Monday, July 16, 2018

Can You Trust Golf Digest?

It is hard to put Golf Digest in the category of serious journalism.  From time to time, it does publish interesting articles, but typically it concentrates on rehashing instructional advice.  Therefore, Golf Digest should not be held to the same standards of accuracy as say the N.Y. Times.  The problem is Golf Digest often doesn't even compare favorably with a weekly shopper when comes to getting the facts straight. 

Here are a few examples:

In a May 30, 2016 article Mathew Rudy wrote:

"A handicap it’s (sic) a calculation of the score you would be expected to shoot based on the difficulty of the course.  It's based on a weighted average of your ten best scores,  A player who has a handicap eight shots higher than another would get a stroke subtracted from his or her score on each of the eight hardest holes on the course.”  

There are three problems with these statements.  First, a handicap is not a calculation of the score you would be expected to shoot.  I assume Mr. Rudy is arguing a player’s expected score is the Course Rating plus his handicap.  It is not.  A player’s expected score will be higher because of the way the handicap is computed.  Second, handicaps are not based on a weighted average of a player’s ten best scores.  A player’s Handicap Index is the average of his ten best differentials multiplied by .96.   A Course Handicap cannot be calculated from the ten best scores since it will vary depending upon the Slope and Course Ratings of the course to be played.  Third, the USGA recommends stroke allocations not be  based on which holes are hardest.  Therefore to state a player gets a stroke on the 8 hardest holes may or may not be correct.  All of this is covered in Handicap 101, which apparently Mr. Rudy cut.

Mike Statchura of Golf Digest writes  ( "A Closer Look at Handicap Data...", February 11, 2017)  Dick Rugge, former Senior Technical Director of the USGA, told him there was a downward trend in handicaps.  Statchura said he called the USGA and confirmed that in the last 25 years the average handicap for a man has improved nearly two strokes.  Mr. Statchura should have written the average "Index" has decreased and not average "handicap."  Also there was no need to call the USGA since the data was available from Golf Digest.com. ("How Do You Stack Up?", March 17, 2014).  Apparently, even Golf Digest writers do not read the magazine.  And of course, the downward trend in average Index does not necessarily mean golfers are getting better.  It is possible the characteristics of the population are changing over time.  For example, if high Index players are are giving up golf at a faster rated than low Index players, the average Index would decline.  Mr. Statchura gave credit for the decline in the average Index to better equipment.   It could be just a coincidence that golf equipment manufactures are the big advertisers in Golf Digest.         

Golf Digest
 ("What People in Golf Make," January 20, 2017) reported Mike Davis of the USGA made $854,803.  In Federal Form 990, the USGA reports Mr. Davis’ compensation in 2016 was $2,013,355.  This is a large error in reporting even for Golf Digest.  

So to answer the title question, "Yes, you can trust Golf Digest when it comes to instructional articles."    Everything else, however, should come under the heading  "Reader beware."









Monday, June 18, 2018

Does the U.S. Open Identify Excellence?


(Note: This article was published 13 years ago.  In light of the 2018 U.S, Open, it remains relevant in evaluating how the USGA sets up the course.)

The USGA argues the U.S. Open is “not designed to embarrass the best golfers, but identify them.”  But does it?[1]  Critics have charged that the way U.S. Open courses are set up has made scoring more a matter of chance than of skill.  For example, well struck irons often bound over greens and into USGA-type rough.  The player's next shot then depends in large part on his lie (i.e., luck).

The merits of the maniacal set-up for U.S. Open courses are problematic.  The U.S. Open is played on a course that exists for only one week every year – the USGA version of Brigadoon.  Golf is unique among major sports in holding its championship under conditions that are not normally encountered during the season.

Are these criticisms valid or just carping from traditionalists who still harbor resentment from Jack Fleck's victory over Mr. Hogan in 1955?  If the critics are correct, the winners of the U.S. Open should be weaker as a class from the winners of other major championships.

Two measures of the strength of champions are used here.  First, if luck rather than skill is a major determinant in winning there should be a larger number of one-time winners.  That is, players who win the U.S. Open, but do not win any of the other majors.

Second, if a player is simply lucky to win the U.S. Open, then he may not have the skills to go on to win many other major championships.  If the critics are correct in their assessment, U.S. Open Champions should not be as strong a group as champions from other majors.  Specifically, the average number of "majors" won by champions of the U.S. Open should be less than the average compiled by champions from the other majors.

To test these two assertions, the winners of the traditional major golf tournaments (Masters, U.S. Open, Masters,The Open, and PGA Championship) were examined over the past 31 years (1974 to 2004). 

First, the number and percentage of champions who did not win any other major were found as presented in Table 1.  The U.S. Open ranked third among the majors with 12 of its 22 champions having never won another major. The PGA has the highest percentage of champions (60 percent) who were not able to win another of the traditional majors in the time period studied.[2]  

Table 1
WINNERS WITH NO OTHER MAJOR CHAMPIONSHIPS (1974-2004)


U.S. Open
Masters
The Open
PGA
Winners With No Other Major
12
9
11
15
Percentage with No Other Major
.55
.45
.50
.60

The U.S. Open did, however, have the most repeat champions (five) who had not won any other major (Andy North, Hale Irwin, Lee Janzen, Curtis Strange, and Retief Goosen).  This frequency may indicate the U.S. Open champion is being selected from a smaller pool of players than at the other championships.  That is, players with only certain attributes to their game appear capable of winning.  The skills for a good U.S. Open player, however, may not translate well to the venues of the other major championships.
              The average number of "other" major championships for each group of winners was calculated as a measure of the quality of the champions.  For example, the 20 different winners of the Masters won 27 other major titles for an average of 1.42 per player.  These results for other majors are shown in Table 2.

Table 2
OTHER MAJOR CHAMPIONSHIPS WON (1974-200)


U.S. Open
Masters
The Open
PGA
Other Championships Won
27
27
27
20
Number of Champions
22
20
22
25
Average Number of Other Majors Won
1.23
1.42
1.23
.80

By the average number of majors won, the U.S. Open is tied for second  with The Open.  And to show the tenuous nature of this ranking, if Tom Watson had not made that fortunate chip shot at No. 17 at Pebble Beach and gone on to lose, the U.S. Open would lose his 7 other major titles.  A loss by Watson would have put the U.S. Open rank down with the PGA by this criterion.

By the two measures used here, there is no clear evidence that the difficult course set-up of the U.S. Open identifies excellence with more precision than any other tournament.  It does, however, identify a certain type of golfer that may not have much of a chance at the other majors.  For example only four U.S. Open Champions in the past 27 years have also won the The Open (Nicklaus, Watson, Woods, and Els).  Only five U.S. Open Champions have also won the Masters in this same period (Floyd, Nicklaus, Watson, Woods, and Zoeller).  Surprisingly, until Woods victory in the 2000 U.S. Open Championship, no U.S. Open champion since Larry Nelson in 1983 had gone on to win another of the majors. 

In summary, the U.S. Open does not produce the “best” champion by any of the criteria examined here.  Nor does it appear to produce any more “fluke” winners than the other majors. The number of repeat U.S. Open champions with no other major championships suggests the U.S. Open set-up may be limiting the winner to a small sub-set of players.

There are signs, however, that the USGA is changing.  Since Pinehurst in 1999, the U.S.Open has had a less severe set-up.  The fairway rough has not been as penal as usual.  Rough around the greens at Pinehurst, for example, was minimized to give the player more options for his short game.  Courses have also been lengthened which favors the long hitters who also sit atop the world rankings—Tiger Woods, V.J. Singh, Phil Mickelson, Ernie Els, and Retief Goosen. These changes seemed to bring more of the marquee players into contention.  Whether this is a case of temporary sanity or a sea change in USGA thinking, only time will tell.



[1] An earlier version of this chapter appeared in Dougharty, Larry, Identifying Excellence, Golf Journal, USGA, July 1993.

[2] Championships won before 1974 were not included in the analysis.

Monday, June 11, 2018

The World Handicap System - Mistaking Motion for Progress


Introduction – The United States golf Association (USGA) recently announced a new World Handicap System (WHS) would be implemented in 2020.  The USGA had a hard time enumerating the benefits of the WHS.  In a paragraph that would make George Orwell proud, the USGA wrote:

“(The WGS) would result in less confusion, easier administration of international events and, potentially, it could allow national associations more opportunity to focus attention on golf development and strategic planning to support the game.  A single WHS would provide the opportunity to aggregate data to help ensure the game remains healthy.[1]

Examining this statement in its parts, it is hard to discern any tangible benefits for players.  Ninety-nine plus percent of players do not participate in international handicap events.  How will spending millions on a select few advance the interest of the game?  How will the WHS create more opportunity for golf’s bureaucrats to focus on “golf development” and “strategic planning?”  And finally, how does aggregating data help ensure the game remains healthy?    To be charitable, the USGA’s statement on the WHS’s benefits is less than convincing.

When the WHS cannot be justified on its merits, the USGA argues that there is an overwhelming demand for the WHS:

Quantitative research was conducted in 15 countries around the world, through which 76 percent of the 52,000 respondents voiced their support for a World Handicap System, 22 percent were willing to consider its benefits, and only 2 percent were opposed.[2] 

The USGA does not subject its research on handicap issues to peer review so it is difficult to evaluate its claim of quantitative research behind the WHS.  It is probable the apparent demand for the WHS rests on an unscientific survey that asked the question “Should there be a universal handicap system?”  Any respondent not knowing the particulars of the WHS or its cost would likely support the idea.  To cite such a survey as proof of the efficacy of the WHS is disingenuous.  

Before announcing the implementation date for the WHS, the USGA should have addressed four research questions:
  1. What will be the investment and operating cost of the WHS?  And secondarily, is it the best use of limited resources to advance the game?
  2. Is the WHS a more valid measure of a golfer’s potential than existing systems?
  3. Does the WHS produce a more reliable estimate of a player’s Handicap Index than other systems?  That is, does the WHS produce estimates closer to a player’s true Index than other systems?
  4. Is the WHS easier to understand and use for the average player than existing syste
The USGA has not provided answers to these questions.  The answer to the first question requires details about the WHS that have not been made available to the public and therefore is not addressed here.  The remaining three questions are explored by examining how the major elements of the WHS impact validity reliability, and ease of use.

Uniformity –The USGA argues the WHS will bring uniformity to handicaps.  This would mean “a handicap of 6.0 in Lima should be the same as a 6.0 in both London and Los Angeles.”  Assume this is true.  How much would a player be willing to pay to ensure the next time he plays in Lima his handicap is equivalent to that of his Peruvian competitor?  And here are some problems the player may encounter in such a match.  Since there is no universal language, our player does not understand the terms of the bet, but can only nod agreeably.   Since there is not a universal measurement system, he mistakes meters for yards and consistently under clubs.  He loses 4 and 3.  Since there is not a universal culture, he questions whether he and his opponent share the same reverence for the strictures of the handicap system.  Since there is neither a universal currency nor a universal exchange rate, he simply hands his opponent a handful of U.S. dollars and hopes the wager will be settled honorably.   As he takes a taxi back to his hotel, the player has time to reflect on the importance of a universal handicap system—“Muy poco,” he sighs.

The USGA argues the WHS would allow for easier administration of international events.  The history of large scale handicap events, however, has been marked by fraud (e.g., the AT&T Pro-Am, the Oldsmobile Scramble).  To believe that such events would be more equitable under the WHS is unreasonable.  There are only two ways a player wins a handicap event.  A player is either lucky or his handicap is not an accurate reflection of his ability.  If there are significant prizes involved, the latter is the most likely determinant of who wins.  To spend millions on the WHS to facilitate such tournaments is a fool’s errand.

Uniformity will bring little benefit to the typical USGA player.  Since the WHS is sponsored by Rolex, maybe the lower- to middle-income player was not its intended target anyway.  
  
Every Round Counts – The WHS will allow “both competitive and recreation rounds to count for handicap purposes (to ensure) that a golfer’s handicap is more reflective of potential ability.”[3]  This component of the WHS is already part of the USGA Handicap System so the American player will not see a change.  Systems that are based on tournament scores (e.g., the Council of National Golf Unions or CONGU), however, will be less reliable due to three attributes of the USGA’s Handicap System that will probably become part of the WHS:
  1. The USGA and R&A present no argument on why the inclusion of recreational rounds will be a more valid indication of ability.  They may reason the inclusion of recreational scores provides a more current sample.   This would be true if a player tried to make the best score at every hole in every round.  Though this is a basic premise of the USGA Handicap System, it is not universally adhered to by all players.  The inclusion of recreational rounds is one of the most effective tools in a sandbagger’s arsenal.  Under the WHS, such players will have the opportunity to more easily manipulate their handicaps by scoring poorly in rounds of little consequence.
  2.  The USGA Handicap System allows Internet posting which makes it difficult to determine if an “away” round was actually played.  This allows the unethical player to manipulate his handicap with a few simple keystrokes.
  3. The USGA is very lax in whom it allows to issue Handicap Indexes.  The USGA only stipulates that a golf club have ten or more members who may or may not know each other.  This has spawned a handicap industry where firms offer an inexpensive USGA handicap.  While such clubs are supposed to have peer review, in reality they do not.  Nor is there any evidence the USGA audits such clubs to ensure its strict rules on handicapping are actually being followed.  In the WHS’s drive to get more players to have a handicap, it is inevitable a debased handicap system will lead to more questionable tournament results.[4]
How will players currently under tournament based systems react to the Americanization of their handicap systems?   Will the British, for example, accept a less reliable handicap system or will they cling to the past by having clubs institute their own handicap controls?[5]  Will Far Hills be seen in the same unfavorable light as Brussels?  Only time will tell.

Why would CONGU give up its tournament based system for the less reliable WHS?  The answer probably lies in the economics of selling handicaps.  In the United States, many golf associations charge a player around $35 for a handicap.  The marginal cost of adding a player to the handicap roll is measured in pennies.  So if CONGU associations can add many recreational players, they stand to earn a substantial amount.  This may be an example of the tradeoff between increasing benefits for the governed and enriching the bureaucracy.  The latter typically wins.[6]  
    
Updating Scores for Abnormal Course and Weather Conditions – The argument is if you shoot a 90 on a windy day, shouldn’t that really be adjusted down to 88 as a better measure of your ability?  The problem is there is no good way to make such an adjustment.  Golf Australia (GA) has been a leader in trying to make such adjustments.  Based on the average net score for the field, the average handicap of the field, field size, and gender of the competitors, GA has a complex equation to derive the Daily Scratch Rating (DSR).  (The DSR is equivalent to the USGA’s Course Rating.)
 
GA, however, has never produced any study on the effects of the DSR on handicaps.  In other words, does all of this massaging of scores lead to significant differences in handicaps?   If bad weather produces high scores, it is probable the score would not be one used in the calculation of a player’s Handicap Index.  The DSR also does not take account of when a round is played.  A competitor, who plays under benign conditions in the morning, will have his score reduced if the wind comes up in the afternoon. 

At best, adjusting for weather conditions is a second order improvement.  The estimate of a player’s Index is subject to many errors.  There are errors in the estimates of Course and Slope Ratings.  There are sampling errors due to limited sample size.  There are rounding errors embedded in the handicap system.  There are errors due to missing variables (e.g., player characteristics such as slicer, short hitter, or familiarity with the course).  Basically, this component of the WHS is like putting lipstick on a pig.  It is still a pig. 
 
Why make the handicap system unfathomable with no proven increase in validity?  It is probably being done for three reasons:
  1. To gain GA’s acceptance of the WHS.  GA has put a lot of work into the weather related adjustment and sold it to its members as a necessary addition to its handicap system.  To reject it as part of the WHS would embarrass the GA. 
  2. The weather adjustment gives the illusion of accuracy which can be sold as “new and improved” by the USGA.   Unfortunately, golf has nothing comparable to the Federal Trade Commission to analyze such a claim for its truthfulness.
  3. The weather adjustment will burnish the reputation of the USGA.  The equations behind the DSR are beyond the understanding of most golfers.[7]   They see a quadratic equation and assume the experts (i.e., the USGA) must know what they are doing.  The USGA will do nothing to disabuse them of this assumption even though it is likely to be false.  
Daily Handicaps – Updating handicaps on a daily basis has a certain appeal, but is not without its problems.  A daily handicap would be more current and reduce the “lag” in the estimate of a player’s handicap.  If this was important, the USGA could have recommended the use of its Trend Index.  The USGA, however, recommends against using the Trend Index since it ”could be missing scores that have failed to be re-routed to the player’s home club before the next handicap revision, including any possible reductions or modifications to handicaps.”[8]

Assuming the routing problem can be fixed through the huge data processing project the WHS requires, there is still a problem with when a player posts.  The USGA does not require a score be posted on the day it is made.  If a player posts two days after the round, his Daily Handicap for the previous day will not be accurate.  Moreover, the Daily Scratch Rating will be in error (probably insignificant) since the player’s round was not included.  (Note: To be effective, the WHS would require a player post on the day he plays.)  

Errors created by late posting are likely to be small.  The administrative problems created by the daily handicap, however, may not be so small.  Under the WHS, a player will need to look up his Handicap Index and calculate his Course Handicap every time he plays.  The WHS assumes players are more diligent than common experience suggests.

Tournament directors will now have to specify which day’s handicaps will be used in the competition.  In order to check on a guest’s handicap, programs such as the Golf Handicap and Information Network (GHIN) will have to store a player’s daily Index rather than his bi-monthly Index.  This is a data processing problem that can be solved, but only with more expense.   If tournament directors opt to use handicaps from the first day of the month for tournaments held in the first two weeks of the month, for example, the daily handicap feature of the WHS will be essentially the same as the current USGA Handicap System.  That is, the WHS will probably have no effect on the equity of such tournaments. 

Will any increase in accuracy due to daily handicaps be worth the daily hassle of calculating that handicap?  If a player’s Index is volatile, daily handicaps could provide a more accurate estimate of his potential.  The Index of most players, however, is marked by low volatility.  For these players, the Daily Handicap will not differ significantly from a handicap commuted twice a month. 

Best Eight Scores – The USGA Handicap Index is now based on a player’s ten best differentials out of his last twenty.  The WHS will use the average of a player’s eight best differentials out of his last twenty.  The USGA has presented no evidence on why reducing the number of differentials used will be a better measure of a player’s potential.   In the one study that analyzed the equity of various handicap systems,[9] the USGA Handicap System was found to be less equitable than some mean based systems (e.g., average of the middle 16 differentials) for individual match play.  A handicap system based on the best five differentials was less equitable than the USGA system.  From that finding, it can be projected that lowering the number of best differentials to eight is likely to decrease validity of the estimated Index rather than increase it.[10]

So why go to eight best differentials?  Lowering the number of differentials makes it appear that handicap controls (i.e., anti-sandbagging efforts) are being strengthened.   This may have been a sop to the associations (i.e., tournament based systems) that are having their handicap controls weakened by the WHS. 
      
The New Equitable Stroke Control – Under the WHS, equitable stroke control (ESC) will allow a player to make a maximum net double bogey on a hole.    The reason for the switch is the WHS ESC is consistent with the Stableford Scoring System which much of the world plays.  Under this system, a player receives no points for a net double bogey.  If the current USGA ESC system were continued, a player would have an incentive to play on even though he would receive no Stableford points (e.g., a 36 handicap player has a net double bogey on a par 3 --7 strokes-- but can take up to 9 strokes under the current USGA ESC).

The table below compares the maximum allowed strokes under the USGA ESC and the WHS ESC for a selection of handicaps.  Under WHS ESC, the maximum hole score for a single- digit player will either stay the same or increase by one stroke.  A 15-handicap player will have his maximum hole score either reduced or stay the same with the exception of a par 5 where he strokes.  Similarly, a 25-handicap will have his maximum hole score either reduced or stay the same except on a par 5 where he gets two strokes.  Therefore, the single-digit player should see a small increase in his Index while higher handicap players should see a small decrease in their Index due to the change in ESC.   

Table
Maximum Allowed Strokes under the USGA and WHS ESC



Par
5 Handicap
15 Handicap
25 Handicap
USGA
WHS
USGA
WHS
USGA
WHS
1S
NS
1S
NS
2S
1S
 3
5
6
5
7
6
5
8
7
6
 4
6
7
6
7
7
6
8
8
7
 5
7
8
7
7
8
7
8
9
8

The change to the WHS ESC illustrates another inconsistency in USGA policy.  In introducing the current ESC back in 1993, the USGA argued it eliminated “par” from consideration.[11]   The USGA argued this made the system simpler and eliminated the problem of clubs having similar holes with different par ratings (e.g., a 401 yard hole might be a par four for women at one course and a par five at another).  The USGA, never hamstrung by consistency, now apparently believes it was wrong back in 1993 as it adopts a par-based system under the WHS.

The USGA goes further, however, and incorporates “stroke allocation” into the mix.  Courses, however, can assign similar holes different stroke allocations.  The USGA currently argues “the difficulty in a making par on a hole is not an effective measure of the need for a stroke.”[12]  Courses that follow the USGA recommendation will often assign the hardest holes relatively high stroke allocations.  Courses that assign stroke allocations based on difficulty would assign the hardest holes relatively low stroke allocations.  It seems logical the WHS should allow a 5-handicap player, for example, to take a triple bogey on the hardest holes and not on easier holes where a triple bogey is improbable.  To remove any inconsistency in stroke allocations, the USGA should change its recommendation for stroke allocations and base it on the relative difficulty of the hole.[13]

Overall, the WHS ESC will be more difficult for the USGA player to understand and for the handicap chairman to administer.  It is unlikely to have any significant impact on a player’s handicap.  Its inclusion is not based on making things better for the USGA player, but on building bureaucratic consensus with the golf associations where Stableford scoring is used. 

Incentives for Increasing the Number of Players with Handicaps – The WHS is intended to provide incentives for more golfers to get handicaps.   The number of rounds needed for a handicap to be issued has been reduced from 5 acceptable scores in the current USGA Handicap system to 3 acceptable scores in the WHS.  In theory, this lets a player get a handicap faster.

The USGA Handicap system currently limits a player’s Index to 36.4 for men and 40.4 for women.  For a course with a 133 Slope Rating, the maximum handicaps would be 43 for men and 48 for women.  The WHS raises the maximum handicap to 54 for both men and women.  This increase is supposed to let the very high handicap player know he or she is welcome—upon paying the requisite fee. 

The premise behind these changes is the health of the game is dependent on the number of handicaps sold.   This may be a wrong assumption and could lead to the USGA misallocating its resources.   When a player is starting to learn the game he should be focused on the challenge to improve and the joy a good shot brings.  If you are teaching children do you want them to think “I can beat Tommy if only I had a higher handicap” or do you want them to realize that to beat Tommy they have to improve their short game? 

There are better ways to encourage a 54 handicap to stick with the game than selling him a handicap.   Public Service Announcements showing golfers challenging the golf course rather than each other would be a start.  Programs such as First Tee for older beginners could also have a place.  There are lots of efforts the USGA could undertake that would promote the game, but convincing beginners they need a handicap is not one. 
    
Conclusion – As judged by three criteria (validity, reliability, and ease of use) the WHS will have little positive impact for the average USGA player:

Validity – The daily handicap and weather adjustment features of the WHS should make for more valid estimates of a player’s potential.  Any improvement in the estimates, however, will be small because of the low volatility in scoring for most players, and the unproven ability to estimate the impact of weather with any precision.  Though much research is yet to be done, going from the best ten differentials to the best eight appears to decrease the validity of the estimate of a player’s potential.  Overall, the WHS does not bring any significant gain in validity.
Reliability – There is no change in reliability for players enlisted under the present unreliable USGA Handicap System.   For players currently using a tournament based handicap system, the reliability of the estimate of the Index will decrease.
Ease of Use – The major selling point of the WHS is that it creates a uniform handicap system.  This benefit seems small for the average USGA player.  The daily handicap feature will burden the player with having to calculate his handicap each time he plays.  This is not an onerous task, but it will lead to errors in handicaps from the more slothful.  The weather adjustment will be perplexing.  A player will not know until the next day what his adjusted score was.   There will be no appeal from any injustice created by the computer since few will know or can replicate what the computer actually did.  The change in ESC should also be confusing to some.  There is little doubt it will lead to more errors in a player’s adjusted score and inevitably lead to less validity in the estimate of a player’s Index.

The WHS is designed to serve the needs of the bureaucracy and not players.   It will add prestige to the Handicap Department which has always been considered the backwater of the USGA.[14]  Kudos will be bestowed those responsible for getting the USGA and the R&A hegemony over the handicap system.  It will also fulfill the bureaucracy’s ambition of increased size, funding, and overseas travel. While the bureaucracy will be jubilant over the WHS, players should be skeptical.  They have seen many changes in the handicap system over the years with no notable change in equity.  Players may see the WHS as just another case of confusing motion with progress.



[1] “World Handicap System: Frequently Asked Questions,” www.USGA.org.
[2] USGA, New World Handicap System Designed to Welcome More Golfers, February 20, 2018, Liberty Corner, NJ.
[3] USGA, op. cit.
[4] Such handicaps have already caused a scandal at the Pacific Amateur Golf Tournament.  The Tournament Committee thought because a player’s handicap had the imprimatur of the USGA it was legitimate. The handicap actually came from an Internet club that lacked any semblance of peer review.  Only when the player won the tournament two years in a row, did an investigation reveal the player did not even post his winning tournament scores.   See “The Pacific Amateur Golf Tournament:  If you Go,”  www.ongolfhandicaps.com, December 5, 2014.
[5] The inability of the USGA Handicap System to produce fair handicaps has led to overlay systems such as Dean Knuth’s Tournament Point System.  See www.popeoftheslope.com.
[6] See “The Cost and Pricing of Handicaps,” www.ongolfhandicaps.com, October 12, 2015.  
[7] The equation for the DSR is:
              DSR = SR +SUM(36+Par-SR-CPA-mh-b-S)/(m’h+b’)2)/SUM(1/m’h+b)2)+1/CSD2)
[8] “Handicapping FAQS,” www.USGA.org.
[9] Scheid, F.J., Science and Golf II: Proceedings of the World Scientific Congress of Golf, E & F Spon, 1994, pp 222-227.
[10]  All USGA players should see a reduction in their Index under the WHS.  Assume a player’s differentials are normally distributed with a standard deviation of σ.   The average of a player’s ten best differentials will be approximately .8∙σ below his mean differential.  The average of a player’s eight best differentials will be approximately .95∙σ below his mean differential.  So players will see their Handicap Index reduced by .15∙σ.   Standard deviations are typically in the 3-4 range, so reductions in a player’s Handicap Index caused by the WHS should be in the .45 to .60 range.  The steady player (low σ) who is typically a low handicap player already has an advantage when only the best ten differentials are used. The WHS will only increase his advantage.
[11]See Position Paper on the New Equitable Stroke Control Procedure, United States Golf Association, Far Hills, NJ, 1992.
[12] The USA Handicap System, 2016-2017, Section 17-1.
[13] The USGA’s stroke allocation procedure examined in “Problems with the Stroke Allocation Procedure,” www.ongolfhandicaps, January 17, 2016.  The USGA’s method does not promote equity and is confusing.  It is no wonder it has not been universally adopted.
[14] The Managing Director of Handicapping is not listed as a key employee on 2016 Federal reporting forms.