Trees are the source of a significant amount of argument at my club. We are in central NJ. We are a middle-tier club, not famous. But the courses surrounding us, many of them nationally or world famous, have been cutting down trees in significant numbers in recent years.

So when the ownership of our club embarked upon a renovation project, the architect, predictably, advised them to remove a significant number of trees.

The general reaction was that the longer one had been a member, the more one was opposed to removing any trees. Younger members were in general strongly in favor. The lowest handicap golfers at the club, regardless of age, were generally in favor of tree removal.

The member arguments against it included that it "made the course too easy," and that "the trees are pretty and should stay," and that "the trees are too much a part of the character of the club and they shouldn't be removed."

The member arguments in favor were that it made the course better, opened up more strategic options, made the playing experience better for high handicappers, and made the course more beautiful by opening up vistas not seen before, and by removing tree species out of place for this part of the country (most of the trees on the course were white pines planted about 60 years ago to define the areas between holes, etc.). 

I am strongly in favor. I love trees, but I believe on a golf course they should be used sparingly. Plant all the trees you want in areas where it doesn't affect play, and where it enhances the look of the course and doesn't block beautiful vistas, lines of sight, lines of play, etc. I like the idea of _some_ trees in play, but so called "specimen" trees, which alter the strategy of a hole or pose a challenge, without being overly penal. In other words, maybe a tree or a cluster of two or three trees on one side of a hole, rather than an entire line of trees separating two holes. With just occasional trees, when you hit a wayward shot, you generally at least can play a recovery shot, possibly even a challenging one requiring an intentional hook or slice. With the "tree-lined" hole approach, often you are chopping out sideways because there is no choice at all. In the case of my club, for years the white pines had branches all the way down to ground level, which meant that any shot into them was an unplayable lie. This is not fun, and it really isn't golf.

The big tree in the middle of your fairway sounds cool. I can deal with that sort of tree. It poses a challenge, but doesn't completely dictate something to you. Having it in the _middle_, with water on either sides is pushing things a bit, but still I think an occaisional fairway tree is ok.

Nice post. JP

Big Lex, thanks for the comments.  I tend to agree with you and many architects that too many trees often is a problem.

Trees certainly affect the playability of a course, but you can make the boundaries of a links course hole almost as penal as deep woods with gorse, heather, deep high grass, or water. Poorly placed trees (like between a bunker and the hole) or completely blocking landing areas do seem pointless to good hole design / strategy.

One reason I think golfers have a love / hate or hate / hate relationship with trees is their potential impact on our scores. I think some 'tree hate' for non-scratch players might be mitigated a bit by a more up to date course rating.

I think that current USGA course rating system undervalues thick stands  of trees. Their explanation of rating system states that tree composition more than 30 yards from the center line of a hole will have little impact on rating or slope. I think this is a somewhat arbitrarily chosen distance arising from a perception of drive dispersion based on course raters' (scratch players) own good swings rather than actual statistics. Jack Nicklaus praised Pinehurst #2 as not having a single tree in play, but there are plenty of holes where I and more skilled, but still 'average' golfers would expect a certain percentage of drives to find the treeline.

The statistical 1 sigma dispersion for a 12 handicap player who drives 225 yards is about 55 yards wide (22.5 yards on either side of hole center line). That would mean about 2/3 of their drives would be within 22.5 yards of the hole center line. Meanwhile a further 27% of their drives would fall between 22.5 and 55 yards from the center line. That means roughly 1 in 5 drives for a 12 HCP player would end up outside the 60 yard wide 'landing zone' (30 yards on either side of the hole center line) outside of which the USGA doesn't take trees into account for rating purposes.

Thick woods within a golfer's average drive dispersion might suggest taking less club, but that's automatically less distance and therefore higher score relative to a scratch player who can ignore the tree line. IMO dense trees stands that overlap high HCP driver dispersion can be viewed like an invisible forced carry / layup, and that kind of differential between the scratch and bogey golfer is why the slope rating was created. The thickness of stands between holes matters too, because if it's a thin line of trees chances are the ball will bound to a spot where you can still play down the original or the adjacent fairway, or maybe poke a low one between the trunks. Water hazards have a demarcation line that often if not usually grants some distance on the shot and usually room for a swing and a line of play to the hole or fairway; while dense woods are almost a certain stroke and distance penalty or worse (think Kevin Na's 16 in TX).

4 hours ago, iacas said:

Yeah, 30 yards from the center line of the hole is pretty wide. If you're that bad… why should you deserve to have a really wild tee shot result in a lower handicap? You hit a horrible shot. It should negatively affect (raise) your handicap; the course rating and slope shouldn't be higher. That would let you "get away with" the trees that really aren't in play.

That's the 'typical dispersion' for a Bogey Golfer per Broadie. Curiously it is down around the values for Scratch Golfers where this 60 yard window starts to contain the normal distribution of drive dispersion out to 2 sigma. I don't think it's conspiracy, just cognitive bias of what is 'normal' or average. A bit of 'false-consensus effect' maybe.

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Slope Rating®: A Slope Rating is the USGA® mark that indicates the measurement of the relative playing difficulty of a course for players who are not scratch golfers, compared to scratch golfers.

Trees in the likely landing area for a significant fraction of a Bogey Golfer's standard distribution of drives seem pretty relevant to this.

1 hour ago, iacas said:

You've missed my point or something… Those golfers who hit the wild drives should be punished for their bigger misses. Making the course rating and/or slope would not punish them as much for terrible shots.

I don't think you're saying slope should not be part of the HCP calculation? My point is that higher handicap golfers are being penalized more / disproportionately relative to their standard normal dispersion distribution than scratch golfers because of that distance from centerline cutoff. The cutoff falls at a different z-value for higher HCP's than scratch golfers. It's not a huge amount, and may not be enough to justify changing the system, but it's there as an effect.

54 minutes ago, natureboy said:

My point is that higher handicap golfers are being penalized more / disproportionately relative to their standard normal dispersion distribution than scratch golfers because of that distance from centerline cutoff. The cutoff falls at a different z-value for higher HCP's than scratch golfers. It's not a huge amount, and may not be enough to justify changing the system, but it's there as an effect.

That's kind of why golf is so hard. If every course was a flat parkland style course with no trees or rough I think it would lose some of it's luster***. I guess I'm just saying that golfers love abusive courses.

Seriously, though. I think it would get boring without all these challenges, and better players should be rewarded for being so good.

***The scenery is really nice and beautiful as long as your ball doesn't go into it.

The higher the slope, the more strokes you receive relative to your index. So natureboy, you are saying that you think that thick stands of trees 30 yards from the centerline should result in a higher slope rating, because they DO come into play often for any double digit handicap player?

It's been a while since I read all the white papers from Dean Knuth's "Pope of Slope" website, but if I recall "slope" was basically the actual slope of the line between what would be expected as average scores of a scratch golfer versus a bogey golfer. When Knuth was inventing the handicap and slope system for USGA, he basically did regression analyses on thousands of scores of golfers at various levels on different courses, and the Course Rating was devised to account for length and Slope for other types of difficulty. It was an empiric process, and if they decided that trees more than 30 yards from the centerline aren't important, it simply reflects that their data suggest that it doesn't significantly affect the score differential between par and bogey golfers over a huge number of rounds.

There could be many reasons. Maybe when the woods are this far away, the chance of having a playable lie are greater. Or maybe really poor golfers, when they hit a shot poorly enough to be that far off the center line, it tends to be a mis-hit that loses distance and doesn't end up in the trees. But whatever the reasons, it's sloped that way because.....that's how it occurs in reality.

When you think about it, slope really should be about how the course's obstacles threaten your GOOD shots, not your terrible shots. The hypothetical golfer you describe who hits a third of his shots that far offline....well, will EVERY instance of this shot be on a hole where there is a thick stand of trees? No. And of course hitting the ball solid but 30 yards off line is only ONE thing that a 12 handicapper does poorly....he is also going to half top some tee shots, or hit some straight that he pops up, etc. Where the course makes a huge difference in difficulty between a scratch and a bogey golfer is when there is serious danger that threatens the GOOD shots of the bogey man, because his good shots are more dispersed and shorter than the good shots of the scratch player.

The slope system isn't perfect and is subject to ongoing revisions, so it's a pretty robust system with good controls.  

4 hours ago, Big Lex said:

The higher the slope, the more strokes you receive relative to your index. So natureboy, you are saying that you think that thick stands of trees 30 yards from the centerline should result in a higher slope rating, because they DO come into play often for any double digit handicap player?

It's been a while since I read all the white papers from Dean Knuth's "Pope of Slope" website, but if I recall "slope" was basically the actual slope of the line between what would be expected as average scores of a scratch golfer versus a bogey golfer. When Knuth was inventing the handicap and slope system for USGA, he basically did regression analyses on thousands of scores of golfers at various levels on different courses, and the Course Rating was devised to account for length and Slope for other types of difficulty. It was an empiric process, and if they decided that trees more than 30 yards from the centerline aren't important, it simply reflects that their data suggest that it doesn't significantly affect the score differential between par and bogey golfers over a huge number of rounds.

There could be many reasons. Maybe when the woods are this far away, the chance of having a playable lie are greater. Or maybe really poor golfers, when they hit a shot poorly enough to be that far off the center line, it tends to be a mis-hit that loses distance and doesn't end up in the trees. But whatever the reasons, it's sloped that way because.....that's how it occurs in reality.

When you think about it, slope really should be about how the course's obstacles threaten your GOOD shots, not your terrible shots. The hypothetical golfer you describe who hits a third of his shots that far offline....well, will EVERY instance of this shot be on a hole where there is a thick stand of trees? No. And of course hitting the ball solid but 30 yards off line is only ONE thing that a 12 handicapper does poorly....he is also going to half top some tee shots, or hit some straight that he pops up, etc. Where the course makes a huge difference in difficulty between a scratch and a bogey golfer is when there is serious danger that threatens the GOOD shots of the bogey man, because his good shots are more dispersed and shorter than the good shots of the scratch player.

The slope system isn't perfect and is subject to ongoing revisions, so it's a pretty robust system with good controls.  

From articles on Dean's site:

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One of the greatest misconceptions faced by proponents of Slope is the notion that the portability problem is alleviated by adjusting handicaps according to course rating. The course rating accurately measures each course's relative difficulty for a scratch golfer. As a golfer's handicap rises, however, the course rating becomes increasingly inaccurate. At handicaps of 20 or more, the discrepancy can add up "to a difference of 12 strokes or more," says Dean Knuth, the USGA's Director of Handicapping.

That's something the bogey golfer already knows. He looks at a course much differently from a par shooter. What may look like trouble off the tee to a long-hitting scratch golfer may be completely out of reach for a 20-handicapper. While a particular pond might not bother the par shooter, it might take on ocean-like proportions to a poorer golfer.

Under the Slope System, each course is re-rated through the eyes of the bogey golfer. This results in the Slope Rating, which is different for each set of tees and ranges from 55 for a very easy course to 153 for Pine Valley, the nation's toughest.

Using the USGA Slope Rating and your scores, your Handicap Index is computed. 

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Length counts for about 90 percent of the final number, 

I understand it's not perfect. Definitely not critiquing Dean Knuth. It's better than the 100% distance rating that used to be in place and that did not account for difference in higher HCP games.

I just observed that the rating guide had a somewhat arbitrary distance cutoff when it's clear from Mark Broadie's statistics that as HCP's rise for typical golfers average distance drops and shot dispersion increases. Margins of error are different for the different types of golfers and that affects scoring. If there was a sliding scale that had a distance from centerline that returned the same appx z-score (same standard deviation value) as for scratch golfers, I would consider that more fair. It may be that looking at trees along the whole hole helps bogey golfers, but I'd put my bet on a higher fraction of tee shots to the woods mattering more.

If you gave a bogey golfer (90-shooter) the length and accuracy of a scratch golfer off the tee on a 'typical course' the value in strokes per yard of improved distance (per Broadie) would be ~ 4 strokes (~60% of total gain) and strokes / degree of improved accuracy would be ~ 2.5 (~40% of total gain).

It's possible that trying for more than 90% for non-distance factors was too difficult politically (too much of a change from the existing system) within the USGA decision-making bodies.

For a higher HCP player regularly playing a tighter / more densely treed course, their HCP is actually likely to be slightly inflated relative to their actual skill so my observation would just make it more accurate and remove a potential avenue for sandbagging or may explain some 'perceived' sandbagging when higher HCP's shift courses with slopes that don't quite capture some potentially significant scoring differences.

@Lihu, the HCP system already includes a 'bonus for excellence'.

@Big Lex got timed out before I could add in response to your basic point. I expect that Dean Knuth did in fact do big data regressions to come up with the 'actual' difference in scoring between courses. He deserves great praise. But I think it's possible this was done once and then for updates the system has relied on the raters using slightly more qualitative rating forms and guidance. I'm not so sure there wasn't also some initial qualitative interpretation of why the score values were different when choosing the rating factors & formula. For one thing, when Knuth came up with the system there was no shotlink database for pros or amateurs. Did Knuth do a multivariable regression on all the non-distance rating factors? If so, was his data for these factors accurate enough to show the correct relationships? Was there guesstimating in the relative weights of some of the factors? You may be right that it's already all in there, but the fact that the rating guide indicated there was no difference in the effect of trees between bogey and scratch golfers makes me question that particular element.

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Recoverability and Rough:  .14 (Scratch)   .15 (Bogey)

Here's an example in the rating factors that goes against Broadie's data which show that being in the rough matters less to higher HCP's than more skilled players. Just saying it might be time for an update / tweak to a generally very good system.

45 minutes ago, iacas said:

Why is that more fair?

They're worse golfers. Why should the scale keep sliding up and reducing their handicaps?

You don't even know how old that article is, or what the current values are.

Because then you would be comparing the same standard deviation of degrees offline between the scratch and the bogey golfer...you would be comparing the same degree or percentile of 'bad shot' relative to the standard normal distribution of shots for each golfer. Apples to apples.

Why have a handicap or slope system at all? The course is the course, the score is the score, right?

Why look at course / hole distance when factoring slope? If you can't hit it as far as a scratch player, tough. You're just a bad golfer - go hide your head in shame, bad golfer, bad! 

More skilled players have a distribution of drive distances that is farther on average than higher handicaps. Slope specifically & explicitly accounts for that. A scratch golfer's shot distribution is also tighter than a bogey golfer's. If slope is meant to 'look at the course from the eyes of a bogey golfer', then the relative difference in shot dispersion should be part of it too. IMO a 90% weight on distance alone (if that's what it still is) doesn't reflect what we now know about the 'typical' bogey golfer.

Besides, IMO re-tweaking the formula isn't going to really change HCP's relative to a scratch golfer just more accurately reflect a 'portable' HCP if one course is actually more difficult for the 'typical' bogey golfer than another.

The point of referencing Dean's proposal article was that there was at least one built in assumption shown incorrect by subsequent data collection. It's very common with models. I think what Dean Knuth did is awesome. Do you think the model is perfect and could not possibly be revisited for accuracy?

38 minutes ago, iacas said:

That's not apples to apples. Ultimately, players will shoot some number over the course rating and that number is affected somewhat by the slope. But poorer players are poorer players, and you're saying they deserve to have their ineptitude softened. I disagree.

If 30 yards from the center line is the +/-1.33 sigma or 80th percentile for scratch players then evaluate the hole at the same 80th percentile for bogey golfers, which will be a larger distance from the center line. Or keep the same distance from center line for bogey golfers and evaluate scratch golfers at the same equivalent percentile distance of their standard normal shot dispersion (which will be smaller / tighter).

Slope inherently accounts for the skill-based difference in the average distance / carry between average / typical scratch and average / typical bogey golfers to account for relative differences in course difficulty. It assumes an average distance for the scratch and bogey golfer even though there is the same individual variance within these HCP groups as with shot dispersion. IMO slope should also incorporate what we now know about the average / typical difference in shot dispersion.

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Besides… guess what? On some courses missing the center line of the fairway by 40 yards is an advantage because it puts you in another fairway corridor. So how do you account for that, now? That's rhetorical, btw.

Well then there are few / no trees in that expected landing zone. The average / typical bogey golfer's drive might be expected to cross that tree line more often than a scratch player. But the adjacent fairway would lower the relative tree density in terms of recovery potential and be reflected in the scoring of the rating factors. Where I'm thinking the current system most under-accounts for trees is courses with dense deep stands (woods) of trees extending from ~30 to 65 yards from center line, not your 'typical course' with a line of trees between holes.

Relevant to this blog, I'm just saying help the bogey golfer have less disproportional disdain for the woods.

23 hours ago, iacas said:

There's nothing inherently "fair" in scaling up the difficulty of things when golfers suck more. That's already accounted for in their higher scores. Guess what? Sucky golfers are more likely to find water hazards, too. Or bunkers. Or hit it OB.

So why have slope at all? Why didn't golf stick with just the scratch rating and no HCP adjustments based on differing skill? Why have flights of competition? Why have different tee boxes?

Slope is primarily distance based to reflect the relative difficulty of courses with many obstacles requiring greater skill in "ability to overcome distance". Accuracy is another fundamental skill that's on the same kind of slope from low HCP to high HCP as distance. "Better players are longer and straighter".

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And if 90% of a course's rating and slope come from distance… any change you make to this will be incredibly small anyway. 

I expect that distance weighted 90% is an inherent assumption that may merit revisiting at the same time they get around to updating the average distances from the 1975 values.

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If you suck and hit the ball into the trees more than you should, your score will reflect the higher handicap that you are.

What is more than 'you should'? Slope's intent is to view the course from the eyes of the bogey golfer. 'Should' a bogey golfer be as accurate on average as a scratch player, when statistics show us that they are clearly less so? If a 'bad shot' for the average scratch golfer falls outside where 67% of their expected shots will fall, judge the bogey golfer on the same 67% cutoff for their average distribution. Slope inherently expects that the average Bogey Golfer 'should' (i.e. does) hit it shorter than a Scratch Golfer.

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No. 40 yards away is not the landing zone.

Sorry used a term found in the rating definitions (by definition 'landing zone' is only fairway). What I meant was the expected area of shot dispersion.

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A golfer who hits the ball regularly offline that far and finds the trees deserves to shoot the higher score and have the higher handicap.

Hitting the ball far is a skill too. By your argument there's no reason a bogey golfer's HCP should be coddled with this slope thingy just because he and the majority of his peers can't hit the ball a lick compared to a scratch golfer. But you've bought into the distance part of slope, yes?

Bogey Rating and Slope is about viewing the course from the perspective of the average bogey golfer. The average bogey golfer is both shorter and more wild in standard deviation of degrees offline than the average scratch golfer.

The 'accuracy table' in the course rating guide (2012-2015) judges the male scratch golfer by a degrees offline (2/3 ~ 1 sigma of shots) that Broadie attributes to a 3 HCP (maybe that's technology change from 1975 scratch?) and the male bogey golfer by a degrees offline that Broadie attributes to the same 3 HCP at a shorter shot distance. So built into the course rating guide is a clear assumption that the average Bogey Golfer should be as accurate as the average Scratch Golfer. I think that's a bias that does not reflect reality or the purpose of slope to 'view the course through the eyes of the bogey golfer'.

Knowing you admire Broadie's work, does that definition of a 'Bogey Golfer' as equally accurate in standard deviation of degrees offline as a scratch player jibe with statistical studies, let alone what you see with your own eyes nearly every day?

22 hours ago, iacas said:

Accuracy is already considered in the slope rating. Green size targets, fairway widths, the entire corridor (mounds, trees, etc.) are considered instead of just those within close proximity of the landing area… etc.

Perhaps not enough, if the Bogey Rating / Slope formula is ~ 90% distance based. On a percentage basis accuracy in degrees offline changes more significantly between skill levels. Distance differences may still impact score a bit more (~ 60 / 40), but not 90 / 10.

On 3/17/2016 at 10:45 PM, iacas said:

I'm still mostly done talking about this, because you've yet to convince me of anything at all, but surely you can see the folly in normalizing to a percentage when one set of numbers is almost 60x the other (250 yards versus 4° or whatever).

Percentage change is actually ideal in comparing the relative difference in distance (yards) and accuracy (degrees offline from target) between the different skill levels that bogey rating / slope is attempting to capture. Even if you convert the degrees offline to a lateral dispersion in yards at the shorter distance the higher HCP's hit the percentage difference / change from Scratch golfers is larger (more sloped) than for drive distance.

On 3/17/2016 at 10:45 PM, iacas said:

Plus, again, trees are already considered. Guess what? This might drive you nuts, but trees rated as a 6 on every hole versus trees rated as a 2 on every hole of the golf course… barely changes the course rating or slope.

I know, because distance accounts for ~ 90% of the formula, which is likely too heavy a weight.

On 3/17/2016 at 10:45 PM, iacas said:

So… if the guys in charge of building course ratings barely give much weight to ALL the trees on the entire course WITHIN your 30 yard boundary… what makes you think they're ever going to care about trees 35 yards away?

Bogey golfers do not have the average dispersion of scratch golfers. Therefore attempting to evaluate the higher relative difficulty they face on a certain course should take this fact into account more in line with its statistical impact on score.

On 3/17/2016 at 11:19 PM, iacas said:

To the point I was making above…

http://textlab.io/doc/1087995/how-trees-impact-usga-course-rating™-and-slope-rating®

I read this already. This is where I learned how little trees affect bogey rating / slope. Their 'simulation' is a tautology comparing the output of the same formula with different inputs. It's just an example / demonstration of how little weight trees have in the existing formula. It's not as Broadie does running a dynamic programming simulation between different course setups with a statistical model of a scratch and bogey golfer to see the expected impact on average score.

Even if an estimate of 3 extra (likely low) tee shots to the trees for a bogey golfer is correct that's 3 potential stroke & distance penalties (6 strokes) because even if the trees are rated as fairly 'recoverable' the chances of a lost ball are going to be quite high.