Introduction Stableford
scoring assigns points based on a player’s score relative to some fixed
score. Choosing the fixed score can
affect the equity of competition and the pace of play. Table 1 below demonstrates the Stableford
point system for three different fixed scores.
The fixed score is assigned 2 points, and more than one over the fixed
score receives zero points.
Table 1
Stableford Points
Player’s Net Score

Fixed Score


Birdie

Par

Bogey


Double Eagle

4

5

6

Eagle

3

4

5

Birdie

2

3

4

Par

1

2

3

Bogey

0

1

2

Double Bogey

0

0

1

Triple Bogey

0

0

0

The pace of play is fastest with the lowest fixed score
(i.e., birdie). After a player has hit a number of strokes equal to a net par
without holing, he picks up and moves on to the next hole—in theory, but there
are some players who will not pick up unless they are out of balls. But how does the fixed score affect equity? A 25handicap player may want a fixed score
of double bogey so he earns points on his less than stellar holes. Is he making the right choice?
Equity To
examine the question of equity, the probabilities of a 5handicap and a
25handicap player making various hole scores used in previous posts are
adopted for this study.[1] It is also assumed that the probability
function is equal across all holes. For
example if the 5handicap had a .45 chance of scoring par, then 5/18^{th}
of the time it will be on a stroke hole, and 13/18^{th} of the time it
will be on a nonstroke hole. Given these assumptions, the probabilities and
Stableford Scores for a 5 and 25handicap player are shown in Tables 2 and 3.
Table 2
Stableford Scores for
5Handicap
Net Score to
Par

Probability

Fix Score = Birdie

Fixed Score = Bogey


Points

Avg. Hole Pts.

Points

Avg. Hole Pts.


3

.001389

4

.005556

6

.008334

2

.042500

3

.127500

5

.212500

1

.226111

2

.452222

4

.904444

0

.411111

1

.411111

3

1.233333

1

.243333

0

.000000

2

.486666

2

.056112

0

.000000

1

.056112

Total

.996389

Total

2.901389

Table 3
Stableford Scores
for 25Handicap
Net Score to
Par

Probability

Fix Score = Birdie

Fixed Score = Bogey


Points

Avg. Hole Pts.

Points

Avg. Hole Pts.


3

.003889

4

.015556

6

.023334

2

.064444

3

.193332

5

.322220

1

.239445

2

.478890

4

.957778

0

.348889

1

.348889

3

1.046667

1

.222222

0

.000000

2

.444445

2

.084441

0

.000000

1

.084441

Total

1.036667

Total

2.878885

Comparing Tables 3 and 4, the 25handicap player has a small
advantage when the lower fixed score (birdie) is used, but loses the advantage
when the higher fixed score (bogey) is used. The tendency for the highhandicap player to benefit from low fixed scores is shown in Table 4. The highhandicap player has an advantage for
eagle and birdie fixed scores, has no advantage for a fixed score of par, and
is at a disadvantage for bogey and triple bogey fixed scores.
Table 4
Average Stableford
Points per Hole
Handicap

Fixed Score


Eagle

Birdie

Par

Bogey

Triple bogey


5Handicap

.31

1.00

1.92

2.90

4.90

25Handicap

.38

1.03

1.92

2.88

4.88

To see why this advantage for the highhandicap occurs at
low fixed scores, Table 5 show the probability of scoring points on each hole
when the fixed score is eagle. (Note:
This is not a realistic fixed score that would actually be used in competition. It is presented here to demonstrate how high
fixed scores benefit the highhandicap player.)
Table 5
Probability of
Scoring Points with an Eagle Fixed Score
Points

5Handicap

25Handicap

3

.001389

.003889

2

.042500

.064444

1

.226111

.239445

Neither player has much of a chance to score 3 points. The 25handicap player can score 2 points (i.e.,
a net eagle) by making a gross par with two strokes or a gross birdie with one stroke. To score 2 points, the 5handicap player
faces a tougher test. He must either
score a gross eagle with no stroke, or a gross birdie with one stroke. In
essence, the highhandicap player has an advantage since he has a better chance
of making a gross par than the low handicap player has of making a gross birdie.
Table 6 shows why the advantage disappears when bogey
becomes the fixed score. The 5handicap player has a much larger probability of
scoring 3 points (i.e., scoring a net par) than a 25handicap. He does this by either scoring a gross par
without a stroke or a gross bogey with a stroke. A 5handicap scores a gross par or bogey 76
percent of the time. The 25handicap
player scores 3 points by either making a gross bogey with a stroke or a gross double
bogey with two strokes. A 25handicap only makes gross bogey or double bogey 68
percent of the time. This edge in 3point
scoring is what levels the competition for the 5handicap player.
Table 6
Probability of
Scoring Points with a Bogey Fixed Score
Points

5Handicap

25handicap

6

.001389

.003889

5

.042500

.064444

4

.226111

.239445

3

.411111

.348889

2

.243333

.222222

1

.061116

.084444

Conclusions –The
narrow focus of this study on just two players and their probability functions,
preclude it from claiming any universal truths about Stableford
competitions. Two general guidelines,
however, do flow from the study.
· Using a fixed score of par appears to be the
most equitable consistent with increasing the pace of play. No fixed score
studied here gave either the high or lowhandicap player a significant
advantage.
· Modified Stableford completion where the points
system is nonlinear (e.g., double eagle = 8, eagle = 5, Birdie =3, and par =1)
would favor the high handicap player. (Remember, from Table 5 the 25handicap
player has a higher probability of making net eagle than the 5handicap
player. Moreover, the relative value of
a net par (the 5handicap player’s strength) is diminished, leaving him at a
disadvantage.
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