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:

- The Rating Committee
assigns a value (usually between 0 and 10) to each of the ten obstacles
for every hole.
- These values are weighted in
accordance with importance (e.g., for the scratch rating use topography
.10, trees .09, etc.)
- The sum of the weighted values and
multiplied by .11.
- 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 *

*de*

*tails 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.