball to miss it in the correct places where getting up and down is at least possible. 

The margins on the Tour are minute, and none of this downplays the importance of the short game or of putting IN THE LEAST!  It seems obvious to all that while Woods (when healthy) is still a great player, he doesn't putt like he once did, and it is hurting him in majors on the weekend at the very least. On the other hand, Johnny Miller once said that if Mickelson wasn't so good with his wedges he'd be selling used cars in San Diego.  So for an individual player, the calculus may be different and may change over time.  But that doesn't invalidate the data or the analysis, which are based on the masses over a long period of time.

[Brent Hutto]

It is an examination of a mountain of data to analyze trends for the entire Tour over a period of years on all courses.

As such, talking about sides of the fairway, or why certain players do or do not play well at the US Open, or anything about Tom Watson, or the "mental" side of golf, are either misuses, misunderstandings, or irrelevancies to the data and the analysis of it.

That's the truth.

[Jon Wiggett]

Michael,

I understand what you re getting at but in the end the only true reflection of how they played the hole is they both shot 4. Using Brent's analogy then Corey is the better player as he hit the green from distance where as Bubba missed from closer. What if Corey's first putt was a long 100' putt with a large swing that was not possible to stop closer than 8'? But that is the problem isn't it, too little info to draw a conclusion as to who played the hole better. By drawing attention to the extra factors it also shows up the greatest flaw. In such matters maybe the 'KISS' principal is the best method

Jon

Jon,

Yes they both shot 4 and we are not trying to say who played the hole better. Clearly they both played the hole overall at the same level, because they both took the same score. What the stats are trying to do is determine where each player's strengths were.

Given the example, which player had the better long game and which one was the better putter? Traditional stats say Corey had the better long game and Bubba was the better putter. The new ones say Bubba had the better long game and Corey was the better putter. Which one do you think is more representative of the facts?

Michael,

so player one has the better long game because he hit the ball further. What  if player one hits the same tee shot but the rough is knee height and he loses his ball does he still have the better long game? As far as I understand on the second method he does.

Brent,

your posts and jibes show the weakness of either the method, your understanding or your ability to explain it. Which ever it is it is a shame you have sunk to such a level and you have gone down in my estimation.

Jon

[Michael Felton]

Michael,

I understand what you re getting at but in the end the only true reflection of how they played the hole is they both shot 4. Using Brent's analogy then Corey is the better player as he hit the green from distance where as Bubba missed from closer. What if Corey's first putt was a long 100' putt with a large swing that was not possible to stop closer than 8'? But that is the problem isn't it, too little info to draw a conclusion as to who played the hole better. By drawing attention to the extra factors it also shows up the greatest flaw. In such matters maybe the 'KISS' principal is the best method

Jon

Jon,

Yes they both shot 4 and we are not trying to say who played the hole better. Clearly they both played the hole overall at the same level, because they both took the same score. What the stats are trying to do is determine where each player's strengths were.

Given the example, which player had the better long game and which one was the better putter? Traditional stats say Corey had the better long game and Bubba was the better putter. The new ones say Bubba had the better long game and Corey was the better putter. Which one do you think is more representative of the facts?

Michael,

so player one has the better long game because he hit the ball further. What  if player one hits the same tee shot but the rough is knee height and he loses his ball does he still have the better long game? As far as I understand on the second method he does.

Brent,

your posts and jibes show the weakness of either the method, your understanding or your ability to explain it. Which ever it is it is a shame you have sunk to such a level and you have gone down in my estimation.

Jon

If he loses his ball, then he would be playing his third shot from the tee. That would mean that he has taken 2 strokes and advanced nowhere. That would give him a strokes gained for that tee shot of -2. So that would indeed imply that it was worse than the other guy who hit it 240 in the fairway.

[George Pazin]

However, the one modification I would like to see in Mr. Broadie's data analysis would be some sort of adjustment for preferred side of fairway miss or preferred side of green miss. This wouldn't seem to be that difficult to add on - merely measuring, on any given hole, how golfers fared from one side versus the other, fairway/rough or green - the difference could be statistically significant, I'd think. Heck, missing the 18th fairway left this week is a much greater penalty than missing the fairway right!

George:

Isn't that a fairly subjective thing? Preferred for whom, and in what situations?

Not the way I would do it, or at least attempt to do it. I would establish strict criteria based on actual results - players who played from the left rough scored X, right Y, etc. I think you could establish some basic criteria that would mitigate some of the shortcomings of just saying distance in fairway, distance in rough, etc.

Give me a little credit, Phil, do you really think I would attempt a statistical study with subjective criteria? I was a math geek before it was cool to be one...

[Phil McDade]

George:

I was loathe to get into a thread with you and Brent, given the last science course I took was in the 10th grade and I've relied on my now-14-year-old for math help for the past four years (he's a little strange....).

Perhaps I'm mis-understanding what you're attempting to get at, but I'd argue -- and my argument may be off the mark -- that misses left or right -- either fairway or green -- may not yield the objective kind of observations that length, fairway, rough, sand and extreme trouble yield. With rare exceptions, being on the fairway (given approximate equal distances from the hole, or off the tee) is better than being in the rough; being on the green is better than being off the green; being closer to the hole with an approach that lands on the green is better than being farther away from the hole on the green. Exceptions to the rule, sure, but those largely hold out over large sets of data of the kind being discussed here.

I'm not yet convinced misses to a particular side would yield the same kind of information.

 

[Jon Cavalier]

Another way look at the same concept, and one that many people find easier to understand, is to consider the simplification that a "good shot" will gain more than 1.000 strokes, while a "bad shot" will gain less.

For the most obvious example, take a 400 yard par 4 with a stroke average of exactly 4.000.
Player 1 swings and misses. He has taken 1.000 strokes and gained 0.000 strokes, so his shot gains -1.000 strokes driving.
Player 2 duck hooks OB. He has taken 1.000 strokes and gained -1.000 strokes, so he has lost 2.000 strokes driving.
Player 3 holes out off the tee from 400 yards out. He's taken 1.000 strokes to make 1 on a hole where he's expected to make 4.000, so he's gained 3.00 strokes driving.

Using this same method, consider the following (on the same hypothetical hole, with all figures approximate):

Player A tops his drive 20 yards in the fairway - he's used 1.000 strokes but since he's still expected to take 3.900 strokes to get down from 380 out in the fairway, he's lost 0.900 strokes to average.
Player B hits his drive 250 in the fairway. From 150 in the fairway, we expect him to take three shots to hole out. So he's used 1.000 strokes and gained 1.000 strokes relative to the hole overall, for a net of 0.000 - a perfectly average drive.
Player C hits his shot 300 yards into the rough. From 100 yards in the rough, he's expected to take 2.500 strokes to hole out, so he's used 1.000 strokes and gained 1.500 strokes, for a net gain of 0.500.
Player D hits his ball 270 down the middle. From 130 in the fairway, he's also expected to take 2.500 shots to get down, so he's also gained 1.500 shots while using only 1.000 strokes, again for a net gain of 0.500 strokes.
Player E hits a 370 yard drive into a hazard, necessitating a drop at 50 yards from the hole in the fairway. From 50 yards out in the fairway, he's expected to get down in 1.500 strokes. So despite the fact that he's taken a penalty, he's also hit a "good" drive and gained 2.500 strokes while using only 2.000 (4.000 strokes expected minus 2.000 strokes used minus 1.500 strokes expected from new position equals a net of 0.500 strokes gained).

The problem with traditional stats is that they regard player A, B and D equally (one fairway hit - despite the fact that we know objectively that player D hit the best drive) and player E worst of all. All strokes gained allows us to do is see that while their drives vary in result, players C, D and E have in fact all hit good drives and have gained 0.500 strokes over the average of the field.

Now, bear in mind that player C could hole out from 150 (1.500 net gain on approach), player B could get up and down (0.500 net gained, most of it on approach if he stiffed it close, on putting if he's outside 15 feet) and player E could take 7 to get home (a net negative 5.5 split between approach and putting in some way), but it doesn't change the fact that all three gained a net of half a stroke to the field with their drives.

The whole point of the these stats is that we can see that and measure it, regardless of the actual score each player posts on the hole.

[Jon Cavalier]

To further expand on the usefulness of strokes gained, consider:

Assume Tiger Woods can swing hard and hit a drive 330 or easy and hit it 280. The caveat is that with the 280 swing, he hits 100% of fairways, but with the 330 swing, he only hits 50%. On a 400yard hole with rough down both sides, strokes gained can tell us which swing is likely to give him yen better result.  

(280 drive) -From the fairway 120 out, he's expected to get down in 2.400 strokes (again, all figures approximate and simplified). So the expected value of this drive is a net 0.600 gain.

(300 drive) - From the fairway 70 yards out, he's expected to get down in 2.00 strokes. So when he hits the fairway, he has a net gain of 1.000 strokes.
From the rough 70 yards out, he's expected to get down in 3.00 strokes. So he's netted 0.000 - one stroke used and one stroke gained.
So the expected value of the 330 yard drive is 0.500 (0.000 half the time when he misses the fairway, and 1.000 half the time when he hits it. We expect the easy swing to net him a tenth of a stroke over the hard swing.

[George Pazin]

George:

I was loathe to get into a thread with you and Brent, given the last science course I took was in the 10th grade and I've relied on my now-14-year-old for math help for the past four years (he's a little strange....).

Perhaps I'm mis-understanding what you're attempting to get at, but I'd argue -- and my argument may be off the mark -- that misses left or right -- either fairway or green -- may not yield the objective kind of observations that length, fairway, rough, sand and extreme trouble yield. With rare exceptions, being on the fairway (given approximate equal distances from the hole, or off the tee) is better than being in the rough; being on the green is better than being off the green; being closer to the hole with an approach that lands on the green is better than being farther away from the hole on the green. Exceptions to the rule, sure, but those largely hold out over large sets of data of the kind being discussed here.

I'm not yet convinced misses to a particular side would yield the same kind of information.

 

If you can compile stats saying "2.87 shots to get down from fairway bunker", why couldn't you say "2.75 from left rough, 2.25 from right rough," hence there is a preferred side? It still overlooks the things Jon worries about - lie, stance, etc - but it adds something that may (or may not) be missing.

Similarly, I think there is a big difference in when misses occur (ie Thursday vs Sunday). The most incredible thing about Tiger and Jack to me is their ability to do it when it counts most.

Phrased in the parlance of Mr. Broadie, I'd guess the strokes gained from Tiger holing that 15 footer on the 72nd hole of the 2008 US Open to be nearly infinite.

I personally would be using the stats to infer things about the course, not the players - that's why I'd like to know the info. I realize Mr. Broadie doesn't care about that at all.

[Michael Felton]

George:

I was loathe to get into a thread with you and Brent, given the last science course I took was in the 10th grade and I've relied on my now-14-year-old for math help for the past four years (he's a little strange....).

Perhaps I'm mis-understanding what you're attempting to get at, but I'd argue -- and my argument may be off the mark -- that misses left or right -- either fairway or green -- may not yield the objective kind of observations that length, fairway, rough, sand and extreme trouble yield. With rare exceptions, being on the fairway (given approximate equal distances from the hole, or off the tee) is better than being in the rough; being on the green is better than being off the green; being closer to the hole with an approach that lands on the green is better than being farther away from the hole on the green. Exceptions to the rule, sure, but those largely hold out over large sets of data of the kind being discussed here.

I'm not yet convinced misses to a particular side would yield the same kind of information.

 

If you can compile stats saying "2.87 shots to get down from fairway bunker", why couldn't you say "2.75 from left rough, 2.25 from right rough," hence there is a preferred side? It still overlooks the things Jon worries about - lie, stance, etc - but it adds something that may (or may not) be missing.

Similarly, I think there is a big difference in when misses occur (ie Thursday vs Sunday). The most incredible thing about Tiger and Jack to me is their ability to do it when it counts most.

Phrased in the parlance of Mr. Broadie, I'd guess the strokes gained from Tiger holing that 15 footer on the 72nd hole of the 2008 US Open to be nearly infinite.

I personally would be using the stats to infer things about the course, not the players - that's why I'd like to know the info. I realize Mr. Broadie doesn't care about that at all.

George - he does talk a little about the difference between courses, but more in the context of which courses are harder to putt on. I would imagine that he could take that to mean which courses are harder if you miss the fairway (i.e. have difficult rough).

The thing with saying it's 2.75 from the left rough and 2.25 from the right rough is that that will change so much from hole to hole that the only useful thing would be to look at each hole individually. I guess that you could do that and the information is almost certainly there if you want it, but it would quickly become unwieldy unless you wanted to purely look at one specific hole, or maybe one specific course.

From an architecture perspective, it might well be interesting to look at a hole like 14 at TPC Sawgrass. You have water and a bunker left and you have mounds and rough right. I imagine that most people stand there and think that right is better, so their aiming point might be the right edge of the fairway. Seeing how people's scores differ on that hole based on whether they hit it left or right might give some indication of whether it's a good model. Difficulty would be it would depend on pin position, so would change from day to day. If the data points become too granular, it ceases to mean anything. As has been pointed out, if you end up with only one shot in your data set, then you could end up thinking that it's better to be 400 yards away in the sand than 100 yards away in the fairway.

One other place that might be interesting to research this from an architecture perspective would be on a driveable par four. Average score of those going for it versus average score of those laying up. That might give you an indication of whether you want to make a hole shorter to tempt people into trying to drive the green, or perhaps how much trouble you need to include around the green to make it 50/50 whether to go for it or not.

[George Pazin]

The thing with saying it's 2.75 from the left rough and 2.25 from the right rough is that that will change so much from hole to hole that the only useful thing would be to look at each hole individually. I guess that you could do that and the information is almost certainly there if you want it, but it would quickly become unwieldy unless you wanted to purely look at one specific hole, or maybe one specific course.

Indeed, that's exactly how I'd use the data!

[Michael Felton]

It's out there if you want it. The PGA Tour site has samples that are available for free. The full set you have to either pay for or show that it's for academic research purposes I think. That's the raw data, not Broadie's data.

[Tony_Muldoon]

For those who have read the book does it say how many times they measured the effectiveness of Tiger hititng from 175-220?  And all the others?


Would some of the doubters be more convinced that this was a meaningful stat, if it was a really large figure?  i.e. it averaged out palying from the left side or the right side, into a wind and with the wind.  Just curious..


Finally Tiger has mostly been one of the longer hitters  so I would have though he'd have hit a smaller proportin of his shots from 175-220 than the field? Thus his strokes gained over this distance actually helps him less than it might appear?



Happy to be put straight as I last had a maths class when I was 18 and without a calculator handy, I can tell you that's a long time.

[Brent Hutto]

I don't have my copy handy but it would include basically every approach shot he hit from 175-225 yards over the course of a decade. In regular Tour events only, no majors, no overseas events. Including Par 3's.

So probably a couple hundred tournaments, call it 800 rounds. What would you think? Maybe one or two Par 3's, a Par 5 possibly, maybe a Par 4 somewhere along the line?

In the neighborhood of a couple thousand shots per player in that range would be my guess. Some from the tee, some from the rough, some from bunkers and quite a few from fairway.

[Michael Felton]

Also remember that Tiger clubs down from the tee fairly frequently. I imagine he would have more shots in that range than a lot of the bomber types.

[jeffwarne]

OK, we all know certain players only play certain courses/events.

What happens if Tiger only plays the 15 toughest(in relation to par) courses on tour, and another player chooses the 15 easiest?

Wouldn't the strokes gained/strokes lost be skewed by the two players playing mainly different level difficulty courses all season?