## Wednesday, September 14, 2011

Is it easier to beat your handicap on a course with a high Slope Rating (e.g., PGA West Stadium Course, Slope Rating = 150) or a low Slope Rating (e.g., Local Muni, Slope rating =90)?  The answer, according to the USGA, is PGA West.
Why is it more likely to score “D” strokes better than the Course Rating on a course with a high Slope Rating than on a course with a low Slope Rating?  Let’s look at the math.  If a player has a net differential less than zero, he has “beat his handicap.”  A net differential in equation form is:
Net Differential = Differential – Index
= (Gross Score – CR) ·113/SR – Index
Where,
CR= Course Rating
SR = Slope Rating

To have a net score “D” strokes under the Course Rating, the Gross Score must be:

Gross Score = CR – D + Handicap = CR - D + Index · SR/113

Substituting, the equation for Net Differential becomes:

Net Differential = (CR - D + Index ·SR/113 –CR) · 113/SR - Index = -D ·113/SR

That is, the net differential for any number of strokes below the Course Rating is not a function of the Course Rating or a player’s index
The net differential associated with scoring 5 strokes under the Course Rating at PGA West would be       -3.8.  The net differential for scoring 5 stokes under the course rating at the Local Muni would be -6.3.  For a player with 13-21 index, the probability of having a net differential of -3.8 is approximately 1 in 80.  The probability of a -6.3 differential for the same player is 1 in 392.  (Note: The probabilities are a linear interpolation between the probabilities presented in Appendix E of the USGA Handicap System.)
This curious result has never been empirically verified.  It is most likely reflects a flaw in the theory behind the Slope System and is not an accurate prediction of how players will perform.