Introduction 
A golf handicap is a rough measure of a player's ability. It is not a perfect measure. It is biased in favor of the low handicap player, biased against a player with a large variance in his scoring, and biased against the player whose scores are trending upward. Even with these flaws, however, it is probably the best predictor of a player's gross score in a stroke play event.
Many tournaments, however, are played in a format where no scoring data is available. In a fourball event, each player may post an individual score, but the team score is not posted. There are clearly practical problems with trying to get a team handicap for fourball events (e.g., not sufficient scores with the same partnership). To get around this problem, studies have been undertaken to examine the relative performance of generic teams. For example, the USGA believes the teams with the higher combined handicap will do better in fourball stroke play than teams with lower combined handicaps. To correct for this inequity, the USGA recommends each player only receive 90 percent of their course handicap (See USGA Handicap System, Sec. 94bii). The 90 percent figure is called an allowance. A tournament committee has a great deal of discretion in choosing the allowance for a particular format. That choice will have a large impact on the equity of the tournament. Typically, there is no ex post facto examination of equity after a tournament is completed. This lack of analysis only ensures the same mistakes will be made next year.
This paper examines the equity of a tournament to provide an example of what should be done to increase equity. The exemplar was a twoday tournament with a twoman scramble and fourball format. Thirty two teams participated and could select to play from any of three sets of tees with their handicaps adjusted according to Section 35 of the USGA Handicap System. Five areas of possible equity problems are studied: 1) Prize format, 2) Scramble handicap allowance, 3) Fourball handicap allowance, 4) The effectiveness of Sec. 35 in ensuring fairness, and 5) The spread in the difference in handicaps between partners. A concluding section suggests possible policy and research implications for the United States Golf Association (USGA).
Many tournaments, however, are played in a format where no scoring data is available. In a fourball event, each player may post an individual score, but the team score is not posted. There are clearly practical problems with trying to get a team handicap for fourball events (e.g., not sufficient scores with the same partnership). To get around this problem, studies have been undertaken to examine the relative performance of generic teams. For example, the USGA believes the teams with the higher combined handicap will do better in fourball stroke play than teams with lower combined handicaps. To correct for this inequity, the USGA recommends each player only receive 90 percent of their course handicap (See USGA Handicap System, Sec. 94bii). The 90 percent figure is called an allowance. A tournament committee has a great deal of discretion in choosing the allowance for a particular format. That choice will have a large impact on the equity of the tournament. Typically, there is no ex post facto examination of equity after a tournament is completed. This lack of analysis only ensures the same mistakes will be made next year.
This paper examines the equity of a tournament to provide an example of what should be done to increase equity. The exemplar was a twoday tournament with a twoman scramble and fourball format. Thirty two teams participated and could select to play from any of three sets of tees with their handicaps adjusted according to Section 35 of the USGA Handicap System. Five areas of possible equity problems are studied: 1) Prize format, 2) Scramble handicap allowance, 3) Fourball handicap allowance, 4) The effectiveness of Sec. 35 in ensuring fairness, and 5) The spread in the difference in handicaps between partners. A concluding section suggests possible policy and research implications for the United States Golf Association (USGA).
The argument for “equal gross
and net” is the lowhandicap player cannot compete against the highhandicap
player in a net tournament. This
argument may be valid when there a large number of players and a wide range of
handicaps. Typically, a highhandicap
player has a larger variance in his scoring so it is likely one of the
highhandicappers has a good chance of winning—as well as finishing dead
last. If the competition is flighted and
the range of handicaps within each flight relatively small, the argument that a
lowhandicap player cannot compete loses much if not all of its strength. This tournament only had one flight with
handicaps ranging from 1 to 28. The lowhandicap players, however, did very
well. For example, the team winning low
gross also had the lowest net score. The
advantage of the lowhandicap player stemmed an inequitable handicap allowance
formula which is discussed next.
Scramble Handicap Allowance
– In the scramble event, the player with the lower course handicap was allowed
25 percent of his course handicap. The
player with the higher course handicap was allowed 15 percent of his course
handicap. The total was rounded off with
fractions of .5 or more rounded up. This
allocation seems inequitable on its face.
A team of tenhandicap players would receive a handicap of 4. A team of scratch players would receive a
handicap of 0. In essence, the tenhandicaps would have to
play even with the scratch players over 14 holes and just lose by a stroke on 4
others just to tie. This seems unlikely.
In an ideal tournament, net
scores should not be correlated with handicaps.
Fig.1 shows a plot of the net scores versus the scramble handicap of
each team. Net scores and handicaps are
highly correlated (R^{2} = .54). The linear regression equation predicts that
for each onestroke increase in team handicap, the net score will increase by 1.3
strokes. This explains why the lowest net scores were posted by the three teams
with the lowest combined indices.
Clearly, the 25,15 allocation was unfair to the high
handicap players. Is there a more
equitable allocation? That is, is there
an allocation that reduces the slope of the regression line to near zero? The USGA suggests a 35,15 allocation. Using the USGA allocation, the estimate of
the slope was reduced to 0.8 for the full sample as shown in Table 1. Based on this data set, the “best” allocation
would be 50,25. This allocation produces
a minimal slope (.2)and the R^{2} value indicates a team’s handicap only
accounts for 14 percent of the variance in net scores. Because of the small sample size, however,
this result only suggests the USGA
recommended allocations may be too low and further study is definitely
needed.
Table 1
Bias in Scramble Handicap Allocations
Allocation

Slope

R^{2}

25,15

1.3

.54

35,15

0.8

.46

45,15

0.6

.31

50,25

0.2

.14

FourBall Allowance – The net scores of
each team are plotted against their average team handicap in Figure 2. The regression equation indicates average
handicap may have a small negative effect (.1 for every increase in average
handicap) on net score. If there is a
wide range in average handicaps, however, even a small effect could be
important. In this tournament there was
a 20 stroke difference in handicap between the lowhandicap and high handicap
teams. This translates (20 x .1) into a
2 stroke edge for the high handicap team.
Handicaps, however, were not reduced by 10 percent as recommended by the
USGA. If they were, it is likely the
effect of average handicap on net score would disappear.
The coefficient for the average
handicap variable, however, was not significant at the 95 percent level of
confidence. The finding of bias found
here is merely suggestive, and a more definitive conclusion waits upon more and
larger samples.
Sec. 35 – In
this tournament, teams were allowed to complete from any of three sets of
tees. The player’s handicaps were
adjusted in accordance with Sec. 35.
The assumption was the particular set of tees chosen would not have an
effect on the team’s net score. This
assumption is examined for the scramble and fourball competitions.
Scramble – To
test for any effect of tee selection a dummy variable (T) was created. The variable was assigned a value of 1 if
the team played from the longest tees.
The variable was assigned a value of 0 if the team played from the
shortest tees. (Note: Only three teams played from the combination tees so they
were excluded from the sample.) The
following equation was estimated:
Net Score = a + b_{1} · Scramble Handicap + b_{2}
· T
The estimated equation was:
Net Score = 60.4 + 1.3 ·
Scramble Handicap  0.2 · T
The coefficient of the T variable was not significant
(tstatistic = 0.17). This would
indicate Sec. 35 adequately compensates for the differences in tees.
Fourball – A similar
model was estimated for the fourball competition. The estimated equation was:
Net Score = 63.8 – 0.4 · Average
Handicap + 1.6 · T
The equation estimates that playing the longer tees
results in a 1.6 stroke increase in the teams net score. Again, the coefficient of the T variable was
not significant (tstatistic = 0.93) at the 95 percent level of
confidence. The equation does suggest,
however, that Sec. 35 has not equalized competition in the fourball event.
Limitation on the
Difference in Handicaps Between Partners  The USGA is convinced, mainly on
the basis of research done in the 1970’s, that the spread between handicaps is
an important determinant of net score in fourball events. The argument is, for example, that a team
composed of a 6 and a 12 handicap is better than one composed of two 9
handicaps. To examine if the USGA’s
assertion is correct, the following model was estimated using data from the
fourball event:
Net Score = a +b_{1} ·
LH + b_{2} ·T + b_{3}· Spread
Where,
LH = Low Handicap of the two players adjusted
in accordance with Sec. 35,
T =
Dummy variable representing tee selection (1= Long tees, 0 = short tees)
Spread = Difference in handicaps between
partners
The estimated equation was:
Net
Score(FourBall) = 64.8 + .01·LH + 1.9·T – 0.5·Spread
The coefficient for LH was not significant as before. The coefficient for the T variable was
slightly more significant (t statistic = 1.24), but still did not pass the 95
percent level of confidence. The
coefficient for the Spread variable was significant at the 95 percent level
(tstatistic = 2.18). This confirms
the USGA’s recommendation of placing a limit on the difference in handicaps
between partners.
USGA research, however, applies to fourball events and
not to scrambles. To examine if “spread”
was important in scramble events a model similar to that above was
employed. The estimated equation was:
Net
Score (Scramble) = 60.4 + 1.3 · H  .3· T  .01·Spread
H
= Scramble Handicap (25,15 allowance)
T = Dummy variable representing tee selection
(1= Long tees, 0 = short tees)Spread = Difference in handicaps between partners
The coefficients of the T and Spread variable were not
significant (tstatistic = .2 and .1 respectively). This would indicate the limitation on the
difference in handicap between partners may not be necessary for scramble
events. Given the peculiar nature of
this tournament (the use of difference tees and a biased handicap allowance),
any finding from the scramble event is not much more than conjecture.
Implications for future Research  The
limited purpose of this paper was to demonstrate a methodology for evaluating the
equity of golf tournaments. In the
course of this research, however, several policy and research questions
surfaced that should be addressed by the USGA.
· The USGA requires clubs to use Sec. 35 when
players are competing from different tees.
The USGA, however, has not reported any research that proves Sec. 35
provides for equitable competition for different formats. This
should be corrected. Moreover, the USGA
should provide guidance on when Sec. 35 should be used and when it should be
avoided if possible. The USGA published "How to Conduct a Competition," but it is of little help in selecting formats to help ensure equity or in analysing tournament results.
·
The fourball allowance recommended by the USGA
was developed around 1978. That was 34
years ago. It seems time to revisit the
allowance since there have been changes to the handicap system since then.
·
The USGA only gives a soft recommendation on the
allowance for scramble events—i.e., 35,15 seems to work, but you can use
anything you want. The USGA could
instruct handicap chairpersons on ways to evaluate the equity of tournaments, as done here, so
they are in a better position to select the appropriate allowances.
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