A group of players participate in a gross skins game and net
skins game. There is a wide range of handicaps with players receiving 0, 1, or
2 strokes on a par three. In the net
skins game, nothing irritates the low handicap player as much a seeing his
natural birdie tied by a bogey made by a player receiving two-strokes. To
right this injustice, the low handicapper suggests that players only receive one-half
of their handicaps strokes on par three. That is, a player receiving two-strokes
would only get one-stroke. The player
receiving one-stroke would only get one-half a stroke.
What are the implications of going to the “0ne-half
Rule”? A rigorous analysis would require
scouring tons of data and using a simulation model to estimate which golfers
win and which golfers lose under the different handicap rules. Even then, the result would be imperfect since
results of skins games depend upon the mix of players[i],
a hole’s difficulty, its stroke allocation, and the abilities of players (e.g.,
long hitter, short hitter). The
importance of this problem does not call for that much work.
In this post, a more slothful approach is taken. It is assumed three players play a par three
with the scoring probabilities of each player shown in Table 1. There are 36 possible outcomes each with its
own probability of occurring. For
example, the probability of all three players making par is (.6 x .2 x .1) .012.
Table 1
Scoring Probabilities
|
Gross
Score |
Player 1 (0 strokes) |
Player 2 (1 Stroke) |
Player 3 (2 Strokes) |
|
Birdie |
0.1 |
0.05 |
0.0 |
|
Par |
0.6 |
0.2 |
0.1 |
|
Bogey |
0.3 |
0.6 |
0.5 |
|
Double Bogey |
0.0 |
0.15 |
0.4 |
|
Average Score |
3.2 |
3.85 |
4.3 |
For each outcome, one of three players earns a skin or there
is no skin. A player’s probability of
winning a skin is the sum of the probabilities of occurrence where he wins a
skin. Table 2 presents these probabilities
for three handicap rules (no handicap, full handicap, one-half handicap).
Table 2
Net Skin
Probabilities
|
Handicap
Rule |
Player 1 |
Player 2 |
Player 3 |
No Skin |
|
No Handicap |
.505 |
.055 |
.020 |
.420 |
|
Full Handicap |
.030 |
.117 |
.435 |
.418 |
|
½ Handicap |
.196 |
.353 |
.198 |
.253 |
If the competition was only net skins, the ½ Handicap Rule
would appear to be best. The No Handicap
Rule gives the low handicap player a big advantage and the Full Handicap Rule
gives the high handicap player a big advantage. But the competition under
consideration has both a net skin pool and a gross skin pool. Table 3 presents
the probability of each player winning at least one skin.
Table 3
Probability a
Player Wins At least One Skin
|
Handicap
Rule |
Player 1 |
Player 2 |
Player 3 |
|
Full Handicap |
.52 |
.23 |
.45 |
|
½ Handicap |
.60 |
.39 |
.21 |
These numbers do not represent the actual probabilities in a
skins competition. With many more players
than the three used in the example, the actual probabilities will be much
lower. The probabilities in Table 3,
however, do indicate the relative advantage of each type of player. The Full Handicap Rule appears to best in
terms of equity and simplicity of administration (1/2 strokes can be
confusing). Moreover, this analysis was done
for par three holes which the high handicapper typically finds the easiest
(i.e., scores the least over par).
Therefore, applying the Full Handicap Rule over all holes would tend to
equalize the chances of all types of players earning at least one skin.
In the long run, this type of skins game is an annuity for
the low handicap player and he should not begrudge the high handicap player who
chips in for a three and wins a skin.
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