Wednesday, September 14, 2011

Beating Your Handicap #2

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
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.

Tuesday, September 6, 2011

Beating Your Handicap #1

The term “Beating Your Handicap” is often misunderstood even by quasi-experts who should know better.  John Paul Newport of the Wall Street Journal wrote a player will only score three strokes better than his handicap once in  43 rounds (“Fighting Back against Sandbaggers,” July 2-3, 2011).  Kelly Neely,  Senior Director of Handicapping of the Oregon Golf Association (OGA), wrote the chance of beating your handicap by 10 strokes is 1 in 37,000 (Handicap Blog of the OGA appropriately named “Preferred Lies”). Both writers apparently misread Appendix E of the USGA Handicap System which presents estimates of the probability of scoring various net differentials.  Net differentials and strokes are not the same thing.  This can be seen in a simple example:
Assume a player has a 13.0 index on a course with a Slope Rating of 131 and a Course Rating of 71.  The player would have a course handicap of 15.  If he played ten strokes better than his handicap he would shoot a 76 (i.e., a net 61).  A net differential is the subtraction of a player’s handicap index from the differential for the score:
                 Net Differential = ((76-71) x 113/131)) – 13.0 = 4.3 – 13.0 = -8.7 rounded to -9.0
Referring to the aforementioned Appendix E, a player has a 1 in 3,577chance of having a net differential of -9 or better.  In this example, Ms. Neely is off by a factor of ten in the likelihood of shooting 10 strokes better than one’s handicap.
Mr. Newport’s error can be forgiven since numbers are clearly not his strength.  It is more difficult to understand how Ms. Neely can make such a simple mistake.  Ms .Neely is not only the Senior Director of Handicapping of the OGA, but also has sat (or sits) on the Handicap Procedure Committee of the USGA.  If anyone should understand the handicap system, it should be her.  More disturbing, when informed of her error, Ms. Neely refused to take down her post. As will be documented in later posts, the inability to admit to an error appears to be a prerequisite for advancement in the bureaucracy that administers the handicap system.