Note: The World Handicap System (WHS) listened to complaints and did away with the USGA recommendation for stroke allocations and adopted those recommended below. This blog likes to think it played a part in the WHS revision, but probably not.
Introduction and
Summary – For 30 years the United States Golf Association (USGA) has
recommended the following handicap stroke allocation procedure for match play:
A handicap stroke should be an equalizer rather than a winning stroke
and should be available on a hole where it most likely will be need (sic) by
the higher-handicapped player to obtain a half (sic) in singles…
The USGA has never demonstrated its recommended procedure
does in fact assign strokes where they are most needed, nor has it demonstrated
the procedure is superior to other procedures in ensuring the equity of
competition. This post attempts to
evaluate the efficacy of the USGA procedure by asking and answering a series of
questions about handicap stroke allocation.
1. Does
the USGA procedure actually identify where a high-handicap player will most
likely need a stroke to obtain a halve?
It does not. As shown in the
USGA’s example in Section 17, the procedure assigns the first handicap stroke
to a hole where it will be of the least use
to the higher-handicap player.
2. Is
there a better procedure for allocating handicap strokes for match play? Probably not.
If the USGA wanted handicap strokes to serve as equalizers, allocations
should be made on the basis of how close the average difference in hole scores
between higher and lower handicap players is to 1.0. This average difference, however, will change
with each handicap pairing. Even if this
equalizer objective is adopted—and there is no evidence it should be—there would
not be one best stroke allocation suited for all matches. Golf Australia recognized this when it
recommended the same match play stroke allocation for all courses.
3. Is the
USGA procedure defined with sufficient specificity to be implemented? No. The
USGA advocates that the first handicap stroke should be allocated so that this
stroke is most useful in a match between players of almost equal ability. The USGA, however, does not identify any
process for determining where a stroke would be most useful in such a match.
4. Can a
case be made for eliminating the stroke allocation procedure for match play?
Yes.
The USGA’s recommended method yields some strange results that are not
easily understood by the average player—e.g., why don’t I get a stroke on a
difficult hole? Moreover, given the
random nature of scoring it does not appear to make a significant difference to
the equity of competition where strokes are given. Given the many failings of its
recommendation, the USGA should eliminate its match play stroke allocation procedure
and replace it with general guidelines for ranking holes.
Each question is discussed in turn:
1. Does the USGA procedure actually identify
where a high-handicap player will most likely need a stroke to obtain a halve?
The USGA’s recommended procedure for allocating handicap
strokes does not ensure a player will get a stroke where it is most needed to
ensure a halve. This can be seen in the
example presented in Sec. 17 of the
Handicap
System which is reproduced in part in the Table 1 below.
Table 1
Stroke Allocation Based on Average Score
Difference
(1)
Hole
|
(2)
Average
Score Difference
|
(3)
Rank
|
(4)
Strokes
|
(5)
Net Average Score Difference
|
(6)
Match
Standing
|
1
|
1.13
|
8
|
1
|
0.13
|
-1
|
2
|
1.41
|
4
|
1
|
0.41
|
-2
|
3
|
0.75
|
14
|
1
|
-0.25
|
-1
|
4
|
2.10
|
2
|
1
|
1.10
|
-2
|
5
|
0.74
|
16
|
1
|
-0.26
|
-1
|
6
|
0.73
|
18
|
0
|
0.73
|
-2
|
7
|
0.93
|
10
|
1
|
-0.07
|
-1
|
8
|
1.22
|
6
|
1
|
0.22
|
-2
|
9
|
0.88
|
12
|
1
|
-0.12
|
-1
|
10
|
1.05
|
13
|
1
|
0.05
|
-2
|
11
|
1.45
|
7
|
1
|
0.45
|
-3
|
12
|
2.04
|
3
|
1
|
1.04
|
-4
|
13
|
1.39
|
9
|
1
|
0.39
|
-5
|
14
|
0.8
|
15
|
1
|
-0.20
|
-4
|
15
|
1.22
|
11
|
1
|
0.22
|
-5
|
16
|
0.75
|
17
|
0
|
0.75
|
-6
|
17
|
1.84
|
5
|
1
|
0.84
|
-7
|
18
|
2.38
|
1
|
1
|
1.38
|
-8
|
The USGA recommends the stroke allocation for match play
be determined by the average difference in score between low- and high-handicap
players. The average difference is used
as a proxy for where the high handicap player needs a stroke. To demonstrate the computation procedure, the
USGA used two groups of players. The
first group had an average handicap of 6.
The second group had an average handicap of 22. The difference in average score between the
two groups for each hole is shown in Column 2 of the Table.
Within each nine, the hole with the largest average
difference gets the lowest stroke allocation.
For example, hole 4 has the largest average difference among the holes
on the first nine. Therefore, it is
assigned a stroke allocation of 2. (Note:
The second nine is considered more difficult so it is assigned the odd-number
strokes.) The next largest difference
(i.e., 1.41) is assigned a stroke allocation of 4 and so on as shown in Column
3.
Does this stroke allocation promote equity? Let’s assume a match between a 6- and a 22-handicap
with the same average score differences shown in Column 2 of the Table. Column 5 presents the net average difference
in score after the 16 handicap strokes are applied according to the recommended
stroke allocation. The last column shows
the standing in an average match. The
22-handicap loses 5 and 3 and would lose 8 down if the match continued.
The problem with the USGA’s method is that it does not
automatically assign strokes to where they would be of most use to the
high-handicap player. In the USGA’s
example, the stroke allocation method ensures that a high-handicap player will
get a stroke where it probably will be of little use. The high-handicap player gets a stroke on
hole 18, but the average difference in scores will still be 1.38 strokes even
after the handicap stroke is applied.
With such a large difference in scores, the high-handicap player can be
expected to have a higher average score than his competitor 92 percent of the
time. In summary, the USGA procedure
assigned the first handicap stroke to where it will likely be of least use to the higher-handicap
player.
2. Is there a
better procedure for allocating handicap strokes for match play?
The USGA procedure allegedly assigns handicap strokes
where they most likely will be needed to obtain a halve. The USGA measures “need” by the difference in
scores between low- and high- handicap players.
As discussed above, the average difference in score is not a good proxy
for “need.”
If the USGA wants a stroke to be an equalizer, it should
be applied to a hole where it evens the probability of winning between
competitors. Using the average score differences
in Sec. 17, Table 2 shows the probability
of winning (i.e., having an equal or lower average score than the lower
handicap player) for the higher-handicap player if a stroke was given on a hole. Holes are then ranked by the closeness of the probability of winning to .50. These changes would make the match more
competitive. The higher-handicap player
no longer wastes a handicap stroke on holes 4 and 18. The 22-handicap would lose 3 and 1 under the
allocations shown in Table 2 rather than 5 and 3 under the USGA’s recommended
procedure.
Table 2
Using the Probability of Winning a Hole as
a Stroke Allocation Rule
Hole
|
Probability
|
Allocation
|
Hole
|
Probability
|
Allocation
|
1
|
.45
|
6
|
10
|
.48
|
1
|
2
|
.34
|
16
|
11
|
.33
|
11
|
3
|
.60
|
10
|
12
|
.15
|
15
|
4
|
.14
|
18
|
13
|
.35
|
9
|
5
|
.60
|
12
|
14
|
.58
|
3
|
6
|
.61
|
14
|
15
|
.41
|
5
|
7
|
.53
|
2
|
16
|
.60
|
7
|
8
|
.41
|
8
|
17
|
.20
|
13
|
9
|
.55
|
4
|
18
|
.08
|
17
|
To determine the allocations shown in Table 2 it is not
necessary to calculate the probabilities of winning for each hole. Instead, holes can be ranked by how close its
average score difference is to 1.0. For
example, if two holes had average score differences of .85 and 1.1, the hole
with the 1.1 score difference would receive the lower allocation. This “proximity to 1.0” rule will yield the
same allocations as the probability rule shown in Table 2.
Unfortunately, the “proximity to 1.0” rule gives
different results depending upon the difference in handicaps. If the difference in handicap between
competitors is halved, for example, the average score differences are also
halved under the USGA assumption. Different
holes would now have an average score difference closer to 1.0. So even if the “proximity to 1.0” test was
the most equitable, it is administratively infeasible and could not be
implemented.
Golf Australia (GA)—Australia’s counterpart to the USGA—
recognized that there is no perfect allocation. It recommended the same stroke allocation
for
all courses. GA argued that it disregarded hole difficulties
(acknowledging that a 30-marker receives 5 strokes from a 25-marker, which is
what a 5- marker receives from a scratch-marker, but that there can be clear
differences in the holes a 5-marker and a scratch-marker will find most
challenging).
GA’s recommended stroke allocation avoids
allocating low-numbered strokes to the last two holes and allocating
low-numbered strokes to the first three holes in case a match goes to extra
holes. In essence, GA is arguing that
any match play allocation, including a “difficulty” allocation, would be
acceptable as long as its recommendations on the opening and closing holes were
followed.
The USGA’s recommendation is also alleged to promote
equity in four-ball matches. The USGA,
however, has never presented any theoretical or empirical evidence to prove
that assertion. The USGA argues that the
optimal allocation in a four-ball match can be determined by the average
difference in scores between low- and high-handicap players. As noted above, however, the best allocation
may vary by the difference in the handicaps of the competitors. When you introduce two more players to the
competition, the analytical problem becomes intractable. Fortunately, there is so much randomness in
scoring the actual allocation is probably not determinant of the final outcome
of the four-ball match.
3. Is the USGA procedure defined with
sufficient specificity to be implemented?
The questionable logic
behind the USGA’s recommendation becomes apparent in the
allocation criterion presented in Sec. 17-1bii:
The first handicap stroke should be allocated so that this stroke is
most useful in a match between players of almost equal ability (e.g., a match
involving players with a Course Handicap of 0 and 1, 10 and 11, and 29 and 30).
The second handicap stroke should be
allocated so that this stroke is most useful in a match between players having
a slightly greater difference in Course Handicap (e.g., a match involving
players with a Course Handicap of 0 and 2, 10 and 12, or 29 and 31). This process should be continued until the
first six strokes have been assigned. (Editorial
note: The USGA does not delineate how stroke allocations for the remaining 12
holes are to be determined.)
The USGA does not present any procedure to determine
where a stroke will be most useful in a match between players of almost the
same ability. The USGA also assumes,
without evidence, that a handicap stroke would be most useful over a broad
range of ability—i.e., would a 1 handicap and a 30 handicap find a handicap
stroke most useful on the same hole?
When 17-1bii is applied to the rankings shown in the USGA
example, the allocations remain the same on the front nine, and only modified
on the back nine to eliminate Hole 18 as the number 1 stroke hole. Stroke allocations were essentially based on
the average difference between players of dissimilar ability and not of equal
ability. There is no mention in the
example of assigning the first stroke hole to where it would be useful in a
match between players of comparable ability.
This criterion is never used, never explained, and should be deleted
from the Handicap System.
4. Can a case be made for eliminating the stroke
allocation procedure for match play?
In matches between players of similar ability (i.e., a 1
to 2 stroke difference in handicap), the difference in average scores is
minimal—maybe around .1 strokes at the most.
Therefore, wherever the handicap
stroke is assigned, it is expected to be a winning stroke. If most matches are between players of
comparable ability, the USGA’s allocation procedure will not increase the
number of halved holes. Strokes could
just as well be allocated randomly and the results of the matches would not be
changed significantly.
The USGA’s match play recommendation creates other
problems. Often the number one stroke
hole is a moderately easy hole. The
handicap chairmen must then explain—often and repeatedly—the arcane procedure
recommended by the USGA. In many cases a
tough hole will get a high stroke allocation.
This leads to the player with the higher handicap (i.e., he gets a
stroke) carrying the load on the difficult holes in a four-ball stroke-play competition. The USGA states the Committee may develop a
separate allocation based on difficulty relative to par to handle stroke-play
competitions. This would be adding more complexity to the
scorecard without any benefit.
The match play allocation procedure recommended by the
USGA should be eliminated.
In its place, the USGA should suggest a
ranking of holes by difficulty subject to certain guidelines such as spreading
low stroke holes evenly over the 18 holes.
This can be done by consensus of the
Handicap Committee. The USGA procedure of
evaluating numerous scorecards implies a level of scientific certainty in the
outcome that is not justified. As long
as the recommendations on the placement of low strokes are followed (Sec.
17-1bii), one set of allocations should serve both for match and stroke play.
The main reason the 22-handicap loses is that the
average scores presented in Table 1 are not consistent with the theory behind
the Slope System. The average score of
the 6-handicap is 74.56. The average
score of the 22-handicap is 98.37. If
the average score of the 6-handicap is correct, the average score of the
22-handicap should be 93.63 (75.56 + 1.13·16).
As it is, the average score difference is approximately 23 strokes, yet
the 22-handicap only receives 16 strokes.
It is also hard to believe a bogey player (a 22 handicap by the USGA’s definition)
averages about a triple bogey on hole 18. If this section is kept, the USGA
should employ a more realistic example.
Op. cit., p. 103.
This
recommendation is in conflict with the USGA’s previous assertion that the first
handicap stroke should be assigned to a hole where a higher-handicap player
most needs a stroke as an equalizer.
To judge the efficacy of its stroke allocation
procedure, the USGA should undertake simulation studies similar to those
conducted by Dr. Francis Scheid, a past member of Handicap Research Team. Scheid took scores from a golf club and used
a computer to simulate matches between players.
This technique could be employed to determine if using the “average difference
in scores” or the “difficulty to par” for stroke allocation has a significant
impact on the outcome of a match.
