It takes a great deal of effort to manipulate a
handicap. A player has to generate
artificially high scores in rounds that are not in competition. This post
examines a sandbagger’s winning percentage as a function of how “many strokes
he has in the bag” – i.e., the difference between his manipulated handicap and his
true handicap.
Let’s assume Tom and Sam play golf together. The winner of a match is the player with the
lower net score. Sam has worked his
handicap so that his average net score is 1stroke less than Tom’s. This does not mean Sam wins every time. The random nature of scoring lets Tom win when
he has an exceptionally good round, or Sam has a bad round. The probability that Sam wins will depend on
the standard deviation of scoring for each player. For simplicity, it is assumed that each
player has a standard deviation of three strokes (i.e., 68 percent of all
scores will be between ±3 strokes of the player’s average score). The probability that Sam wins a match is
presented in Table below for various levels of sandbagging. (Note: The methodology for calculating the
probabilities is shown in the Appendix).
Table
Probability That Sam Wins the Match
Sam’s’ Average Net Score Advantage

Probability Sam Wins the Match

1

.59

2

.68

3

.76

4

.82

The best longterm strategy for the sandbagger would be to
have only a 1stroke advantage. He wins,
on average, six out of ten matches. Tom may not realize he is at a disadvantage since having four wins and six loses
is not unreasonable record. For just a little
handicap manipulation (1stroke), Sam gets an annuity as long as Tom does not figure out the game is rigged.
Tom, however, is not a complete idiot and realizes if his net
score was 1stroke lower he would do better. He can do this by a) decreasing his average gross
score in competition by 1stroke while maintaining his current handicap, or b) artificially increasing
his handicap by 1stroke while maintaining his average gross score in competition. Option b) is the easier of the two and the
one most often chosen. In essence, sandbaggers beget sandbaggers.
Sadly, many players do not look at their USGA Handicap as a
measure of performance—How good am I?—but as weapon in their arsenal to beat
their opponents. The best evidence of this is watching players
post their score. Are players more
jubilant when their trend handicap goes down or up?
Appendix
Suppose there are two scores, X_{1} and X_{2}
drawn randomly from the normal distributions N(µ_{1}, σ_{1}^{2})
and N(µ_{2}, σ_{2}^{2}). We want to find the probability that X_{1}
< X_{2}.
Now X_{1} X_{2 }is normally distributed
with mean,
µ = u_{1}
– u_{2}
and variance,
σ^{2}
= σ_{1}^{2} + σ_{2}^{2}
Hence, the variable (X_{1} X_{2} µ)/σ is
distributed normally with a mean of zero and a variance of 1 (i.e., the
standard normal distribution N(0,1).
And so, the probability that X_{1} is less than X_{2},
is the cumulative probability up to µ /σ.
In our example, the standard deviation of scoring for each player is
3. Therefore,
σ = (3^{2} +3^{2})^{½ } =
4.24
For a 1stroke advantage,
µ = 1
The probability that X_{1} is less than X_{2}
is
= f(1/4.24)
= f(.24) = .59
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