Saturday, July 4, 2020

Eliminating the Blind Draw with Mr. Par

This blog has previously examined ways to eliminate the blind draw (Eliminating the Blind Draw,” October 22, 2019) when threesomes competed against foursomes. The post concluded giving the threesome a phantom player who always scores par (Mr. Par) led to equitable competition if the Course Rating and Par were not too far apart.  Since the publication of the post, the World Handicap System has made par and not the Course Rating the target score of the handicap system.  This eliminates the caveat about par and the Course Rating mentioned in the previous post.

The previous post was based on theory and urged playing groups to provide actual tournament results to verify the equity of using Mr. Par.  One group, playing two-bests balls of four, has used Mr. Par over the season.  The question addressed here is whether actual tournament results match up with what theory suggests?

What does theory suggest?  Let’s assume you are the captain of a threesome and have the choice of selecting a handicap player at random or taking Mr. Par.  You realize the handicap player will only have a net score below par twenty percent of the time.[1]  If the game was aggregate four- ball, Mr. Par would be the clear choice.  In two-best balls of four, however, the handicap player may contribute some net birdies while Mr. Par will not. If you take the handicap player, the standard deviation of the team score will be higher than with Mr. Par.   That means you will have a better chance of coming in first, but also a better chance of coming in last.  Since you are not risk averse, you opt for the handicap player.  Let’s look at the data to see if you made the right choice.

Empirical Test - A group plays two-best balls of four format and assign Mr. Par to the threesome.  At the end of the season, the mean score and standard deviations of threesomes and foursomes are computed (Team scores are presented in the Appendix):

              M3 = Mean team score of threesome relative to par = -12.09

              S3 = Standard deviation of threesomes scores = 3.49

              N3 = Sample size of threesomes = 23

              M4 = Means team score of foursomes relative to par = -12.67

              S4 = Standard deviation of foursome scores = 4.77

              N4 = Sample size of foursomes = 101

The null hypothesis is that the difference in the true means of each distribution (threesomes and foursomes) is zero.  The alternative hypothesis is the difference is not zero.  These hypotheses constitute a two tailed test.  The null hypothesis will be rejected if the absolute difference between the sample means is too large. 

The standard error of the sampling distribution is given by:

              SE = sqrt((S32/N3) + (S442/N4)) = 0.87

The t statistic is then: 

              t = (M4 – M3)/SE = (-12.09 – (-12.67))/ .87 = 0.67

The t-Distribution Calculator for 51 degrees of freedom shows the probability of the t-value less than -.067 and greater than 0.67 is 0.50.[2]  Therefore, the null hypothesis that the difference between the two means (threesomes and foursomes) is zero cannot be rejected.

If the threesome could deduct one stroke from its score, the t statistic would be 0.48 ((12.67-13.09)/0.87)).  The probability of a t-value less than -.48 and greater than 0.48 is .68.  Due to the small sample size it would be difficult to choose between giving a threesome zero or minus one stroke on statistical grounds.  It is clear, however, that either of these two options would be equitable.

Other Considerations – The smaller standard deviation for threesomes indicate it is more difficult for a threesome to go low. A look at the winners of competitions bears this out.   The data shows 14 competitions where threesomes competed against foursome.  The table below presents the probability of each type winning assuming threesomes and foursomes had an equal chance.

Table

Probability of Winning

Team1234567891011121314Total
Three0.250.50.170.140.330.40.40.290.430.140.40.140.20.173.96
Four0.750.50.830.860.670.60.60.710.570.860.60.860.80.8310.04


The table shows the threesomes are expected to win four times and foursomes 10 times.  Threesome had two outright firsts and one tie for first.  Had threesomes been given an additional stroke, they would have had three wins which is close to what was predicted.  As expected, threesomes do not go as low as foursomes, but they also do not go as high.  Threesomes only had one tie for last. 

Whether the threesome captain made a good choice in selecting the handicap player depends in part on the payoff structure.[3]  If the payoff structure pays a winning team the same regardless of its composition, a threesome’s smaller chance of winning is offset by a 33 percent larger payoff per player.  Even if the payoffs are per player, a threesome with Mr. Par may have a better chance of being in the money even though they do not win.  The examination of expected payoffs is beyond the scope of this study, but a cursory review indicates if payoffs are per man, neither threesomes nor foursomes have a significant advantage.  

In formatting a competition, there should be no team that realizes it has little or no chance before teeing off (e.g., a team of three low handicappers and Mr. Par in a two-best ball of four game).  If in the game under consideration, the handicaps among teams are evenly spread, threesomes with Mr. Par (possibly with a stroke deduction) and foursomes should have an equitable competition.  Importantly, this conclusion should hold for all courses regardless of the Course Rating

 

Appendix

Team Scores

<
Team12345678910
Three -10 -10-10  -4-15-14
Three   -9    -14-14
Three   -7      
Four-22-12-26-12-18-18-17-14-11-20
Four-19-8-20-10-14-12-16-8-11-10
Four-19-9-16-5-9-12-15-6-9-7
Four-16 -13 -8-11-11-5-8 
Four-10 -13 -7-9-10-3  
Four     -8-7-3 

 

 



Team11121314151617181920
Three-13 -16 -14-19-14 -12-17
Three-10 -14 -14 -11   
Three    -9     
Four-19-20-15-25-18-19-15-17-15-21
Fours-9-16-15-15-16-18-13-17-15-19
Four-7-14-13-13-15-18-11-15-14-14
Four -10-11-9-12-14 -14-11-14
Four -8-9-7 -14 -14 -12
Four   -7 -11 -11  
Four   -4   -10 

[1] Under the USGA Handicap System (UHS), a player had a net score below the Course Rating about 20-25 percent of the time.  Under the World Handicap System (WHS), a player’s eight best score are used in calculating his Index instead of his ten best in the under the UHS.  This lowering of a player’s Index under the WHS is offset by the elimination of the Bonus for Excellence (.96).  The WHS now makes “par” the standard of performance and not the Course Rating.  Therefore, a player will have a net score of par or better approximately twenty percent of the time.

[2] The degrees of freedom is estimated by:

              DF = (S32/N3 + S42/N4)2/ ((S32/N3)2/(N3 -1)) +( (S42/N4)2/(N4 -1)) = 57

[3] Weather is also a factor.   If the weather is bad, most players will have net scores over par, which would make the consistent Mr. Par a better choice.     


Wednesday, April 29, 2020

Golf, Bureaucracy, and the Virus


Government reaction to the corona virus pandemic has wreaked havoc on the golf industry.  Initially many golf courses were ordered closed.  When allowed to open, courses were under restrictions that make profitability uncertain.  Motorized carts, a big source of revenue, have been sidelined at many public and resort courses.  Food and beverage service have all but been eliminated. Was this necessary, or was it a demonstration of bureaucracies acting to protect themselves to the detriment of the public?  To try to answer this question, this post examines government action in Riverside County which includes over 100 golf courses in the Coachella Valley.

Golf courses were ordered closed on April 4, 2020 and citizens were required to wear face masks when in public.  The order was supposedly to “flatten the curve” though there were no evidence hospital facilities would be overwhelmed--which it turns out they were not.  There was also no indication healthy outdoor activity was a major source for transmitting the disease.  The order did not discriminate by age or health status and ordered everyone to shelter in place.  The effect of the order was to show the County was doing something and to shift attention away from government’s poor and tragic performance in regulating nursing homes where deaths were occurring.
.   
The order had a tenuous legal basis.  The County  listed numerous government sections and the State Constitution for its authority.  Most of these citations did not substantiate the government’s action. For example, the order cited Article XI of the California Constitution which deals with the formation of counties within the State and has no mention of health regulations.  Riverside County Code Sections 442 and 533.6 also do not detail any powers given to the health officer.  Though not cited, which makes its enforcement questionable, section 533.16 does set forth the ability to fine and imprison:

A fine of $1000 is possible for and “any act forbidden by any lawful rule, regulation or order issued pursuant to this ordinance; if such act is of such a nature as to give, or be likely to give, assistance to the enemy, or to imperil life or property, or to prevent, hinder, or delay the defense or protection of person or property ; “

The Sheriff of Riverside County has made it clear he would not enforce the part of the order requiring face coverings.  His decision seems reasonable since the order would not stand up in court.  A law that is not enforced is not a law,

Bureaucracies argue their actions are science based but can never cite the science being relied upon.  There is no science behind the requirement to wear a mask on a golf course. There is no empirical evidence in the incidence of the virus among golfers playing with and without masks.  The current order as it is applied to golf is not evidence based but is a judgment call by the County Health Officer.  That officer, however, is not an epidemiologist, but a family practitioner.  Given his lack of experience and education, it is probable he just cut and pasted his order from another jurisdiction while ignoring the Center for Disease Control guidelines which stipulates masks are recommended but voluntary.  He also did not consider the deleterious effects of masks.  If not properly cared for, masks can become a hazard.  Remember when re-usable bags were going to save the planet?   Now they are considered carriers of disease and not permitted inside stores.  And what about those with limited lung capacity?  Should they be forced to breath through layers of material even though with social distancing they represent no threat to themselves or others?  The health officer knew he would be graded by outputs that could be measured (deaths, incidence rates) and not on the economic upheaval his order would cause.  Various City Councils and County Supervisors were in support of the order even though it came from a doctor they would view as marginally unqualified when it came to select a physician for their own treatment.

A revised order on April 21 let golf resume with some restrictions.   What changed? It's possible government officials realized outside exercise was more beneficial to health than sitting inside watching Netflix.  It is more probable political pressure from politicians prompted the revised order.  When they realized much of the order was not science based and was just an exercise in “confusing motion for progress,” their survival instincts kicked in and they asked for a more sensible policy.  No use irritating a voting  bloc of 50,000 golfers.  Again, this is just another case of the bureaucracy fighting for self-preservation. 
  
The restrictions placed on golf in the revised order demonstrate its basis is politics and not science.  Measures were imposed on golf to minimize the chance of hand-to-hand transmission of the virus even though there were no reported cases of such transmissions.  But how does that work in tennis which is also now allowed?  The City of La Quinta, home of PGA West, opened tennis courts for singles play.   Doubles play was prohibited because maybe four people touching the same ball is catastrophic while only two players touching the ball is deemed safe.  The City, just like the Riverside County, is making it up as it goes without regard to science or common sense.

There is little doubt the short-term restrictions will have a long-term impact on the golf industry.  The whole shut-down movement is based on classifying other human beings as potential death threats.  The golf industry, however, is based on the pleasure of interaction—playing together, eating together, traveling together.  If that interaction is either curtailed through social distancing requirements or stigmatized as unhealthy, the industry will suffer.  It is reasonable to expect golf club membership sales to decline, resignations to increase, daily rounds to decrease, and food and beverage sales to decrease.  

Golf has implicitly been labeled a health risk by many of the nation’s governors and the industry has gone along.  Courses have decreed walking only, no rakes in the bunker, players must wear face coverings, closed waster stations, etc.  An independent observer would conclude a golf course must be a petri dish for the virus.  Admittedly, many of these actions have been taken to get permission from the bureaucracy to open golf courses.  But the image of the golf course as the safe haven it was meant to be has been badly damaged.  How many courses in the Coachella Valley have the financial strength, will, and management skill to navigate  troubled waters?  Time will tell.  One thing is certain, the bureaucracy will claim credit no matter the outcome.  "Things would have been much worse without the science-based policies of the Riverside County Health Department and the courage of politicians who implemented life-saving orders without regard to politics..." 

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:



            


Where
              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,” www.golfhandicaps.com
[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 www.popeofslope.com.
[2] Ewen, Gordan, What the Multi-ball Allowances Mean to You, www.usga.org, 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, Golfdigest.com, 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.