(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
five 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.)
A sandbagger is defined as a player who has artificially
inflated his handicap. As a group, sandbaggers
are generally considered both vile and corrupting to the game of golf. Why do some golfers become sandbaggers? One theory is based on genetics. Golfers are descendants of winners since the
losers were generally eaten. A genedriven
insatiable desire to win can only be quenched by getting really good or
establishing a phony handicap. Because
of Original Sin, certain golfers—the more slothful—will opt for the phony
handicap route and become sandbaggers.
This note puts forth a different theory. Moderate sandbagging is
necessary since the USGA Handicap System does not make for equitable
competition. The USGA is in part to
blame for a problem it spends so much effort trying to solve. To quote Pogo, “We have met the enemy, and he
is us.”
What is a moderate
amount of sandbagging? Moderate
sandbagging, or more politely termed “rational index supplementation,” is
defined as that increase in a player’s index that gives him an even chance at
winning a singles match—not of winning the MemberGuest three years in a
row. Moderate sandbagging is necessary
for equitable competition because the USGA Handicap System discriminates against
the highhandicap player. Specifically,
there are the three elements of the System that penalize the highhandicap
player: 1) The bonus for excellence
(BFE), 2) Only using a player’s ten best scores out of twenty to compute his
handicap, and 3) Equitable Stroke Control (ESC). The size of the penalty assessed by the three
elements is examined in turn. The
concluding section combines these penalties and estimates the number of strokes
the highhandicap player must add to his true index for equitable competition. The number is roughly 9 percent of a player’s
index.
The Bonus For
Excellence (BFE) –The USGA argues “bonus for excellence is an incentive for
players to improve their game that is built into the USGA Handicap System. It is
the term used to describe the small percentage below perfect equity (emphasis added) that is used to calculate a
Handicap Index.”[1] The BFE is currently set at .96.
There are several problems with the USGA’s thesis. To be an effective incentive, players must be
aware of the incentive. Few players know
of this 4 percent reduction in index and the USGA goes to no great lengths to
inform them. Like most merchants, the USGA is reluctant to tell their customers
they are being shortchanged 4 percent this month. The USGA hesitancy to promote the BFE can
also be attributed to another important problemthe BFE is not an incentive to improve for the vast
majority of players.[2]
In most cases, player improvement does not diminish the
advantage given to the low handicap player by the BFE. To illustrate the ineffectiveness of the BFE
as an incentive, let’s assume matches between a scratch player and players with
various handicaps. Table 1 presents the
perfect equity handicap as defined by the USGA and the handicap using the BFE
for players of various skill levels. If a
player’s ten best differentials average 30.0 (Slope Rating = 113), the BFE
reduces his handicap by onestroke.
Assume the player improves to the point where his ten best differentials
average 20.0. The BFE reduces this
player’s handicap by onestroke. In essence, even though he has improved
dramatically, he is no better off in his match against a scratch player. In both cases, he is getting one less stroke
than the USGA considers perfect equity.
Table 1 also shows improvement does not improve his competitive
position among his fellow highhandicappers.
The difference between the perfect equity handicap(PE) and the bonus for
excellence handicap(BE) is the same for all players with an average tenbest
differentials between 35.0 and 13.0—i.e., approximately 59 percent of players
with a USGA index.[3]
Table 1
Bonus for Excellence Penalty (Slope Rating
= 113)
Avg.
of 10 Best Differentials

Perfect
Equity(PE) Handicap

Handicap
with Bonus for Excellence(BE)

Bonus
for Excellence Penalty

35.0

35

34

1

30.0

30

29

1

25.0

25

24

1

20.0

20

19

1

15.0

15

14

1

12.0

12

12

0

The incentive effect for players with indexes of 12.0 and
below is also negligible. Those with
integer 10best differentials between 0.0 and 12.0 will have identical PE and
BE handicaps.[4] So the only real incentive is for a player to
become less than a 12.0 index. (Note:
This limit will vary with the Slope Rating).
For a great number of players this is a difficult, if not an impossible
task. So the BFE is not an incentive for
most golfers. It is simply a penalty
assessed to the highhandicap player in competition against lowhandicap
players.[5]
Basing the Handicap
on the Best Ten of Twenty Scores – The USGA bases a player’s handicap on
his best ten out of twenty differentials.
The USGA argues it want to measure a golfer’s potential ability and not
his average ability. This is disingenuous. If the USGA wanted to measure potential it
should take the best score out of twenty.
A more likely explanation is the USGA wanted to give an edge to the
lowhandicap player. By only using the
better half of a player’s scores, an advantage goes to the player who is more
consistent or in statistical parlance has a smaller variance in his scoring. The
players who are steadier are, most likely, the lowhandicap players.
Here is an example of how it works. Assume Player A always plays to the Course
Rating (i.e., his handicap is 0). Assume
the scores of Player B have probability distribution shown in Table 3.
Table 3
Scoring Probability Distribution of Player
B
Strokes Above Course Rating

Probability

Expect No. of Scores Out of 20.

18

.10

2

19

.20

4

20

.40

8

21

.20

4

22

.10

2

Assuming a Slope Rating of 113 and forgetting the BFE for
this exercise, Player B would be assigned a 19 handicap. Playing against Player A, Player B would win
on 10 percent of the time. He would tie
20 percent of the time and lose 70 percent of the time. If Player B sandbagged
1stroke, however, he would be a 20 handicap. Playing to his true probability
of scoring distribution, he would win 30 percent of his matches, tie 40
percent, and lose 30 percent. In other words, perfect equity has been achieved
thanks to sandbagging.
Kupper(2001) estimated the size of the bias using a
sample of 130 golfers.[6]
He estimated how golfers with large standard deviations in scoring (Wild
Willie) would do against players with small standard deviations in scoring
(Steady Eddie). Better players had small
standard deviations of around two. Less
skilled players (mean handicap differential of around 20.0) had standard
deviations around four. Table 4 presents Kupper’s estimates for Wild Willie
winning a stroke play match against Steady Eddie assuming standard deviations
of 2.0 and 4.0 for the two players.
Table 4
Probability That Wild Willie Beats Steady
Eddie
Average Difference in Handicap Indexes

Eddie’s Standard Deviation

Willie’s Standard Deviation

Probability (Willie Defeats Eddie

0

2

4

.37

10

2

4

.34

20

2

4

.31

30

2

4

.28

It should be noted that Kupper did not examine actual
matches. He examined the standard
deviations of a sample of players, calculated the biased USGA handicap
differential, and predicted a winner based on the normal distribution table. In other words, Kupper predicted who should
win, not who does win.
The empirical question is “Does the highhandicap player
lose about a third of the time?” Casual
observation indicates he does not.[7] A player who loses a third of the time either
quits playing matches and/or adjusts his handicap to make for equitable
competition.
Equitable Stroke Control – As discussed in
a previous post,[8]
changes in the ESC procedure have greatly reduced the discrimination against
the high handicap player. Under the new procedure, a player’s average adjusted
score is about .5 strokes lower than his average score. There appears to be no
disparate impact by handicap. Therefore, ESC cannot be considered a motivation
for moderate sandbagging and is eliminated from further discussion.
Moderate Sandbagging Defined  What is the
size of the adjustment to ensure equitable competition? The size can be estimated both empirically
and theoretically.
Empirically – A straightforward method of estimating the bias in
the handicap system is to plot the average differential versus index for a
sample of players. The slope of the
regression line through the data is the estimate of the bias moderate
sandbagging must overcome. An example of
this method is shown the figure below.[9]
The slope of the regression line
through the data was 1.095. The
difference in average differentials between players with a difference in index
of 10.0 would be approximately 1stroke.
Theoretically  To overcome the bias introduced by the BFE, a
player should increase his true index by 4 percent.
The adjustment necessary to
overcome the inequity caused by taking the best ten scores out of twenty is
more complicated. Let’s assume equity
for singles matches can be achieved if all players all players had a handicap
differential equal to their mean differential.
This is consistent with Scheid’s argument that “an accurate system for
match play must use a central measure of ability, like the mean.”[10]
Therefore, the necessary adjustment is
the difference between a player’s true index and his mean differential.
To make a rough estimate of the
adjustment it is first assumed that a player’s differentials are normally
distributed.[11] The handicap differential is the average of
the better half of his scores. This
average will be approximately .8 of a standard deviation from the mean. For example, if a player’s differential is
10.0, and his standard deviation is 4, the best estimate of his mean score 13.2
(10.0 + .8 x 4). To have his handicap
be equal to his mean score, a player must adjust his index upward by an amount
equal to .8 of his standard deviation.
Kupper plots the handicap
differentials versus the mean handicap differential for 130 players.[12] Based on this plot, a rough approximation of
a player’s standard deviation as a function of his handicap index (i.e., 96
percent of the mean of his best ten scores) is:
Standard
Deviation = 2.0 + .0667 · Handicap Index
Given these assumptions the necessary
adjustments for equitable competition are calculated and presented in Table 5. The gross adjustment is .8 times the player’s
index. The gross adjustment consists of
a fixed component (1.6) and a variable component. The net adjustment eliminates the fixed
component, and reflects the necessary adjustment for various handicap
differentials.
Table 5
Handicap Adjustment Needed to Overcome Bias
from Using on Ten Best Scores
Index

Standard
Deviation

Gross Adjustment

Net
Adjustment

0

2.000

1.600

0.000

10

2.667

2.134

0.534

20

3.333

2.666

1.066

30

4.000

3.200

1.600

The adjustment can be represented
in equation form by:[13]
Net
Adjustment = .05 · Index
Since the player must also
adjust his true index by 4 percent to account for the BFE, the final adjustment
equation becomes:
Final Adjustment = .05 · Index + .04· Index
= .09 ·Index
For example, if a player’s true
handicap differential is 20.0, he needs to adjust his index upward by 1.8 for
equitable competition.
Both the empirical and theoretical methods yield the
approximately the same estimate of bias—9 percent. Does this give a player carte blanche to inflate his index in the name of equity? It does not.
Equity could only be achieved if every player increased his/her handicap
by 9 percent. This is not likely. If only one player inflates his handicaps and
competes with players with like handicaps, then he becomes the sandbagger. This, of course, should be avoided.
To
win the hearts and minds of golfers in the war against sandbagging, golfers of
all types must be convinced they are being treated fairly. The USGA
Handicap System, however, discriminates against the highhandicap
player. It is clear that this inequity
gives some players extra motivation to inflate their handicaps. This extra motivation may be small in
comparison to other factors such as greed.
To minimize the motivation, however, the USGA should make the Handicap System fairer. The first step in moving toward this goal would
be to eliminate the Bonus for Excellence. The USGA’s War on Handicapping – Part
IV, examines the history of the Handicap
System to estimate whether movement toward a more equitable system is
likely.
[1] The USGA Handicap System, 20122015,
USGA, Far Hills, NJ, p. 77.
[2]
Dean Knuth, former Director of Handicapping for the USGA is more forthright
about the purpose of the BFE. He writes “Historically, the USGA wanted to
reward the accomplishments of better players…For a sixstroke difference in
handicaps the better player gains a oneshot advantage (due to the BFE) and
should win 60 percent of the matches. See
www.popeoflope.com/magazine/bonus_for_excellence.
[3] Men’s USGA Handicap Index Statistics,
www.usga.org/articles_resources?MensUSGAHandicapIndexes.
[4] A
player A 7.8 index will have a PE handicap of 8 and a BE handicap of 7. If he improves to 6.8 he is still has a BE
handicap of 7.0. If he adds onestroke
to his ten best scores, he becomes a 7.9 index and has a BE of 8. In essence,
he has a disincentive to improve. This
is due to the necessity for rounding to integer handicaps, however, and is not
a result of the BFE. Check thsi
[5]
The effectiveness of the Bonus for Excellence is examined in more detail in
Dougharty, Laurence, “The USGA’s Bonus
for Excellence” Ruse, www.ongolfhandicap.blogspot.com,
2013.
[6]
Kupper, Lawrence L., et al., “Is the USGA Golf Handicap System Equitable?”, Chance, Vol. 14, No. 1, pp.3035.
[7]
When Scheid took scorecards and simulated matches, he found a 90 percent
allowance was fairest for fourball stroke play (See Ewen, Gordon, “What the
Multiball Allowances Meant to You1978,” USGA.org/handicapping/articles). In
an examination of actual competition, Dougharty found the 90 percent allowance
was probably too high (See “Handicapping FourBall Stroke Play Events1997,”
Ongolfhandicaps.blogspot.com). This
would indicate players have adjusted their handicaps (in some cases by too
much) to make for equitable competition.
[8] What a Difference an ESC Makes, March 7,
2013, www.ongolfhandicaps.blogspot.com.
[9] Ibid.
[10]
Scheid, F.J., The search for the perfect handicap, ”Science and Golf II: Proceedings of the World Scientific Congress of
Golf, Edited by A.J. Cochran and M.R. Farrally, E&F Spon, London, 1994,
p. 224.
[11]
See, Scheid, F.J., “On the normality and independence of golf scores, with
various applications,” in Science and
Golf : the Proceedings of the First World Scientific Congress, Rutledge,
Chapman, and Hall, London, 1990, pp. 147152.
[12]
Kupper, op. cit., p. 33.
[13] A
coefficient of the handicap index of .0534 would indicate a greater level of
accuracy than exists. Therefore the
coefficient is rounded to .05
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