[Sven Nilsen]

I'd bet this has been covered elsewhere, but I can't find any threads addressing this specifically.

Here's the basic formula:

Distance / (Par - (2 x # of holes))

The resulting number is the average distance for each non-putt on the course.

Applying the formula to a quick sample, here's what one of the recent top tens looks like:

1.  Pine Valley - 207
2.  Augusta National - 206
3.  Cypress Point - 181
4.  Shinnecock Hills - 207
5.  Oakmont - 207
6.  Merion - 202
7.  Pebble Beach - 189
8.  Winged Foot - 201
9.  Sand Hills - 202
10.  Fishers Island - 182

The formula obviously discounts a slew of factors, including elevation (both on the course and above sea level), size and difficulty of greens, hazards, conditions, wind, turf, etc. 

What adjustments would you add, and can they be quantified?

Should the number of par 3's, 4's and 5's make a difference? 

[David Harshbarger]

Sven, it may seem obvious bt the USGA approach to slope and rating do provide a "comprehensive" model.  I understand distance dominates the formula, but the other factors you list are incorporated also.

[Jeb Bearer]

Isn't this just a funny way of ranking courses by distance?

[Sven Nilsen]

David:

I'm actually more interested in coming up with something that works for courses that don't have a modern slope/rating.  The idea being if you have some basic information about a course from 80-100 years ago, you can come up with basic idea of how hard that course was compared to others of its era.

Jeb:

Yes and no.  It allows you to compare courses that have different pars.  You could have a par 70 that is a shorter course than a par 72, but ranks higher in average distance per shot.

Sven

[Jeb Bearer]

Ahhh, true. I see what you're trying to do now.

[David Harshbarger]

Sven,

You might be able to take the modern approach and apply it back in time.  I don't know the specifics but I believe the modern approach includes evaluating the course for difficulty, with regards to water, bunkers, rough, length, greens, etc.  

The modern approach is applied by trained raters, and I believe it is validated by statistical models fit to actual scores from many courses, and many levels of players.  If you could get a hold of the current methodology you might be able to reverse engineer it into something you apply to aerials or other artifacts.  

For example, you might take the approach that you compute a scratch and bogey score for each hole.

Start with fractional par bands per hole, one for scratch, one for am.
Add in modifiers for bunkers, dog legs, OB, water, etc.
Come up with adjusted scratch and par for each hole.
sum the values
Fit a line between scratch and bogey scores to get slope.

It would be some work, but, I bet oping you do it you'd find holes and courses score close to where they are now.

Dave

[Jason Connor]

The USGA has a FAR better way to measure course difficult that they ignore.  (Im a PhD statistician)

The USGA has thousands of rounds of data for every course that they ignore -- they use it to calculate your handicap, but they could also use it to calculate course ratings.  And they could fire their raters.

Imagine this:

I shoot 88 at my home course every day.

Tim shoots 90 at his home course every day.

Phil shoots 76 at my course, 80 at Tim's course, and 74 at the muni he plays regularly.

We'll clearly my course is easier than Tim's course.    And my handicap would reflect that.

Now imagine not just 3 people to compare, but a million golfers.

Furthermore we all know that courses play differently on different days.  The model could similarly account for that.  For instance the last time I won the (net) game in the men's group at my club I shot a so-so 92.    92 would generally NEVER win the game, except that the winds were blowing at 30 miles an hour.  So my 92 that day was an excellent score.  That would never be reflected in my USGA handicap, in fact that round doesn't count toward my USGA handicap.  Though it was one of the better (handicap adjusted) rounds that day.

Given that we enter scores immediately either at our club or online this would be an amazing simple algorithm to implement.

And each course would have it's own course rating and slope that is basically updated daily.  The club could post the update the 1st of every month or a new rating every Monday. 

And when design changes occur, you wouldn't need to re-rate.  The math would take care of itself.

Furthermore courses whose difficult changes with the season would automatically have their ratings change.

[Pete_Pittock]

Jason,
That would work great where I play golf, which has two golf courses which were built with two very different philosophies, and are also have different maintenance practices. We play one course for half a month, and then switch ad nauseum. Our handicaps are a mishmash. In competitions on the first course the winning net is usually in the mid to lower sixties. On the other course it is around par 72.

[Sean_A]

Sven

I don't understand the formula input - why is your formula valid?  It looks to me like you already think you know which courses are tougher and then created a formula to fit your perception...or something like that.  David is right, the only way to really understand difficulty is by comparing scores over a lengthy period of time, but I am not sure there is much call for that sort of analysis. 

Ciao

[Sven Nilsen]

Sean:

Who's talking about validity?

All the formula does is tell you the average length of each shot on a course (based on getting on in regulation) that is not a putt (assuming 2 putts per hole).  If you don't think that result is valid then you and I disagree on how math works. 

It would be hard for a course where the average shot is 150 yards to be tougher than a course with an average over 200, but I suppose it is possible.  I also fully appreciate (and noted above) that this basic formula does little to capture many of the additional factors that can make a golf hole or a golf course difficult.

As I wrote in my response to David, I'm trying to come up with a way of providing a base line (or starting point) to analyze courses for which we do not have that much information, namely courses as they were 80-100 years ago.  In a sense, its a way of going beyond the basic statement that "Course X was Y yards when built," especially in cases where we really don't know much about what Course X was like during that era other than its par and its distance. 

The idea was to put the basic formula out there, and see if anyone had any ideas about variables that could be added in to build upon the basic premise - that being that the distance that has to be covered between the tee and the green is a large factor in the difficulty of a golf course.

The application to the top ten was merely an exercise in providing context, and I probably should have noted the inputs for each course (they're easy to find for anyone who wants to question my arithmetic).  I did find it interesting that applying the formula to the ten courses I noted (using their par and distance numbers as cited in the GD rankings) produced results pretty much in line with my preconceptions.  However, Merion and Sand Hills were a bit of a surprise.  Makes one wonder how this basic calculation would stand up to the "test of golf" criteria in the full slate of GD rankings.

Sven

[Sven Nilsen]

To follow up on my last post, here's a break down of the the latest GD Top 100 showing the Resistance to Scoring rankings and the rankings based purely on average length of a non-putt, with the differential between the two noted.

For example, if you look at the numbers for Pine Valley, it is ranked as the #1 course for resistance to scoring (RTS) by Golf Digest, yet it only has the 25th highest average distance per shot (ADS), suggesting that its difficulty is due to factors other than its length.  Whistling Straits, on the other hand, is ranked 10th for RTS, but 3rd overall for ADS, leading one to think that the primary factor in its difficulty relates to distance.

Pine Valley   1   25   -24   Oakmont   2   25   -23   Winged Foot West   3   56   -53   ANGC   4   31   -27   Shinnecock   5   25   -20   Bethpage   6   13   -7   Ocean Course   7   39   -32   Merion   8   49   -41   Oak Hill   9   13   -4   Whistling Straits   10   3   7  Oakland Hills   11   2   9   Olympic Club   12   49   -37   Medinah   13   9   4   Butler National   14   5   9  Pebble Beach   15   91   -76  Spyglass Hill   15   84   -69   Crystal Downs   17   88   -71   Pikewood   17   13   4   Muirfield Village   19   39   -20   Victoria Natl.   19   56   -37   Baltusrol Lower   21   35   -14   Sawgrass   22   63   -41   Hazeltine   23   7   16   Pinehurst   24   22   2   Southern Hills   25   39   -14   Seminole   26   91   -65   Riviera   27   22   5   Sand Hills   28   49   -21   Honors   29   31   -2   French Lick (Dye)   30   1   29   Castle Pines   31   7   24   Prairie Dunes   31   56   -25   Inverness   33   25   8   TCC   34   3   31  Friar's Head   35   78   -43  Pete Dye G.C.   35   39   -4   LA North   37   31   6   Pac Dunes   38   91   -53   Alotian   39   25   14   Golf Club   39   31   8   Olympia Fields   39   10   29   Aronimink   42   10   32   Sebonack   42   18   24   Wade Hampton   44   49   -5   Congressional   45   49   -4   Scioto   46   13   33   Chicago   47   56   -9   Dallas National   47   39   8   Blackwolf Run   49   35   14   Peachtree   49   35   14   Rich Harvest   49   5   44   Canyata   52   56   -4   Cypress   52   99   -47   Gozzer Ranch   52   46   6   Valhalla   52   18   34   Eagle Point   56   56   0   Baltusrol Upper   57   80   -23  Crooked Stick   58   22   36  NGLA   58   87   -29  Plainfield   58   75   -17   Fishers Island   61   98   -37   Harbour Town   61   49   12   Hudson National   63   18   45   Quaker Ridge   63   35   28   Winged Foot East   63   94   -31   Whispering Pines   66   25   41   Arcadia Bluffs   67   49   18   Old MacDonald   68   69   -1   Kapalua   69   63   6   Sahalee   69   81   -12  Bandon Dunes   71   96   -25   Calusa Pines   72   63   9   San Francisco   72   78   -6   Bandon Trails   74   84   -10   Kinloch   74   63   11   Laurel Valley   76   46   30   Old Sandwich   76   73   3   Shoal Creek   76   63   13   Black Rock   79   71   8   Diamond Creek   79   10   69   Flint Hills   79   71   8   Shadow Creek   79   13   66   Boston   83   56   27   Milwaukee   84   73   11   Preserve   84   75   9   Forest Highlands   86   63   23   Mountaintop   86   18   68   Cherry Hills   88   39   49   Mayacama   89   94   -5   Double Eagle   90   69   21   Grandfather   91   81   10   Interlachen   92   84   8  Estancia   93   46   47  Garden City   93   97   -4   Ballyneal   95   39   56   Kittansett   96   81   15   Monterrey Penn.   97   89   8   La Quinta (Quarry)   98   75   23   Somerset Hills   99   89   10   Maidstone   100   100   0

Using the differential between the two rankings, you could surmise which courses rely the least on distance (or the most on architectural and other features) for their perceived difficulty.  These courses include:

Pebble Beach (-76)
Crystal Downs (-71)
Spyglass Hill (-69)
Seminole (-65)
Pacific Dunes (-53)
Winged Foot West (-53)
Cypress (-47)
Friar's Head (-43)
Merion (-41)
Sawgrass (-41)
Fisher's Island (-37)

On the other hand, the courses that seem to rely on distance the most as a component of their difficulty look like this:

Diamond Creek (69)
Mountaintop (68)
Shadow Creek (66)
Ballyneal (56)
Cherry Hills (49)
Estancia (47)
Hudson National (45)
Rich Harvest (44)
Whispering Pines (41)
Crooked Stick (36)
Valhalla (34)

I think the breakdown gives you a pretty good idea of which courses are hard predominately because they are long, as opposed to courses where other factors come into play.  There are a few anomalies.  For example, I'd suggest that the differences for Ballyneal and Cherry Hills are inflated due to their being at altitude.  If the distances for those courses were adjusted to sea level numbers, they'd be lower in the average shot ranking.

DISCLAIMER:  This breakdown should in no way be deemed scientific.

[Matt Schmidt]

What yardage are you using for each course?  Is it the max yardage?

[Sven Nilsen]

The yardage given in the GD Top 100 rankings, which is probably pretty close to max yardage. 

[Matt Schmidt]

My first thought is that people tend to play about the same yardage no matter where they play. And that is nowhere near the max yardage on most courses (except on courses without an inflated tee set, like cypress, pacific, etc).  So the raters resistance to scoring data has nothing to do with max yardage, at least on many (most?) courses.

Speaking of the course I'm most familiar with, the max yardage tees are in play only once a year, for a member only test of manhood. No rater played those tees, and most were likely 1,000 yards short of them.  The max daily tees are 500 yards short of the stated max. 

When you visit this summer, I'll show you!

[Matt Schmidt]

Sven, I think I mixed two threads by including rated difficulty!  Maybe I need to visit the site more and keep up!

But perhaps the main point still is relevant here. People play a different course than what you are using in your calculation, and they tend to play the same length, more or less, at different courses.  They do this so the average shot length is similar and familiar to them. Does that make any sense here?   

[Sven Nilsen]

Matt:

I considered the max yardage v. average yardage played issue.  From what I understand, GD raters are asked to think about a course from different yardages, and part of the reason for their handicap cutoff is to ensure that they are getting the opinion of a golfer that probably could play from the back tees.  

I'm also not sure if the numbers on the GD list represent the normal placement of the back tees, or the yardages the courses could be stretched out to if you tried to max it out all the way around.  In some cases, I was actually a bit surprised that the yardages given weren't higher.

If I had the numbers for how these courses played from the normal members tees, I'd be happy to run the same test.

When you come out to Chicago this spring, we can discuss it further.

Sven

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