Introduction
– This paper explores problems with the United States Golf Association
(USGA) Handicap System. These problems
stem from a failure to understand the theory behind the Slope Handicap System, and
the dearth of USGAsponsored research on handicap issues for the past 20 years. This in turn has led the USGA to make changes
in the handicap system that reduce the equity of competition.
The device chosen to illustrate these problems is a case
study involving Section 103, Reduction
of Handicap Index Based on Exceptional Tournament Scores, of the Handicap
System. The following example and question were posed to the USGA:
Player A plays two tournaments
at a course with a Slope Rating of 150. His two net scores are five strokes
under the Course Rating.
Player B plays two tournaments
at a course with a Slope Rating of 87. His two net scores are also five strokes
under the Course Rating.
Assume these Tscores are the
only ones in each player’s file. Under Section
103, Player A receives no reduction in index. Player B’s index is reduced by 4.8. Why is
the player on the "easier" course treated so harshly?
The problems are examined in three parts. First, the USGA’s response is analyzed for its understanding of the Slope Handicap System. The USGA’s answer is found to be unresponsive at best and invalid at worst. Second, a flaw in the Slope Handicap System is demonstrated. This flaw is partially responsible for the counterintuitive result of the above example, and its existence has been steadfastly denied by various officials at the USGA and state golf associations. Third, the mistakes made in the development of the Handicap Reduction Table of Section 10.3 are documented. The USGA changed the vocabulary used in the table to be consistent with the Slope Handicap System (e.g., “strokes under the course rating” became “index minus average tournament differential.” The USGA didn’t know or didn’t care that these two concepts of exceptional performance are not synonymous. This mistake has led to inequity and the counterintuitive result of the example. In a concluding section, the state of research at the USGA is assessed and recommendations for improvement made.
The USGA Response
– Scott Hovde, Manager of Course Rating and Handicap Education at the USGA,
made the following response in an attempt to answer the questions posed in the
example:[1]
As Slope Rating is a relative measurement of difficulty (not absolute),
essentially an indication of how scores are spread out…a performance of 5 under
the Course Rating on a Slope Rating of 87 is more significant. On a course with an 87 Slope Rating, scores
are expected to spread out at a rate of .77 (87/113…rounded) per difference of
1.0 in the Handicap Index. To beat a
scratch golfer (who is a very good player) by 5 strokes on a course where
scores are very tight for players of all handicap levels, is more difficult
than doing it on a course with a 150 Slope Rating, which spreads out scores by
1.32 per 1.0 in the Index.
The advantage of a player with a lower Index grows as Slope Rating goes
up and shrinks as Slope Rating goes down, regardless of which side of scratch a
player is on.
Hovde argues scores are very tight on courses with low slope ratings and therefore performances of 5under the Course Rating are more difficult to achieve. There is no empirical or theoretical basis for such a claim. Papers proposing the Slope System only argue a player’s average score increases with the Slope rating.[2] These papers do not argue the Slope Rating affects the distribution of a player’s score.
Hovde next argues the advantage of a player with a lower
Index grows as Slope Rating goes up and shrinks as Slope Rating goes down. This is true by the definition, was never in
question, and is irrelevant to the question posed in the example. The question is whether indices are assigned properly,
and not whether the handicap calculation based on those indices is correct. Why does the USGA consider the player who
scores 5under the Course Rating at the PGA West Stadium Course (Slope Rating =
150) less skilled than a player scoring 5under the Course Rating at the Oasis
(Slope Rating = 87)? This question is
examined next.
Flaw in the Slope
Handicap System – To understand the flaw in the theory behind the Slope
Handicap System, it is important to review its theoretical underpinnings. The Slope Handicap system was introduced by
the USGA in order to bring more equity to the game. The previous handicap system had computed
handicaps by measuring the difference between a player's score and the course
rating. It was believed, however, the course
rating did not properly measure the difficulty of the course for the higher
handicapper.
Figure  Player’s Score at Panther Mountain and Perfect Valley Versus
Perfect Valley Handicap
The figure plots players' expected scores (defined here as
96 percent of the average of the ten best out of the last twenty rounds) on a
tough course named Panther Mountain (slope rating = 155) against their
handicaps on a course of average difficulty named Perfect Valley (slope rating
= 113). For example, a 10handicap at
Perfect Valley would be expected to have a score of 83.7 at Panther Mountain or
13.7 strokes over the course rating of 70.
Also shown in the figure is the score on Perfect Valley plotted against
a player's Perfect Valley Handicap. For
convenience the course rating at each course is assumed to be the same (70),
though that is not necessary to the argument.
Therefore, as illustrated in the figure, players from
Perfect Valley with handicaps greater than scratch (i.e., 0 handicap), will
score higher at Panther Mountain than they will at their home course. The Slope Handicap System increases these
players' handicaps at Panther Mountain reflecting the difficulty of the course.
While the USGA has never presented any
empirical evidence of this “slope effect,” it does make intuitive sense. Obstacles at Panther Mountain such as length,
water hazards, and rough may cause problems for bogey golfers that are not
incorporated in the Course Rating. Perfect Valley players with plus handicaps (i.e., less than scratch), however, are expected to score lower at Panther Mountain than at Perfect Valley. Therefore, these players will have their handicaps reduced when they play at Panther Mountain. The Slope Handicap System assumes a course with a high slope rating is relatively easy for players with indices less than scratch. There is no empirical evidence indicating this assumption is valid. Nor is there any theoretical reason to believe a player who scores 5under the Course Rating at Perfect Valley is a much better player than one who scores 5under at Panther Mountain.
The problem arises because the USGA chose to set the scratch
golfer as the standard. Had the standard
been set at the “perfect golfer” (e.g., a +10) there would be no negative
differentials and all players at Perfect Valley would have their handicap stay
the same or increase when traveling to Panther Mountain.[4]
Even if negative scoring differentials were eliminated,
however, the peculiar result of the example would still exist. It is a mistake made in the development of
the Handicap Reduction Table that leads to the much harsher treatment of the
player at the course with the low Slope Rating.
We turn to this next.
Handicap Reduction Table (Abbr.)
Avg. of 2 Lowest TScore Differentials
Below Index

Number
of Eligible Tournament Scores


2

3

4

59

1019


4.04.4

1.0


4.54.9

1.8

1.0


5.05.4

2.6

1.9

1.0


5.55.9

3.4

2.7

1.9

1.0


6.06.4

4.1

3.5

2.8

1.9

1.0

6.56.9

4.8

4.3

3.7

2.9

2.0

The table shows the higher the tournament differential
(Index  Average of 2 lowest tournament differentials), the greater the
possible reduction in index. The problem
is there is no research indicating the reduction should be a function of the
tournament differential. The basic research
was done by F.P. Engel who used Bogevold’s data in 1983 to determine the
likelihood of a player recording a low negative differential defined as net
score minus the course rating.[5] Dean Knuth, former Senior Director of
Handicapping at the USGA, developed a probability table for a player’s two best
scores to beat his handicap.[6] Even though Knuth is credited with inventing
the Slope Handicap System, he used strokes below course rating and not index
differentials in his analysis. In a
recent interview with the Wall Street
Journal,[7]
Knuth said “the odds of a midrange player shooting eight strokes
better than his handicap are 1 in 1,138.”[8]
In other words, the handicap research done under Knuthwhich
practically speaking is all of the research done by the USGAviewed
exceptional scores as strokes below the Course Rating. Knuth’s work estimates the probability of being
5under the course rating is independent of the Slope Rating. This makes intuitive sense as well. A player’s score and handicaps are not
affected by the Slope Rating if a player only plays at home. If scores are normally distributed with a
constant standard of deviation, a player has an equal chance of scoring
nstrokes under the course rating whether the Slope Rating is 87 of 150.
So why did the USGA change “Strokes Under Course
Rating” to “Index  Average Tournament
Differential ” as the measure of exceptional performance? The
two culprits were probably sloth and ignorance.
Sloth kept the USGA from doing any new research on the problem. When the current Appendix E, Exceptional Tournament Score Probability
Table, of the Handicap System is
based on 30year old data, it is
a good indication no one in the Handicap Section of the USGA is working
overtime.[9]
Ignorance probably guided someone at the USGA to make the
change thinking it made little difference.
According to Appendix E, a net
differential 8.0 has a 1 in 1138 chance of occurring. A player would have a net differential of 8.0
if his net score was 10.6 strokes under the Course Rating at a course with a
Slope Rating of 150 or if his net score was 6.2 strokes under the Course Rating
at a course with a Slope Rating of 87. To believe those two events are equally
likely, one has to suspend all judgment and disregard the bulk of USGA
research. Apparently, that was no
problem for some USGA staffer and the Handicap Procedures Committee.
Conclusions and
Recommendations – This paper has identified a flaw in the Slope Handicap
System and problems with Sec. 10.3 of
the Handicap System. The flaw is not a major impediment to equity
since:
1.
The flaw primarily affects players with plus
indices who constitute a very small minority of all golfers,
2.
Plus indices are typically not concerned about
their handicap in interclub net scoring events,
3.
The flaw does not affect intraclub events where
players’ handicaps are based primarily on scores from their home course.
Moreover, to correct the flaw would be very difficult, and only confuse the golfing community that is already sufficiently addled by the present Slope Handicap System.
Updating
Research on Exceptional Performance  Both Appendix E and the Handicap
Reduction Table appear to be based on data and analysis that are 30 to 40years
old. Due to limits in computing power
back then, the sample size was probably small.
With the advent of GHIN and modern computers, research no longer has
such restraints. It would not be a
difficult task, for example, to find the percentage of golfers who have a score
of 7under the course rating in their last 20 scores. This empirical finding could be used to revise
the probabilities presented in Appendix E.
ReExamine
sec. 10.3  As discussed above, equivalent performances (i.e., nstrokes
under the course rating) are treated differently depending on the Slope Rating.
It is doubtful the USGA can demonstrate
Sec. 103 as presently constituted is equitable. Armed with new results on exceptional
performance, the USGA would be in position to construct an equitable Handicap
Reduction Table. This reexamination
should also review if Sec. 103 is serving its intended purpose (e.g., Is the
lack of uniformity in the application of Section 103 affecting the equity of
competition? Is the present method of
measuring tournament performance equitable?)[10]
Research on golf performance has undergone resurgence
recently. Pope and Schweitzer have
analyzed success rates when players are putting for par and birdie.[11] Minton has explored the effect of randomness
in golf and the mathematical strategies behind the sport.[12] Wells and Skowronski examined the evidence on
whether players choke under pressure.[13] What all of these studies have in common is
that they were performed with data made available by the PGA Tour. There is no similar set of studies dealing
with equity in amateur golf or using data from the USGA.
The dearth of research on handicapping is due to policies of
the USGA. The USGA has not directed much
attention or resources to research in years.
The present policy of restricting public access to its research has also
not served the USGA well. Without
external peer review, the probability of mistakes similar to those made in Sec.
103 and Appendix E will continue to be high. The USGA needs something equivalent to perestroika to breakdown the insular
barriers between it and the research community.
If history is any judge, such an “opening” is decades off.
[2]
R.C. Stroud and L.J. Riccio, Mathematical underpinnings of the slope
handicap, in Science and Golf: The
Proceedings of the First World Scientific Congress of Golf, Rutledge,
Chapman and Hall, London, 1990, pp. 135140.
D. Knuth, A two parameter golf
course rating system, Ibid, pp. 141146.
[3] The figure is a slight modification from
that found in R.C. Stroud and L.J. Riccio, loc.
cit. Stroud and Riccio wisely did not
show or discuss the effect on plus handicaps at Perfect Valley.
[4]The USGA did not believe it had a problem
even when the Slope Handicap was first adopted. Dean Knuth, Senior Director of Handicapping
wrote “The hurdle of negative differentials could be bypassed completely by
setting the course rating at a low enough level to ensure their
nonexistence…The effect would be exactly the same as what we have and want
now. What really is happening is that
ability differences are being magnified or contracted, as appropriate.” (Letter from Knuth to Russ Palmer, Executive
Director of the Connecticut State Golf Association, Sept. 13, 1994.) The effect, of course, would not be the same.
[5] D.L. Knuth, F.J. Scheid, and F.P. Engel, Outlier identification procedure for the reduction in handicap, Science and Golf II: Proceedings of the
World Scientific Congress of Golf, E & F Spon, London, 1994, p. 230.
[7] John Paul Newport, Fighting
Back Against Sandbaggers, Wall
Street Journal, July 2, 2011. Also see John Paul Newport, The Genius of Handicapping, Wall Street Journal, November 1, 2008
where Newport cites the odds(sic) of beating your handicap by three strokes is
1 in 20.
[8] Kelly Neely, a
member of the USGA Handicap Procedures Committee and Senior Director of
Handicapping of the Oregon Golf Association wrote “Your chances of beating your
handicap by 10 strokes in one round is (one in) 37,000.” See www.oga.org/index.php/handicapping. Apparently, Ms. Neely relied on an old version of
Appendix E.
[9] As an another example of sloth, Appendix E formerly showed the
probability of a 1321 handicap player having a net differential of 0 or better
was 1 in 6. For every other index range,
the probability was 1 in 5. When the
USGA was alerted to discrepancy, it changed this probability to 1 in 5 for all
players in the 2012 Handicap Manual. No
new research was done. Someone just
replaced a 6 with a 5—problem solved.
Equally disturbing, the 2012 Handicap
System Manual contains typographical and editorial errors in Appendix
E. When these were brought to the
attention of the USGA, Mr. Hovde blamed the errors on the printer. Email to
author, February 9, 2012.
[10]
Under the old Section 103(1994), the penalty for exceptional performance was a
function of how well you played in tournaments.
Under the current version of Section
103, the penalty is a function of how well you played relative to your
current index. This leads to some
peculiar and perhaps inequitable results.
See Dougharty, Laurence, Reduction
in Index for Exceptional Tournament Performance: Some Conceptual Problems, Measuring Golf Performance, Golf
Economics, Manhattan Beach, CA, 2005.
[11]
Pope, Devin and Schweitzer, Maurice, Is Tiger Woods Loss Averse? Persistent Bias
in the Face of Experience, Competition, and High Stakes, American Economic Review, 101 (February
2011), pp. 129157.
[12]
Minton, Roland, Golf by the Numbers, The Johns Hopkins
University Press, Baltimore, MD, forthcoming June, 2012.
[13]
Brett
Wells & John Skowronski, Evidence of
Choking Under Pressure on the PGA Tour, Basic and Applied Social Psychology, March/April 2012, Pages
175182.
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