Wednesday, May 10, 2017

Southern California Golf Association Errs Badly in Explanation of the Slope System

From time to time the USGA and regional golf associations publish articles explaining the USGA Slope System.  More often than not, the articles get it right.  On too many occasions, however, the articles demonstrate a lack of understanding of the Slope System.  Such articles tend to confuse rather than inform their readership.  The latest example comes from Fore Magazine, the publication of the Southern California Golf Association (SCGA).[1]  The article is entitled “Slippery Slope: Comparing Course Difficulty” and was written by Doug Sullivan, the Director of Course Rating for the SCGA.  The article contains three major errors.  First, the suggested criterion for measuring course difficulty is not adequate for many situations.  Second, the article incorrectly describes how the Slope Rating is determined.  Third, the article’s explanation of why a player gets more strokes is not consistent with the theory behind the Slope System. Each error is reviewed in turn
Error No. 1 – Misleading advice on measuring course difficulty
Sullivan follows in the footsteps of several other articles that claim the Course Rating is the dominant criterion for ranking courses by Course Difficulty.[2]  Sullivan is more adamant, however, and claims the Course Rating should be the sole criterion is measuring course difficulty.  He writes:

… Slope Ratings should not be used to compare the difficulty of different golf courses.  Instead a Course Rating is generally a better indicator in determining the difficulty of one course compared to another. 

To make the case for the Course Rating as the measure of difficulty, Sullivan creates a straw man.  He describes two courses.  Course A has a Course Rating of 68.5 and a Slope Rating of 130.  Course B has a Course Rating of 71.8 and a Slope Rating of 120.  Sullivan asks which course is more difficult.  Sullivan argues your answer should be “Course B because Course B has a higher Course Rating.”   Sullivan never defines a “difficulty.”  For the sake of argument, difficulty is defined here as the score a player needs to play to his handicap (i.e., Diff = Course Rating + Course Handicap).   Because of Sullivan’s fortuitous selection of ratings, a player’s Diff will always be higher on Course B.  Sullivan used this faux example as definitive proof the Slope Rating should not be used to compare the difficulty of courses.[3]
Sullivan concludes:

So the next time someone asks you which course you think is more difficult, compare the Course Ratings, not the Slope Ratings.  Not only will your answer be more accurate, but your friends will be more than a little impressed with your knowledge of SLOPE.    

Sullivan is wrong.  While the Course Rating may be the dominant factor in measuring difficulty, it is not the only factor.[4]  If the definition of difficulty shown above is accepted, then:

                            Diff = Course Rating + Index∙Slope Rating/113

If there is a large difference in Course Ratings (e.g., 3 strokes), the course with the highest Course Rating will also have the highest Diff.   If the difference in Course Ratings is small, then Diff will be influenced by the Slope Rating and the player’s Index.   To demonstrate how Sullivan is wrong, two fantasy courses are constructed.  Course A has a Course Rating of 70.0 and a Slope Rating of 69.0.  Course B has a Course Rating of 70.5 and a Slope Rating of 155.  The vast majority of players would score higher (i.e., have a higher Diff) on Course B since it has both a higher Course Rating and Slope Rating.  But what if a player’s Handicap Index was +4.0?  Course A would have a Diff of 67.6 while Course B would have a Diff of 65.0. This player would find Course A more difficult.  In essence, Course Difficulty for an individual player cannot be determined by simply comparing Course Ratings as Sullivan suggests.

Since Sullivan did not acknowledge the importance of Index and Slope Rating in determining difficulty, his knowledge of SLOPE should not impress his friends.  Moreover, though left unstated in Sullivan’s article, course difficulty will vary by a player’s characteristics (hooker, slicer, short hitter, etc.).  If you really want to determine which course is more difficult, you should play them and draw your own conclusion.  To try to determine the most difficult course solely by USGA Ratings that are prone to error will only yield answers of little reliability and even less consequence.

Error 2 – Incorrectly describing how the Slope Rating is determined
Sullivan demonstrates a lack of understanding behind the derivation of the Slope Rating when he writes:

This is the type of graph (shown below) that is created to compare scores of golfers of different abilities.  As you can see, scores increase as a player’s Course Handicap increases.  A line is created to connect as many scores as possible.  The steeper the line, the higher the Slope Rating.  The flatter the line, the lower the Slope Rating.  The concept of SLOPE simply refers to the slope of this line – that bit of trivia should help you make a few bucks on your next friendly bet.

Sullivan is simply wrong.  Since the advent of the Slope System, the slope of the line relating average scores to handicap is the same for all courses.  After all, that was the purpose of the Slope System. To be correct the horizontal axis in Sullivan’s graph should have been labeled Handicap Index and not Handicap.[5]   If you followed Sullivan’s advice and placed a bet—you lost!

Sullivan makes a technical error when he writes the “line (shown in the graph) is created to connect as many scores as possible.”  Connecting as many scores as possible is not the appropriate criterion for determining the slope.  The line is typically determined  by linear regression techniques where connecting the scores is definitely not a requirement.

Error No. 3 – Confusing the reader on how Course Handicaps are determined
In trying to explain how and why the Slope System assigns additional strokes, Sullivan writes:

In simple terms, SLOPE is designed to make sure a golfer receives more strokes when playing a more difficult course and fewer strokes when playing an easier golf course compared with the USGA Course Rating.

This sentence is so poorly constructed it is hard to discern what Sullivan means.  Since Sullivan has just proclaimed the Course Rating is the measure of difficulty, he seems to be saying a player should receive more strokes at the course with the higher Course Rating.  This would be incorrect.  The handicap player does not receive more strokes because the Course Rating is higher and the course more “difficult.”  Handicap strokes are given as a function of the difference between the Bogey Rating and the Course Rating at a course.  Even in Sullivan’s own example, most players will get more strokes at the course Sullivan has declared to be the easiest (Course A).

So why do articles such as Sullivan’s continue to be published?  It’s probably because neither the SCGA in this case nor the reader are sticklers about accuracy.  The SCGA is looking to fill its magazine and assume the Director of Course Rating must know what he is talking about.   And if he doesn’t, it doesn’t really matter.  SCGA members can be divided into three groups.  The first will pass on any article about the Slope System so the image of the SCGA will not be harmed.  The second group will assume the article must be accurate since it came from the experts at the SCGA.  The third group that recognizes the article as nonsense is a very small subgroup of the SCGA membership (i.e., approximately 1) that can easily be dismissed.  

[1]Sullivan, Doug, “Slippery Slope: Comparing Course Difficulty,” Southern California Golf Association’s Fore Magazine, Spring 2017, p. 94.
[2]Cowan, Jim. “An Explanation of Slope,” Northern California Golf Association website,  Metropolitan Golf Association, “How do the Course Rating and Slope numbers affect my Handicap Index?”
[3] It is not clear why the authors of these articles have chosen peculiar Course and Slope Ratings to make their point.  Jim Cowan of the Northern California Golf Association, for example, used a course with a Course Rating of 72.8 and a Slope Rating of 114.  Since Course Ratings are highly correlated with Slope Ratings, it is very likely such a course does not exist.  Real courses could have been selected to demonstrate how difficulty is measured, but no author has taken that path.    
[4] Cowan, loc. cit.
[5] Stroud, R.C. and L.J. Riccio,  “Mathematical Underpinnings of the slope handicap,” Science and Golf, E & FN Spon, London, 1990, pp. 129-140.  Stroud shows the Perfect Valley Handicap as the label for the horizontal axis.  The Perfect Valley Handicap is a player’s Handicap Index. 

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