Friday, March 13, 2020

Why There Is No Perfect Golf Handicap System

Noted golf writer George Peper recently wrote a column where he proposed a personal handicap system (PHS) based on both course and player characteristics.   For example, he argued if a player sprays the ball, his handicap should be adjusted upward if he ventures onto a tree lined course with narrow fairways.  Similarly, if the course is wide open, the player’s handicap should be reduced. What may sound reasonable in a weekly column, however, may actually prove infeasible under closer scrutiny.  

Peper rejects such pessimism, however, and believes the PHS can be constructed by Big Tech applying its analytic tools to Big Data.  And from where does he derive his confidence that science can solve the quest for a perfect handicap that has plagued the sport since its inception?   Apparently, Peper is awed by Netflix recommending movies he might like based on his past viewing history and believes golf data can be studied to obtain similar results.  He fails to mention that a handicap system only as accurate as Netflix suggestions cannot be viewed as a step forward (e.g., if you liked Caddyshack does not mean you will like Caddyshack II). 
Peper goes on to argue that with “enough scores the computer knows your game, knows about your power outage, your two-way miss, your chip yips, etc., etc., etc.”   Peper is mistaken.  The computer knows none of this.  The computer only knows your adjusted score, and the Course and Slope Rating. Peper appears to suggest a handicap should be a function of more explanatory variables and specifically the obstacle value ratings in the USGA Handicap System now the World Handicap System (WHS).

“Can a system be devised to attain this dream handicap system? “  To answer this question, the three basic elements of any handicap system are reviewed for both the WHS and the PHS.  Those elements are: 1) rating the difficulty of a golf course, 2) measuring the player characteristics, and 3) a method of combining course and player ratings to determine a player’s handicap.   

 Rating Course Difficulty-

WHS - The WHS uses the effective distance of a hole and the rating of ten obstacle factors (e.g., trees, bunker, etc.) to determine the rating of a hole.  Obstacle factors are rated for only two types of players--the scratch and bogey golfer. The USGA assumes the relative difficulty of a course for all other players can be measured by a linear function of the Bogey Rating minus the Course Rating (i.e., the Slope Rating). 

PHS – Peper requires the PHS to describe a course by its obstacles values, but that raises the circular reasoning problem that faces rating systems.  For example, what is the course rating?  Historically, the course rating is the average of the ten best scores of a scratch golfer.  What is a scratch golfer?  It is a golfer whose ten best scores average the course rating.  To escape the circle, the USGA had to define a scratch golfer without regard to a course rating.  It chose competitors at the U.S. Amateur as scratch golfers.  

The development of the PHS would require either the course rating or a player’s characteristics to be fixed without regard to the other.   A solution, but not one without problems, is to rate courses by their effective distance and the ten obstacle values of the USGA Course Rating System.  The USGA Rating System rates holes which are then added together to get the Course and Bogey Ratings for the Course.  For simplicity, it is assumed a course rating under the PHS is its effective length and the average value of each of the obstacle value ratings (i.e., the sum of the scratch and bogey obstacle values for the ith obstacle variable summed over 18 holes and divided by 36).  A course is then described by its effective length and the rating of ten obstacles. 

Even with this simplification, there would still be two problems to overcome.   First, the definition of an obstacle variable is so obtuse as to be immeasurable—i.e., what is “psychological factor” and isn’t just a combination of the other nine factors?   Second, assigning values to obstacle factors is the responsibility of the rating committee which in most cases is not highly trained.   Golf associations do not sponsor seminars on how to distinguish a 5 from a 6 “green surface.”  It is unlikely rating committees would be consistent in assigning values to the nebulous definitions of the obstacle factors. 

Measuring Player Characteristics -

WHS - As discussed above, the WHS is not concerned player characteristics.   A player’s ability is only measured by his score, and not how it was obtained.

PHS – The PHS gives more handicap strokes to a “wild” player on a tree line course.  How does the PHS identify the wild player?  One approach would be to estimate the effect of each obstacle variable using linear regression analysis.  The estimated equation would be of the following form:

              Differential(j)  = Adjusted Score(j) – Course Rating(j) = a(0) + a(1)Y(j) + a(2)T(j) + a(3)F(j)                                    +a(4)R(j) +a(5))X(j) + a(6)W(j) + a(7)T(j) + a(8)B(j) + a(9)G(j) + a(10)S(j) + a(11)P(j)

  Where, the obstacle value ratings for the jth course are:

   Y(j)=Effective Playing Length, T(j)=Topography,  F(j)=Fairway, R(j)=Rough,
   X(j)=Out of Bounds, W(j)= Penalty Areas, B(j)=Bunkers, G(j)=Green Target, 
   S(j)= Green Surface, P(j)=Psychological

The linear regression analysis will yield estimates of coefficients (i.e., a(i)) which indicate how a player is affected by each obstacle value.   The player would not be defined by his WHS Handicap Index but by the value of twelve coefficients.  For example if a player is a short hitter, the value of a(1) (i.e., Effective Playing Length ) should be relatively high.  A player’s ability would no longer be identified by his Handicap Index, but by string of 12 numbers which will be termed his Peper Rating.  For example, a player could have a PHS Index of 3,3,4,2,6,7,4,8,3,2,4,6. (Are you starting to see the problem?)  

A player’s expected differential on course j would be:


              a(i) = Player’s characteristic rating for the ith obstacle value,
              c(i,j) = Course characteristic rating for the ith obstacle value on course j

In estimating the equation, however, more problems arise.  First, a general rule of thumb is the minimum sample size should be twenty observations for each independent variable.  That would mean 220 observations (i.e. courses) would be required for each player. It is reasonable to assume many players will not play that many different courses in a year.  The inclusion of numerous “Home” scores would decrease the statistical significance of any estimate.   For example, if only Home scores were included, the coefficient of all variables would be zero and the estimated Differential would just be the the player’s average Differential.  To eliminate this problem, it is assumed that all players have the same free time and access to courses as Peper who notes he has played over 750 different courses. This assumption eliminates the sample size problem even though it is unrealistic.

The second problem is obstacle variables do not have a large impact on a player’s differential.  The total scratch obstacle value typically accounts for less than two percent of the Course Rating.[1]  Individual variables will then have an even smaller impact on scoring.  This would be like Netflix judging a viewer’s taste based on a movie’s sound editing.  It is likely the estimated coefficients of most variables will not be significantly different from zero.  

Third, it is likely the “independent “variables are not independent.   Tough courses may have high scores on most of the obstacle values.  For example, if courses had fast greens and numerous strategically placed bunkers it would be difficult to estimate the effect of each variable on a player’s differential.

Method Determining a Player’s Handicap -

WHS - The WHS computes a player’s Handicap Index by averaging his best 8 of 10 scoring differentials ((adjusted score – Course Rating) x 113/Slope Rating). The player’s course handicap is his Handicap Index multiplied by the Slope Rating/113 plus the (Course Rating - Par).

PHS - A player’s PHS at this course could be some percentage (e.g. 90%) of his Expected Course Differential that would reflect a player’s potential ability and not his average ability.

Major operational problems are inherent in the PHS.  For example, how is the PHS updated?  The present system is based on 20 scores and the oldest is eliminated when a new score is posted.  For most players, the present handicap system provides an acceptable estimate of current ability though there is some lag. Peper argues the PHS should be capable accessing a lifetime of rounds.  If it necessary to go back years to get enough data to satisfy the data requirements of the PHS, the player’s PHS may be a function of how he played years ago rather than how he is playing this month.  Therefore, if the PHS cannot reflect a player’s current ability, it fails an important criterion for an equitable handicap system.

Since a player’s handicap is now defined by 12 different coefficients, the process of determining course handicap would need a computer.   It’s possible an app could be constructed that would embed a player’s twelve-digit characteristic rating and apply it to a directory containing the obstacle ratings for each course to be played.  A handicap system should produce easily understood results.  The PHS would not provide such clarity.  

Conclusion – Thirty years ago the Handicap Research Team (HRT)of the USGA wrote:[2]

The HRT is considering a solution of adopting a normal model handicap formula which would mean a two dimensional handicap to the Slope System  The solution could result in a Steady Eddy receiving more strokes on a high Slope Rated Course than a Wild Willy of equal Handicap Index would receive.

The HRT never developed such a handicap system probably because of the problems outlined above.  Or perhaps the HRT realized such an advance was not important.  Handicaps should be used to measure improvement and in competitions with reasonable stakes.  To seek perfect equity in every handicap match is a fool's errand.  As Peper has written elsewhere, golf is not all about winning.  It is about camaraderie.  It is about testing yourself under pressure.   And, it is about the beauty a round of golf can present.  So, if you find yourself on a course that does not fit your game, consider yourself lucky and suck it up!

[1] Dougharty, Laurence,” Is Your Course Overrated,”
[2] Knuth, D. A two parameter golf course rating system, Science and Golf, E & FN Spon, London, 1990, p. 146.

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