(The United States Golf
Association (USGA) has made various attempts to control players who manipulate
their handicaps in order to do well in tournaments. The name for such manipulation is “sandbagging.”
If the USGA’s effort can be characterized as a war, then it is not
winning. A series of six posts examines
the history and effectiveness of the USGA’s war plan. Part I details the flaws of the USGA’s
earliest attempt at controlling sandbagging.
Part II examines a proposed policy that increased the penalties for
alleged sandbagging. Part III argues the current handicap system may actually
encourage sandbagging. Part IV explains
why the USGA could be losing the effort to win the hearts and minds of local
golfers. Part V examines the flaws in the USGA's current war strategy. Part VI asks if the USGA's efforts are counterproductive and suggests it may be time for the USGA to withdraw from the battlefield.)
The United States Golf Association (USGA) first introduced
the "reduction of handicap index for exceptional tournament scores"
into its handicap system as
Sec. 103 in 1992. This was an opening
salvo in the war against sandbagging. Under the new handicapping procedure, a
player could have his index reduced if his tournament performance is significantly
better than his current index would indicate.
The reduction is based on the lowest two tournament scores over the past
year.[1] The index reduction is clearly intended to
restrict the prevalence of sandbagging  players having handicaps much higher
than their ability would dictate. It is
possible, however, that this new system could also penalize the ethical player
who plays in many tournaments. A system that does not clearly distinguish
between the ethical player and the sandbagger is worse than no system at all.
What is the probability the ethical player is penalized
under Sec. 103? We start with the
assumption that a player's differentials (adjusted score minus the course
rating times 113 over the slope rating) are distributed normally.[2] The player’s mean differential
is X with a standard deviation of s.
A player's expected current index is then:
Current Index = .96(X  .8s)
(The .96 is the bonus for
excellence adjustment in the USGA handicapping system. In the normal distribution, the average of
the better half of all scores is approximately the mean minus .8 of the player’s
standard deviation.)
For an index reduction to be imposed two conditions must
be met. First, the player's second
lowest tournament differential must be at least 3.0 lower than his current
index. Second, for players with six or
more tournament rounds, the difference between the average of the two lowest tournament
differentials and the player’s current index must be at least 5.5 to trigger an
index reduction.
To estimate the probability of an index reduction, we
simplify the problem by estimating the probability of two tournament differentials
being at least 5.5 below a player's current index.
In equation form:
CI  TD > 5.5
Where,
CI = Current Index
TD = Tournament Differential
Then,
TD < .96 (X  .8 s)  5.5
In the standard normal
distribution, the distance (measured in standard deviations) to the nearest TD
meeting the condition of the equation above is:
D = {X  ( 96 (X  .8s)  5.5}/s = .04X/s + .77 + 5.5/s
Where,
D = Number of standard deviations from the mean
differential to the nearest tournament
differential
meeting the inequality condition.
The probability of receiving an
index reduction is inversely proportional to the value of the D. That is, the
larger the value of D, the lower the probability of receiving a handicap index
reduction.[3]
The probability of a player having a differential at
least 5.5 below his current index is a function of his average differential, X, and the standard deviation of the
distribution of differentials, s. In a small sample of players, standard
deviations were found ranging from 3.5 to 5.5.
It was also observed that standard deviations typically increase with a
player's index. Scheid has reported
standard deviations of approximately 4.0.[4] The probability of having an exceptional
round (defined here as 5.5 below your current index) is shown in Table 1 below
for players of different average differentials and for a range of standard
deviations.
Table
1
Probability
of an Exceptional Round
Standard Deviation

Ave. Differential = 0

Ave. Differential = 20

3.5

.0096

.0051

4.5

.0233

.0150

5.5

.0384

.0274

The probability of having an exceptional round on any one
day is quite low. If you play in enough
tournaments, however, the probability of having two such rounds and incurring
an index reduction is not negligible.
Table 2 presents those probabilities under our assumptions of the mean
and standard deviation of the distribution of scoring differentials.[5]
Table 2 indicates that a player has a good chance to
receive an index reduction if he plays in a sufficient number of
tournaments. A player with an average
differential of 20 and a standard deviation of 4.5 (a typical bogey golfer),
for example, is estimated to have a 23 percent chance of a reduction if he
plays in 60 tournaments. It is likely
that the USGA did not design this system for such heavy tournament
participation. Some clubs, however, are
designating weekly couples events, intraclub matches, and bimonthly club
tournaments as "tournaments." By including minor weekly tournaments,
the number of tournaments entered in one year can easily rise to above 60
tournaments per year. In this case, a
player can be penalized not because he is a sandbagger, but because he
participated.
Table
2
Probability
of Two Exceptional Rounds in N Tournaments
Number of Tournaments(N)

Average Differential = 0

Average Differential = 20
 
Standard Deviation

Standard Deviation
 
3.5

4.5

5.5

3.5

4.5

5.5
 
10

.00

.02

.05

.00

.01

.03

20

.02

.08

.18

.00

.04

.10

30

.03

.15

.32

.01

.07

.20

40

.06

.24

.46

.02

.12

.30

50

.08

.32

.58

.03

.17

.40

60

.11

.41

.68

.04

.23

.49

70

.15

.48

.76

.05

.28

.57

80

.18

.56

.82

.06

.34

.65

Almost all of the index reductions due to the random
nature of scoring will be small. In most
cases it will only be one stroke. The
inability to distinguish between the ethical player and the sandbagger,
however, may weaken the credibility of the index reduction procedure.[6] To correct this deficiency the USGA could
either: 1) increase the exceptional tournament performance limit for increased
levels of play, or 2) narrow the definition of "tournament" to
include only major events as measured by prize money, entry fee, or some other
indication of importance. The latter
procedure is recommended, since the former allows the sandbagger to minimize
his index reduction by competing in a large number of minor events.
The problem with USGA policy is that it does
not differentiate between a player who enters 6 tournaments and one who enters
40 tournaments a year. When informed of
this analysis, the USGA took the position that no problem was likely to
exist. Dean Knuth, USGA Director of
Handicapping wrote:[7]
“The handicap reduction procedure
was developed with the use of data from about one million golfers that use the
USGA’s GHIN handicap service…The most active group of tournament players on
GHIN are two Northern California women’s golf associations. These most active tournament players average
five tournament scores per year, and the top one percent average sixteen….For
the present, we believe that taking the table to six tscores is sufficient.”
The war is off to an inauspicious start
when the Commanding General does not recognize and obvious flaw.[8]
There was never any reporting on the
success of Sec. 103 (e.g., body counts of sandbaggers snared). Sec. 103 was adopted to show the USGA was
doing something, Whether that “something” was effective did not appear to be a
concern. The USGA did try to improve the “reduction in index formula” over the
years. Unfortunately, those changes were
also plagued with flaws as will be seen in Part II of the USGA’s War on SandbaggingShock and Awe.
[2]Scheid,
F. J., "On the Normality and Independence of Golf Score, with Various
Applications," in Science and Golf:
The Proceedings of the First World Scientific Congress, Rutledge, Chapman,
and Hall, London, 1990.
[3]
Note that the higher handicap player has less chance to receive a reduction
than the low handicap player if both have the same standard deviation in
scoring. This stems from the current
index being based on differentials reduced by .96 while tournament differentials
are not similarly affected. It is not
clear why the USGA included this bias against low handicap players in handicap
system.
[5]If
we have N tournaments, the probability of having at least two exceptional
tournaments is 1 minus the probability of having no exceptional tournaments and
one exceptional tournament. In equation
form:
E = 1.0  {(1  p)N + N(1  p)N1(p)}
where,
E = Probability of at least 2 exceptional
rounds in N tournaments
p = Probability of an exceptional round
[6]If
clubs use different definitions of what is a "tournament," the equity
of the handicap system among clubs would be lessened. That is, some clubs may generate more index
reductions simply because they designate more events as tournaments.
[8]
It was only two years later, however, that the USGA had to correct the
procedure by adding categories for up to 40 or more tournaments. The change greatly reduced the probability of
both the ethical player and the sandbagger
receiving an index reduction for exceptional tournament scores..
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