The USGA recommends different procedures for adjusting
handicaps under Section 35 depending upon the format of the competition. In foursomes and Chapman competitions, the
team playing the course with the higher Course Rating adds dstrokes (d being
the difference in Course Ratings) to its team handicap. In fourball competitions, however, each
player has dstrokes added to his handicap.
In foursome and Chapman formats, the effect of the
adjustment is certain and known in advance.
The teams playing from the tees with the higher Course Rating will have
their net scores reduced by d‑strokes. The effect in fourball stroke play, however, is not
certain. If the two players have the
same handicap, the effect will be to reduce the team score by dstrokes, the
same as in foursome and Chapman competitions.
If the difference in handicaps between partners is equal to or greater
than d, the expected reduction in team score will be dstrokes but can range
from zero to 2dstrokes.
The probability that a team will gain more than dstrokes
increases with the value of d. As shown
in the Appendix below, if d is equal to 3, a team has a 34 percent chance of
reducing its team score by more than 3strokes.
In a large field competition, the overall winner will most likely come
from the teams playing the tees with the higher course rating.[1] To eliminate this inequity and to make the
handicap adjustment under Sec. 35 consistent over all forms of competition, it
is suggested the adjustment for fourball should also be a reduction in team
score by dstrokes.
Appendix
Expected Reduction in Net Score
To simplify the model, it is assumed that only five scores
on a hole are possible—eagle. birdie, par, bogey, and double bogey. The probability of making each score for the
two players is shown in Table A1 below.
Table A1
Probability of Making Various Scores
Score

Player
1

Player
2

Eagle

a1

b1

Birdie

a2

b2

Par

a3

b3

Bogey

a4

b4

Double Bogey

a5

b5

Now on any hole there are 25 possible outcomes as shown in
Table A2. Assuming the scores by each
player are independent, the probability of each outcome is shown column 3. Assume that d is equal to 1 so that each
player gets an additional stroke, and the handicap of Player 1 is at least one stroke
lower than the handicap of Player 2.
Column 4 shows the results for when Player 1 gets an additional
stroke. As an example, if both players
have eagled the hole, the additional stroke does not result in a reduction in
the total score (i.e., player 2 by definition already has a stroke on that
hole). That is why zero is shown in
Column 4 for the eagleeagle outcome.
Similarly, Column 5 shows the reductions when Player 2 gets
an additional stroke, but Player 1 does not.
The eagleeagle outcome results in a reduction of 1 since Player 2 now
strokes on the hole.
Table 2A
Reduction in Net Score for Possible
Outcomes
(1)
Player
1

(2)
Player
2

(3)
Probability

(4)
Player
1 Gets

(5)
Player
2 Gets +1 Stroke

Eagle

Eagle

a1·b1

0

1

Eagle

Birdie

a1·b2

1

0

Eagle

Par

a1·b3

1

0

Eagle

Bogey

a1·b4

1

0

Eagle

Double Bogey

a1·b5

1

0

Birdie

Eagle

a2·b1

0

1

Birdie

Birdie

a2·b2

0

1

Birdie

Par

a2·b3

1

0

Birdie

Bogey

a2·b4

1

0

Birdie

Double Bogey

a2·b5

1

0

Par

Eagle

a3·b1

0

1

Par

Birdie

a3·b2

0

1

Par

Par

a3·b3

0

1

Par

Bogey

a3·b4

1

0

Par

Double Bogey

a3·b5

1

0

Bogey

Eagle

a4·b1

0

1

Bogey

Birdie

a4·b2

0

1

Bogey

Par

a4·b3

0

1

Bogey

Bogey

a4·b4

0

1

Bogey

Double Bogey

a4·b5

1

0

Double Bogey

Eagle

a5·b1

0

1

Double Bogey

Birdie

a5·b2

0

1

Double Bogey

Par

a5·b3

0

1

Double Bogey

Bogey

a5·b4

0

1

Double Bogey

Double Bogey

a5·b5

0

1

The probability that Player 1 successfully uses an
additional stroke on a hole to lower the team score is:
1) p =
a1·b2+a1·b3+a1·b4+a1·b5+a2·b3+a2·b4+a2·b5+a3·b4+a3·b5+a4·b5
The probability that Player 2 successfully uses an
additional stroke on a hole to lower the team score is:
2) q =
a1·b1+a2·b1+a2·b2+a3·b1+a3·b2+a3·b3+a4·b1+a4·b2+a4·b3+a4·b4 +a5
Assume the difference in Course Ratings is “d” strokes. The probability that Player 1 lowers the team
score on “n” holes is:
3) P1(n) =
(d!/(n!(dn)!) )· p^{n}·(1p)^{dn}
Similarly, the probability that Player 2 lowers the team
score on “n” holes is:
4) P2(n) = (d!/(n!(dn)!))·q^{n}·(1q)^{dn}
To evaluate these probabilities, it is necessary to know the
likelihood of making each score for both players. In previous posts, reasonable estimates of
these likelihoods have been used and are presented in Table 3A below.
Table 3A
Probabilities of Scoring
Score

5Handicap

10Handicap

Eagle

.005

.003

Birdie

.140

.090

Par

.450

.350

Bogey

.310

.380

Double Bogey

.095

.177

Based on the assumptions in Table 3A, the estimates of p and
q are shown in Table 4A.
Table 4A
Probability of a Reduction in Team Score
for One Additional Handicap Stroke
Player

Probability

Estimated
Probability

Player 1

P

.44

Player 2

q

.56

Two cases are examined to demonstrate how the competition
could be affected by using Sec. 35. In
the first case “d” is one stroke. The
probability of each player lowering the team score is shown in Table 5A below:
Table 5A
Probability of Team Score Outcomes When d
=1
Outcome

Formula

Estimated
Probability

0

(1p)·(1q)

.25

1

p·(1q) + q·(1p)

.50

2

p·q

.25

The expected reduction in team score is 1 stroke. There is a 25 percent chance, however, a team
will lower its score by 2 strokes.
Table 6A shows the probability of various outcomes when the
difference in course ratings is 3 strokes and the difference in handicaps is 3 or greater.
Table 6A
Probability of Team Score Outcomes When d=3
Outcome

Formula

Estimated
Probability

0

P1(0)·P2(0)

.015

1

P1(1)·P2(0) +
P1(0)·P2(1)

.092

2

P1(2)·(P2(0) +P1(1)·P2(1)
+ P1(0)·P2(2)

.235

3

P1(3)·P2(0) +
P1(2)·P2(1) + P1(1)·P2(2) +P1(0)·P2(3)

.315

4

P1(3)·P2(1)
+P1(2)·P2(2) + P1(1)·P2(3)

.235

5

P1(3)·P2(2) +
P1(2)·P2(3)

.092

6

P1(3)·P2(3)

.015

Table 6A indicates the probability of reducing a team
score by the full 2d strokes declines as d increases. The probability of reducing a score by more than
dstrokes, however, increases with d. In
this case, a team has a 34 percent chance of reducing its net score by more
than 3strokes.
[1]
The winner will most likely come from the teams playing the tees with a lower
course rating if those teams have their handicaps adjusted downward by
dstrokes.
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