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.

Friday, January 31, 2020

World Handicap System Adopts a Few Recommendations from this Blog

Over the years, this blog has pointed out some deficiencies and oddities of the USGA’s Handicap System.  The new World Handicap System (WHS) has addressed some of the points made in the blog and instituted minor improvements. This post reviews what the blog recommended and how the World Handicap Committee(WHC) responded.

Bonus for Excellence- The Bonus for Excellence, .96 in 2019, is multiplied by the average of a player’s 10 best scoring differential to calculate a player’s Handicap Index.  Dean Knuth, former Senior Director of Handicapping for the USGA, described the purpose of the BFE when he wrote in Golf Digest:

 “Historically, the USGA wanted to reward the accomplishments of better players…For a six-stroke difference in handicaps the better player gains a one-shot advantage (due to the BFE) and should win 60 percent of the matches.”[1]

In a post, “The USGA’s Bonus for Excellence Ruse, January 15, 2013,” it was shown the BFE is neither an effective incentive to improve nor a reward for superior performance and should be eliminated from the USGA Handicap System.  The WHC, perhaps heeding the wisdom of the post, eliminated the BFE.
Treatment of Women – The USGA’s treatment of women was analyzed in “Why Does the USGA Treat Women Differently, October 2, 2014.“  Before the WHS, the USGA recommended different handicap allowances for men and women.  For example, in four-ball stroke play men are allowed 90 percent of their handicap while women are allowed 95 percent of their handicap.  Why are women treated differently?  Much of the USGA’s research on multi-team events was done over 35 years ago and there appears to be no mention of any differences due to the gender of the player. [2]   It is likely the USGA had no empirical evidence for the women’s allocation, and the percentage was just a consensus guess by members of the Handicap Procedure Committee.   If women were studied, it is probable any difference in the estimated optimal allowance for men and women would not be statistically significant.  Remember, all the studies used to justify four-ball allowances were completed long before the introduction of the Slope System.  With this error and others, it is likely any difference as small as five percent was not significant.  Since the USGA does not release its research for peer review, the accuracy and validity of the USGA’s allowance may never be known. 
The following recommendation was made in the post: 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 WHC has followed this recommendation and eliminated separate allocations for women.

Sec. 10-3 - Index Reduction for Exceptional Tournament Performance – Section 10-3 supposedly cracks down on Sandbaggers by reducing their Handicap Index based on exceptional tournament performance.  A post, “The Truth About Section 10-3, April 15, 2014,” made the following observation:
“The USGA has never published any research on the effectiveness of Sec. 10-3.  When asked recently how many players receive a reduced index, the USGA replied “We do not keep such statistics.”[3] Apparently the USGA does not want to know the effectiveness of this section.  Sec. 10-3 lives on since it: 1) gives the illusion of curing the sandbagging problem, 2) does not generate negative feedback since so few are affected, and 3) relieves the indolent handicap committee of the responsibility for rooting out the unethical player.  In essence, Sec. 10-3 is the perfect bureaucratic solution.”   
The WHS has eliminated Sec. 10-3 and placed more responsibility on the Handicap Committee to monitor tournament performance.   Such an approach has not been successful in the past and is not likely to be successful in the future.   But the WHS did put the onus on the Handicap Committee where it belongs and not on a statistical formula that was never effective. 

Four-ball Stroke Play and Four-ball Match Play Allowances – Under the USGA Handicap System, players are assigned their full handicap (Sec 9-4aiii) in four-ball match play.  In four-ball stroke play, men are assigned 90 percent of their course handicap (Sec. 9-4bii). 
A post, “Chapman Handicaps and Sec. 3-5: Proposed Changes in Allowances, August 19, 2013,” questioned the different treatment of the two types of play.  If high handicap teams have an edge in stroke play, why don’t they also have an edge in match play?  And why does the USGA recommend a maximum difference in handicaps for four-ball stroke play, but not four-ball match play?  The USGA is of no help in answering these questions.  As mentioned above, the USGA’s research on the equity of multi-ball competitions (e.g., four-ball match four-ball-stroke play) is clearly out-of-date. 
The WHS includes several changes.  First, it now recommends a 90 percent allowance for four-ball match play.  Second, it reduces the allowance for four-ball stroke play from 90 percent to 85 percent.  Third, it omits any mention of a restriction of the difference in handicaps between partners.  It is difficult to describe these changes as an improvement.  The WHC has not presented any evidence the new allowances provide more equitable competition than the old allowances.  The new allowances do have one thing in common, however. All changes in the allowances favor the low-handicap player. This suggests the changes were based more on politics than statistics. 
Stroke Allocation -Under the USGA recommended stroke allocation procedure, holes were ranked by the difference in average score by low and high handicap players. The USGA argued this allocation would produce the most halved  holes but never explained why this should be a criterion for choosing an allocation procedure.  In a post “Problems with the USGA Stroke Allocation Procedure, January 17, 2015,” defects in the USGA’s method were exposed.  The USGA gave an example of where strokes should be given.  In the example, however, the high handicap player lost 5 and 3, hardly an equitable competition. The post recommended holes should be ranked by difficulty subject to certain guidelines such as spreading low stroke holes evenly over the 18 holes.
The WHS adopted this recommendation as presented in Appendix E: Stroke Index Allocation.  Holes are now ranked on playing difficulty relative to par subject to the same conditions mentioned in the blog post.  It is not known why Stroke Allocation was changed to Stroke Index Allocation. Index plays no part in the allocation procedure. But the change is gratefully received, and the superfluous language is overlooked.

Summary and Conclusion - The minor improvements discussed above do not impact on the efficacy of the WHS.  The evaluation of the WHS requires an experimental design that measures performance against various criteria (cost, equity, consumer satisfaction, etc.).  Does the World Handicap Committee have such an evaluation plan?  Probably not.  Bureaucracies rarely fund evaluations whose results could prove embarrassing.  

[1] Knuth, Dean,”Handicaps,” Golf Digest, September 2008  as reprinted at
[2] Ewen, Gordan, What the Multi-ball Allowances Mean to You,, Far Hills NJ, 1978.  The USGA has not released the original research for peer review. 
[3] E-mail to author from Annie Pollock, USGA, November 20,2013.

Friday, January 17, 2020

Dean Knuth: Is the Pope of the Slope Fallible?

The World Handicap System (WHS) has a feature called the par adjustment.  Basically, a player’s course handicap is just his former USGA handicap plus the difference between the course rating and par—usually a negative number.  In an article (The flaw in the new World Handicap System,, January 1, 2020) Dean Knuth, who has promoted himself as the “Pope of the Slope,” made arguments against the par adjustment.  He relies on his credentials (e.g., former Director of Handicapping at the USGA, etc.), and foregoes any reliance on theoretical or empirical evidence to make his case.   His arguments against the par adjustment are either specious, untrue, or unsubstantiated.  Unlike his namesake, the Pope of the Slope is clearly fallible.  Golf Digest did Knuth a disservice by printing his article without the proper vetting.     

Excerpts from Knuth’s article are presented below in italics.  After each excerpt, a brief analysis demonstrating the “flaws” in Knuth’s arguments is shown.

Knuth: Let’s start with the fact that par is hardly the most reliable measure of course difficulty (that would be course rating). Almost any golfer can list two courses that are both par 72s but vary greatly in how tough they play. Differences in length, in obstacles, in penalty areas, make one drastically harder than another even when they have the same par. Par as a metric, then, is somewhat arbitrary…. Maybe you don’t want to go that far, but calculating a handicap around a less reliable measure of difficulty inherently makes for a less equitable system.

Knuth is correct that “par” is not a accurate measure of course difficulty, but that claim is irrelevant to the equity of the WHS.  For stroke play (i.e., not Stableford) competitions, the WHS could have picked any number to subtract from the Course Rating and competitive results and handicap differentials would remain the same.  The par adjustment simply adds or subtracts a fixed number from a player’s handicap under the expired USGA Handicap System.  If players are competing from the same tees, differences in handicaps among players remain the same.  There might be small changes in handicaps due to rounding, but they are random and would not affect equity.    When players compete from different tees, the course handicap is calculated with all players playing to the highest (or lowest) par.  Again, what particular par number is used will not affect the equity of competition.  Knuth’s conclusion that the par adjustment makes for a less equitable system is not substantiated. 

Knuth: …the new formula changes course handicap values from tee to tee as you compare the WHS to the USGA system at any course.  For example, where once a course handicap was a 12 from the back and middle tees, and an 11 from the front, under the new WHS calculations there will be much larger variations—as many as 18 shots in some instances—between tees. Part of the reason for this is that during the calculation, an approximation is being approximated again by adding Course Rating minus Par creating an imperfect “over-spreading” of the course handicaps  Knuth adds “ It’s why, to me, the WHS produces an unacceptably large course handicap variation for the same ability player.”

Knuth never explains why a large course handicap variation for the same player is unacceptable.   The reader just has to take his word for it.  It is not the variation of handicaps, but the difference in handicaps among competitors that determine fairness as discussed above.  Knuth states the par adjustment creates an imperfect “over-spreading”   of the course handicap. He never sets forth the criterion for “perfect spreading.”  He simply hopes his readers will assume “over-spreading,” whatever it is, must be bad.  

Knuth:  Golfers competing from more forward tees will be receiving fewer strokes than is truly equitable.  And if you want to follow the USGA’s “Tee it Forward” initiative, there is a disincentive because playing from shorter tees more drastically lowers your course handicap.

This is where an editor at Golf Digest should have interceded and asked for evidence.  Instead, Golf Digest was complacent and just assumed Knuth, with all of his credentials, must know what he talking about.   If Knuth’s claim that the forward tee player is treated unfairly was true, it would drive a stake through the heart of the WHS.  Of course, it is not true.   A player competing from the forward tees will receive a reduction in handicap, but so will his fellow competitors.   There is no change in equity due to the par adjustment.   Even one with a rudimentary knowledge of the WHS (e.g., Jerry Tarde, Editor of Golf Digest) should know this. 

There is a lot not to like about the WHS and its par adjustment. The USGA simplified the Rules of Golf to make them more understandable to new and casual players.  Then, paradoxically, the USGA adopted an arcane handicap system that baffles and discourages these same players.   This blog has openly opposed the WHS, but firmly believe its efficacy should be determined on empirical evidence and not on conjecture by so-called experts.   Knuth’s article makes no contribution to that end.  If Golf Digest had any integrity, Knuth’s flawed article would be taken down from its website.