[Garland Bayley]

Reducing golf course design to numbers is really a waste of time.  The Slope System is quite imperfect when it comes to areas such as strategy and angles of approach ... it assumes that people are playing from the middle of the fairway and assesses how hard it is to get there.

You can have a marvelous course with a course rating of 61 and a slope rating of 93. And, you can have a marvelous course with a course rating of 78 and a slope rating of 155. These ratings have nothing to do with architectural quality.

Garland:  In theory, that's true, but in practice, can you name an example of your first type?

There must be many executive courses that have ratings like the first one. The courses at Chabonneau near where I work come close. The only thing preventing existence of marvelous courses with those ratings is the emphasis on par 72 or so. There probably would be greater chance of such course across the pond where courses were built before the idea of 18 holes/par 72 became so prevalent. Shiskine comes to mind as a possible example.

[Philip Caccamise]

PV 153
ANGC only Old Tom knows for sure
CPC 140
Shinny 138
Oakmont 134
Merion East 149
Pebble 136
Winged Foot West 134
Sand Hills not rated near as I can tell
Fishers Island 143

I'm not advocating slope as the best or even a good measure of gca. But I am saying a smart statistician somewhere at MIT would be able to demonstrate they're correlative. Put another way, an architecturally respected course will probably be considered hard enough by bogey golfers relative to scratch players to have a higher slope than a course that is not regarded. The converse is not necessarily true - a course with a high slope could be a gca train wreck.
 

Oakmont is highlighted because of the overall fallacy in slope rating. The primary drivers for high slope are hazards and OB. There is no water and as far as I can remember, there is no OB really in play except for on #3 where one might play away from the Church Pews.
Next door is Oakmont East GC, which from the white tees plays 5700 yards and a slope of 117 (it is virtually devoid of anything interesting, a true Doak 1). The Red tees at Oakmont CC are 5600 yards and a slope of 128 for men. Now, comparing the slope ratings and based on score distribution at those points, a bogey golfer should shoot a lower score at Oakmont "East" from the white tees about 8 out of 10 times vs. the "West" red tees... but in reality we all know it would be more like 99 out of 100 because of the difficulty of the greens and slopes at "West". Conclusion: in my humble opinion, from analyzing hundreds of scores of all levels of players in our tournaments, the slopes assigned are generally too low on very difficult layouts and too high on moderate to easy layouts.

[Brent Hutto]

Conclusion: in my humble opinion, from analyzing hundreds of scores of all levels of players in our tournaments, the slopes assigned are generally too low on very difficult layouts and too high on moderate to easy layouts.

I have not examined the wealth of data that you have but my instinct is the same. I am a "bogey golfer" through and through, pretty much a living example of the definition USGA provides. And the courses rated 116-118 that I'm familiar with ought to be around 100 (roughly 10% below 113) while a few courses I've seen rated 130-134 ought to be at least 140 (about 20% above) in order for my 25th-percentile scoring to work out correctly at both types.

From a number-geek perspective I suspect that the system's fundamental constraint is that distance is both the most important contributor to the "difficulty for the scratch golfer" but then in fact distance is once again the dominant component in the ratio of 'difficulty for scratch" and "difficulty for bogey". As a result, both parameters are forced to reflect a lot of distance effect and the effect of all other factors has a hard time getting represented sufficiently.

It's a common problem in flattening out a multidimensional parameter space into two parameters.

[George Blunt]

"i.e. it is equally easy and equally hard for the scratch golfer as it is for the bogey golfer?

Give us an example of a hole and a course that fit that mandate."

Pat,
I hope it is understood that I mean the scratch golfer is attempting to play to scratch, and the bogey golfer to bogey.  Under normal non-tournament playing conditions I would offer Royal Melbourne West (played hundreds if not thousands of times), St. Andrews Old (played once) & NGLA (played once) as examples of courses which offer the same level of challenge to each type of golfer. 

To use the course with which I am most familiar, in my opinion RM West does not get incrementally harder for the less skilled golfer.  For this golfer there is more room off the tee and easy landing spots short of the greens.  As has been discussed here many times the scratch golfer must challenge the hazards to find the correct angles of play into the greens to make his par.  When either golfer presses beyond their ability the course shows her teeth, allowing heroic recovery while also punishing the poorly executed shot.

Tom,
I agree with the general sentiment here that trying to analyse golf course architecture via any statistical or numerical basis is nonsensical.  And in my opening post I preface the discussion by stating that slope is an output and not an input of the design process. 

What I am hearing loud and clear is that there is not much support for my argument that the fall in slope indicates the renovation is a success, but there is also no basis for complaint that the fall in slope indicates a poor or weak renovation.

[Brent Hutto]

I think that's the gist of it. There can be good designs that work out to a slope of any number you care to name (within the typical 120-140 type of range that's most common) and there can be poor designs with exactly the same slope rating as a good one.

It's roughly as predictive of quality as yardage might be. Sure it would be hard to build a really good 4,000 yard course or 9,000 yard course but in the usual 5,500-7,500 yard range you can find good, great, bad, mediocre and everywhere in between.

[Jim Nugent]

Now, comparing the slope ratings and based on score distribution at those points, a bogey golfer should shoot a lower score at Oakmont "East" from the white tees about 8 out of 10 times vs. the "West" red tees...

Unless you know either the course rating or the bogey rating from each course at those tees, how can you predict scores? 

[Philip Caccamise]

Now, comparing the slope ratings and based on score distribution at those points, a bogey golfer should shoot a lower score at Oakmont "East" from the white tees about 8 out of 10 times vs. the "West" red tees...

Unless you know either the course rating or the bogey rating from each course at those tees, how can you predict scores? 

1) you can predict score distribution from the slope alone
2) course rating OCC from reds for men is 70.9 (bogey 94.7), "East" whites is 67.3 (bogey 89.1)

[Jim Nugent]

Philip, so without knowing BR or CR, you can predict score distribution?  In that case, it wouldn't matter if CR is 65 or 75... or BR is 84 or 100:  those two slope scores imply bogey shoots a lower score at the one course 8 of 10 times? 

On the face of it, that seems unlikely to me.

[Philip Caccamise]

Philip, so without knowing BR or CR, you can predict score distribution?  In that case, it wouldn't matter if CR is 65 or 75... or BR is 84 or 100:  those two slope scores imply bogey shoots a lower score at the one course 8 of 10 times? 

On the face of it, that seems unlikely to me.

Why?

Like anything correlated and distributed, there is an implied probability based on the two numbers. I have a database of thousands of scores from all levels of players and an advanced degree in mathematics. If you want to see the numbers I can run them for you.

[Philip Caccamise]

OK since I was bored I ran the study again for some results last year. Keep in mind these are tournament scores so no question of accuracy in reporting.
- Courses were grouped by slope in intervals of 5 (<120,120-125,125-130,130-135,135-140,>140.)

- For the 14-18 handicap group (bogey golfers):
Slope Average Std Dev
120-125 90.7 5.9
125-130 92.3 5.9
130-135 93.2 4.3
135-140 94.1 6.3

So as I said, as slope increases, scores increase (no surprise). 10 points slope = 3 strokes. Based on the fact that these are normally distributed scores, we can calculate the probability of one beating another. It works out to about 72%.

[Tom_Doak]

Tom,
I agree with the general sentiment here that trying to analyse golf course architecture via any statistical or numerical basis is nonsensical.  And in my opening post I preface the discussion by stating that slope is an output and not an input of the design process. 

What I am hearing loud and clear is that there is not much support for my argument that the fall in slope indicates the renovation is a success, but there is also no basis for complaint that the fall in slope indicates a poor or weak renovation.

George:

In theory, if the fall in slope means anything -- and I am not convinced that it means anything -- it means that the course is less severe for higher-handicap players, and that they will not lose as many shots on their bad holes as they did before.  I agree with your premise that for many clubs, that would be a proper design goal.  Just as long as you don't try to get them to admit it.  The real problem here is one of perception, that the course might be perceived as "easier," and that the members might be perceived as weaklings who wanted to make it easier.

The change in slope doesn't necessarily mean anything for the scratch player.  The course rating and not the slope is the difficulty for the scratch player.

Also, while slope ratings are supposed to be objective, the results can vary as much as 10 points depending on who is completing them and what their assumptions are regarding the difficulty of the rough, the speed of the greens, and the wind on the "average" day.

[Jim Nugent]

Philip, slope alone tells you nothing.  Slope plus the historical data you have tells you more.  Slope plus the historical data for those two specific courses would tell you a whole lot.  

[John Connolly]

OK since I was bored I ran the study again for some results last year. Keep in mind these are tournament scores so no question of accuracy in reporting.
- Courses were grouped by slope in intervals of 5 (<120,120-125,125-130,130-135,135-140,>140.)

- For the 14-18 handicap group (bogey golfers):
Slope Average Std Dev
120-125 90.7 5.9
125-130 92.3 5.9
130-135 93.2 4.3
135-140 94.1 6.3

So as I said, as slope increases, scores increase (no surprise). 10 points slope = 3 strokes. Based on the fact that these are normally distributed scores, we can calculate the probability of one beating another. It works out to about 72%.

Phil,

You're going to wish you never came out as a mathematician! Because I have a question. Despite the fact there seems to be a general consensus amongst most here that there is no good correlate between design quality and difficulty/rating/slope, I would love to see a statistical analysis proving that. If "quality" of a course can be evaluated with ordinal data (which it often is, see "Doak scale") and those same courses contain rating data, correlations could be made. Of course there is debate as to whether ordinal data can be used in this manner and if this board cannot agree on the qualitative value of course rating, it's unlikely to reach consensus on whether it's statistically appropriate to use ordinal data in this way (as opposed to interval data). But, for the sake of this exercise, wouldn't it be neat to apply a statistical tool (student t test for example) to see if quality and difficulty are correlative. I've listed slope for "the top 10" above. Do you have it in you to dig up Doak's rating for each, crunch a student t test and see if we can get to p<.05? Admittedly, I may be over my skis on this one and I'm putting on my protective gear for what's coming but I'm a believer in math - it ultimately validates or dispels most of what we believe to be true.

[Philip Caccamise]

OK since I was bored I ran the study again for some results last year. Keep in mind these are tournament scores so no question of accuracy in reporting.
- Courses were grouped by slope in intervals of 5 (<120,120-125,125-130,130-135,135-140,>140.)

- For the 14-18 handicap group (bogey golfers):
Slope Average Std Dev
120-125 90.7 5.9
125-130 92.3 5.9
130-135 93.2 4.3
135-140 94.1 6.3

So as I said, as slope increases, scores increase (no surprise). 10 points slope = 3 strokes. Based on the fact that these are normally distributed scores, we can calculate the probability of one beating another. It works out to about 72%.

Phil,

You're going to wish you never came out as a mathematician! Because I have a question. Despite the fact there seems to be a general consensus amongst most here that there is no good correlate between design quality and difficulty/rating/slope, I would love to see a statistical analysis proving that. If "quality" of a course can be evaluated with ordinal data (which it often is, see "Doak scale") and those same courses contain rating data, correlations could be made. Of course there is debate as to whether ordinal data can be used in this manner and if this board cannot agree on the qualitative value of course rating, it's unlikely to reach consensus on whether it's statistically appropriate to use ordinal data in this way (as opposed to interval data). But, for the sake of this exercise, wouldn't it be neat to apply a statistical tool (student t test for example) to see if quality and difficulty are correlative. I've listed slope for "the top 10" above. Do you have it in you to dig up Doak's rating for each, crunch a student t test and see if we can get to p<.05? Admittedly, I may be over my skis on this one and I'm putting on my protective gear for what's coming but I'm a believer in math - it ultimately validates or dispels most of what we believe to be true.

Yes, I sure can. However I would note that we would need to analyze a lot more than just 10 courses, especially given that all of these are invariably a Doak 9 or 10, to get a definitive answer one way or the other. So what we need is a variety of rated courses, ideally American so we can easily pull up the slope ratings, and I'll crunch the numbers.

[Ken Moum]

I've played courses with slope ratings of 114-116 a few times but can't recall any with 113 or less. Even 114-116 seems to be a sign of an extremely wide-open, relatively hazard-free course on very mild topography. Not sure that's really a good thing.

Why would you consider a slope of 113 a sign of quality rather than wide-openness? Those few low slope rating courses I've seen have been rather boring. Even a bit of contour of the greens probably gets a bit more than 113.

The average golf course in the USGA handicap system ratings is probably a bit over 120 so 113 is at the very, very low end of that spectrum.

Brent, this is just one more example of why I think the US handicapping system is effed up beyond repair.

Under the guidelines of the slope system 113 is supposed to be average, or a "standard" course.  As you note, there are virtually no courses under 113 so IMHO it is patently impossible for that to be average.

Since no course wants to be under 113, and course raters are remarkably unwilling to hand out a bogey rating that would result in a slope over 150, we have compressed the range to a point where it simply doesn't work.

Everyone knows that a person who plays a higher sloped course all the time will absolutely kill a player (in handicap matches) who plays at a course with a slope down under 120. If the damned system is working as intended, that would not be the case.

K

[Jim Nugent]

Under the guidelines of the slope system 113 is supposed to be average, or a "standard" course. 

This idea of an 'average' or 'standard' course for slope is a problem.  Average based on what?  The mean of all courses?  The median? 

How bogey and scratch players score on a course depends on lots of things, but especially the design and maintenance meld.  The architects certainly are not held to any 'average' slope considerations.  I doubt the supes are either. 

I'm curious to know exactly what average is supposed to mean here. 

Again, slope is mostly pointless.  You're much better off knowing bogey and course ratings. 

[Jud_T]

There was a thread a while back on the ratio of slope to course rating.  The thought was that a course with a high rating and a low slope might embody the ideal of being fun and challenging for the most golfers.  This idea appealed to me at the time.  If this were the case, and appealing to the most golfers drove ratings (!), Talking Stick North would be near the top of most lists.   The course is 7133 yards from the Blacks with a CR of 72.7 and a slope of 125.  However, how do you then explain my and others' fascination with places like Kingsley which are the other way 'round (6450, 70.8/133 Member Tees)?  Bottom line is that ultimately you can't quantify art.  Comparing, for instance, Medinah #3 and Shoreacres, both Doak 7's, solely on their Doak rating and plugging it into this formula is silly.  Hence the descriptions in the CG.  Even Tom, whose numerical ratings are vastly superior to most of the rags IMO, isn't immune to the undue respect for difficulty promulgated by Digest et al. (In regards to Shoreacres, "Alas, the overall yardage is quite short, but it's still a real gem".)  Furthermore, I wonder if our brethren from across the pond aren't in fact better critics of courses as they're immune from posting every round as an equivalent medal score and only play in 3 comps a year, and not always at their home club?  I used to go to state math competitions in high school.  I was a dweeb then and I fear this discussion veering dangerously into Mathlete territory... When you can take Led Zeppelin 4 and Coltrane at the Village Vanguard and plug 'em into a formula and get something beyond mental masturbation out of it, please let me know...

[Garland Bayley]

...
Everyone knows that a person who plays a higher sloped course all the time will absolutely kill a player (in handicap matches) who plays at a course with a slope down under 120. If the damned system is working as intended, that would not be the case.

K

I think you must mean everyone presumes. Unless you can provide data, I won't even presume that.

[Garland Bayley]

There was a thread a while back on the ratio of slope to course rating.  ...

Jud,

I think the more significant factor is the type of golf you play. If you prefer medal play, some of the difficulty and craziness is undesired. If you prefer match play, difficulty and craziness is welcomed.

I would suggest that Tallking Stick would be preferred by medal play enthusiasts, and Kingsley would be preferred by match play enthusiasts.

[John Connolly]

Jud,

I'm not at all sure you're wrong. This notion of correlating course difficulty with architectural quality may indeed be fanciful. It is mostly art, agreed. However, when you start saying one course is "better" than another and then another, you've started to flirt with quantification. And numbers help establish a vocabulary for that quantification - math naturally follows. And once you start assigning numerical values to certain courses, and those same courses contain objective data such as yardage, ratings and slope, no mathematician worth a darn wouldn't start to wonder about relationships between those numbers. That we as lovers of gca would believe that this field is above mathematical analysis is a bit too provincial for my taste. An attempt at establishing statistical correlates will probably demonstrate what many of us inherently believe - there is no correlation whatsoever. But how fun it would be to look at the graph and the equations.

[Jud_T]

John,

OK, Just use my example above.  Shoreacres has a slope of 130 from the Raynor tees and Medinah has a slope of 147 from the Silvers (both 1 in from the tips).  They are both Doak 7's.  What this tells you I have no idea.  I guess you could look at a scatterplot of every course ranked 6 or higher and their respective slopes and try to see if there's some correlation and meaningful R squared.  All this would tell you IMO is Tom's bias towards difficulty for the higher handicapper in assigning numerical ratings.  You'd have to go to the writeups themselves to actually figure out which of the 2 courses above would be of more personal interest to you.  I guess perhaps if Shoreacres was more of an outlier on the downside of slope at that point in the graph it might peak the interest of someone like myself, but I really don't need a graphical representation to figure that out.  I just need to read the damn book! 

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