Friday, February 12, 2021

USGA Cover-Up for the World Handicap System

The World Handicap System defines the difficulty of as:[1]

              Hole Difficulty – Scratch Value + Bogey Value – 2 x Par

This equation implies holes are rated for the scratch player and the bogey player.  For example, a hole could be rated 4.2 strokes for the scratch player and 5.3 strokes for the bogey player. However, an examination of previous USGA Course Rating Manuals[2] and a description of the USGA Course Rating Model by its creator[3], Dean Knuth, does not reveal how holes are rated for difficulty.  The USGA Course Rating Model does indicate how “courses” are rated, but not “holes.”  The USGA’s Course Rating equation is:

              Course Rating – Effective Distance/220 + 40.9 + Scratch Obstacle Value (SOV)

Course Rating Committees does not assign a stroke value to the obstacles on each hole.  Instead, the process goes as follows:

  1. The Rating Committee assigns a value (usually between 0 and 10) to each of the ten obstacles for every hole.
  2. These values are weighted in accordance with importance (e.g., for the scratch rating use topography .10, trees .09, etc.)
  3. The sum of the weighted values and multiplied by .11.
  4. The SOV is the product found in step 3 minus 4.9.

If this sounds more like a cookbook recipe than an empirically based econometric model, that is because it is. But put that aside.  The USGA model will at least give consistent, if not accurate, estimates of the SOV.  That is, courses with similar obstacles will get closely the same SOVs.  The USGA model as described above will not, however, yield a stroke obstacle value to each hole.

So how are ratings for each hole determined?  The question was put to Scott Hovde, Director of Course Rating and Handicap Education, at the USGA. Below are excerpts from the email exchange:

OnGolfHandicaps: Appendix E of the Rules of Handicapping gives an example of how playing difficulty is determined.  In the example, the scratch value of a par four hole is 4.2 as "provided by the Course Rating procedure."...Can you direct me to a source that details how such scratch values are determined?  


Hovde: A scratch value for a hole would be based on the combination of a (sic) the length rating and the obstacle stroke value.  The length rating has not changed in a while (other than name, which used to be yardage rating)...It is probably listed as an 18-hole formula, so would have to be scaled down to a single hole, but a hole over 420 yards for men (effective playing length) would have a length rating of 4.2 or greater.  The obstacle stroke value can add or subtract from that, but on average it adds to it.


OnGolfHandicaps: Your example implies there is a formula for converting hole length into the scratch and bogey values mentioned in Appendix E.  Can you cite a reference that explains how the course distance rating is scaled down to a single hole?


Hovde has not replied to this request for details on how hole estimates are actually made.  Equally disappointing were responses from the Southern California Golf Association (SCGA) and the Oregon Golf Association (OGA).  Doug Sullivan, Director of Course Rating at the SCGA, has published hole ratings but has tacitly refused to explain his method for doing so.

Gretchen Yoder, Manager of Handicapping and Course Rating at the OGA, wrote the following:

I guess the best way to think of it is separately for both Scratch and Bogey, the number of the full shots, plus the distance of the shots to the green and then +/- any difficulty in addition to yardage.


Yoder’s description is not definitive of the method.  How does a 140-yard distance to the green translate into an incremental hole rating?  And how is the +/- difficulty determined?


Why are the USGA and regional golf associations so secretive about the hole-rating process?  One explanation for the cover-up is the USGA does not want to expose the lack of scientific rigor in the Course Rating process. The USGA, for example, has never published any research indicating its hole ratings  predict scores with any accuracy.  The USGA thrives on a on a reputation of omnipotence (Chambers Bay aside).    To be forthcoming about much of its work on the handicap system is not in its own best interest.




[1] Rules of Handicapping, Appendix E, United State Golf Association, p. 98.

[2] USGA Course Rating Manuals, 21012-2015, 2016-2017.

[3] Knuth, Dean, “A two parameter golf course rating system,” Science and Golf, E & F Spon, London, 1990, pp. 141-146. 

Sunday, February 7, 2021

World Handicap System is Confused About Course Ratings


The World Handicap System (WHS) seems confused about what the Course Rating should measure.  In the WHS’s Rules of Handicapping (p.103) the Course Rating is defined as the expected score of a scratch player.  By “expected score” it is assumed the WHS means “average score.”  The WHS also defines a scratch player as one with a 0.0 Handicap Index (p.15).   To have a 0.0 Handicap Index a player’s low 8 differentials out of 20 must equal 0.0.  In equation form:

Avg. of 8 low differentials = 0.0 = ((Score1 – CR) + (Score2 – CR)…+ (Score8 – CR))/8 x 113/SR

                            CR = Course Rating

                            SR = Slope Rating

For this equation to hold. the average of the player’s 8 low scores must equal the Course Rating.  His expected score, therefore, would be higher than the Course Rating.  So, what is the Course Rating?  Is it a scratch player’s expected score of the average of his 8 best scores?

Complicating matters is the USGA Course Rating Model does not use either of the WHS’s definitions of the Course Rating.  That Model estimates the Course Rating as the average of the better half of scores of a scratch player’s latest 20 scores.  Has the Course Rating Model been updated to reflect the new definition (or definitions) of the Course Rating?  There is no evidence of any change in the Model.

Does any of this affect the accuracy of the Course Rating?  Probably not. A Course Rating is an imaginary number that cannot be measured like height, weight, and temperature.  The Model provides estimates of the Course Rating that should be consistent, but not necessarily accurate.  By that it is meant that if two courses are similar in distance and obstruction, the Course Ratings should be roughly the same.  The confusion about Course Ratings in the WHS will not affect handicaps, but does suggest the WHS needs to hire a better copy editor for its next edition.