The USGA does not have an enviable record when it comes to its view of women:
- The USGA has a “separate but equal” handicap system for women that codifies them as the weaker sex.
- While the United States Tennis Association provides equal prize money for men and women at its Opens, the USGA awards more than twice as much prize money to men than women at its Opens.
- No woman has ever served on the USGA’s Handicap Research Team.
- In recommended handicap allocations, the USGA seems to presume women and men are different psychologically (i.e., men are bigger risk takers and women are more conservative on the golf course).
The first two actions of the USGA can at least be defended on physiological and economic grounds. The third result could stem from no women wanting to work in area where the possibility of publishable research is nil. It is the fourth action—the USGA’s perceived difference is the psychological make-up of men and women –that is the subject of this post.
The typical reason given for reducing handicaps in multi-ball events is that the higher handicap player has a larger standard deviation in his/her scores and hence an advantage. Given that women get a smaller reduction in handicap, the USGA must believe women have as smaller standard deviation in their scoring. Women must be steadier and/or less prone to risk taking as noted above. In the appendix below, it is shown that the difference in standard deviations between teams is the same regardless of gender. Therefore, it is difficult to defend the different allocations based on differences in standard deviations of scoring.
While the allocations should be reviewed and revised, it is doubtful the USGA will take such action. The allocations were never based on sound science, but rather on the internal politics at the USGA. The allowances are considered “settled law” by the myriad of attorneys that guide the USGA. To make a small step toward the equal treatment of women, however, the USGA could keep the hallowed men’s allowances and simply eliminate any allowance specific to women.
The Slope Handicap System assumes that the standard deviation of a player’s scores increases linearly with handicap. The standard deviation for each gender would be:
1) σ (m,h) = σ(m,0)·(1 + a·h)
σ(m,h) = standard deviation of a male player with handicap h
σ(m,0) = standard deviation of a scratch male player
h = handicap of the player
2) σ (f,h) = σ(m,0)·(1 + b·h)
σ(f,h) = standard deviation of a female player with handicap h
σ(f,0) = standard deviation of a scratch female player
h = handicap of the player
The USGA assumes that the line plotting average scores versus handicap would have a slope of 1.13. The equation for males reflecting this assumption is:
3) 1.13 = (Average Score(h) –Average Score(0))/h
If a normal distribution of scores is assumed, then:
4) Average Score(h) = ATBD(h) + .8 ·σ(m,h)
ATBD(h) = Average of Ten Best Differentials of a player with a h-handicap
Substituting eq. 4 into eq. 3:
5) 1.13 =(ATBD(h) + .8·σ(m,0)·(1 +a·h) - (ATBD(0) + .8·σ(m,0))/h
6) h = ATBD(h)·.96
Eq. 5 can be rewritten as:
7) 1.13 = (h/.96 +.8·σ(m,0)·(1 + a·h) – .8·σ(m,0))/h
1.13 = 1.04 + .8·σ(m,0)·a
Since the same equality must hold for women, it follows that:
8) σ(m,0)·a = σ(f,0)·b
Using eq. 8, the equations for the standard deviations can be rewritten as:
9) σ(m,h) = σ(m,0) ·(1 +a·h)
10 σ(f,h) = σ(m,0)·(a/b) (1 +b·h) = σ(m,0)·(a/b +a·h)
For simplicity, assume we have a team where both players have a handicap of h1, and another team where both players have a handicap of h2. The difference in the average standard deviation of the two teams is:
11) Average Male Difference = σ(m,0)·(h1 - h2)
12) Average Female Difference = σ(m,0)·(h1 - h2)
Therefore, the difference in average standard deviation between teams is the same regardless of gender (i.e., any advantage a team has is the same for both genders). This finding makes it difficult to justify different handicap allocations for men and women in four-ball stroke play.