Monday, May 21, 2018

Quota System Vs. Stableford System


The Quota System and the Stableford System are two common methods for tournament scoring.  In the Quota System a player is given a quota equal to 36 minus his handicap (e.g., a 15 handicap would have a quota of 21).  As shown in the table below, a player earns points based on his gross score on each hole.  A player’s tournament score is the total of points earned minus his quota.  For example, if a player earned 24 points with a quota of 21, his tournament score would be +3.  In the Stableford System, a player earns points on his net score as shown in the table. The total number of points earned is his tournament score.

Table
Points for Quota System and Stableford System

Quota System
Stableford System
Gross Double Eagle
5
Net Double Eagle
5
Gross Eagle
4
Net Eagle
4
Gross Birdie
3
Net Birdie
3
Gross Par
2
Net Par
2
Gross Bogey
1
Net Bogey
1
Gross Double Bogey
0
Net Double Bogey
0

It would seem a system based on gross scores would not necessarily produce the same winners as one based on net scores.  A closer analysis reveals that is not the case.  (For simplicity, eagles and double eagles have been excluded from the proof.)
The Quota System is described by equation 1):

1)                  Q= 3(Xs + Xn) + 2 (Ps + Pn) +1(Bs +Bn) – (36-H)

Where,
Q= Quota Score
Xs = Number of birdies on stroke holes
Xn = Number of birdies on non-stroke holes
Ps = Number of pars on stroke holes
Pn = Number of pars on non-stroke holes
Bs = Number of Bogeys on stroke holes
Bn = Number of Bogeys on non-stroke holes

The Stableford system is described by equation 2):

S = 4∙Xs + 3∙Xn + 3∙Ps +2∙Pn + 2∙Bs + 1∙Bn + 1∙Ds

Where,
              S = Stableford Score
              Ds = Number of Double Bogeys on stroke holes

Now a player’s handicap must equal:

H = Xs +Ps + Bs + Ds

Substituting equation 3) into equation 2):

S = H + 3Xs + 3Xn + 2Ps + 2Pn + 1Bs +1Bn

The difference between a player's Stableford score and his Quota score is shown in equation 5):

S – Q = H + 3(Xs + Xn) 2(Ps + Pn) + 1(Bs +Bn) – (3(Xs +Xn) + 2(Ps + Pn) + 1(Bs +Bn) - (36 – H)) = 36

In summary, a player’s Stableford score will be 36 points higher than his Quota score.  The rank order of player scores, however, will be the same under both systems.



Tuesday, March 27, 2018

Should the Wall Street Journal Cover Golf?

This blog has been critical of the Wall Street Journal's (WSJ) golf columns.  John Paul Newport, the Journal's first golf columnist, was low hanging fruit. His columns were often fatuous (see his column on a day with Donald Trump) and frequently filled with errors.  Newport was replaced by Brian Costa, but it would be hard to notice any change unless you read the byline.  In Costa's latest column (Patrick Reed Wins the Masters, April 9, 2018), he writes:

Fowler added more late pressure to Reed by making a birdie on the 17th hole to cut his lead to one. 

In fact, Fowler made a birdie on the 18th hole not the 17th hole.  How do such errors get by the editors?  An examination of how a previous error was treated by the staff at the WSJ provides a clue.

The Wall Street Journal (WSJ) recently ran an article that referred to Tony Romo as having a 0.3 Handicap.  Of course no one has a 0.3 "handicap," but it was a small error and not worthy of correction. The next day, however, the WSJ ran a correction that noted  Romo actually had a +0.3 handicap and not a 0,3 handicap. If the WSJ bothers to make a correction, it should get it right.  I sent the following correction to the editor at the WSJ:

Your correction is still in error.  Tony Romo has a +0.3 Handicap Index not a +0.3 Handicap.  A player's Course Handicap is determined by multiplying his Index by the Course Slope Rating/113 and rounding the product to the nearest integer.  A player's handicap is always an integer.  Your golf writer should have known this.  

I expected the WSJ to acknowledge the error and pledge not to do it again.  Instead, the editor (Tim Carroll) defended the error with rather curious reasoning:


Thank you for your email.

While the term "handicap index" is the one used by the USGA and in the exacting Rules of Golf, it is not the term in general use. In 50 years of playing golf, including with many USGA officials, I am not sure anyone has ever asked me on the first tee for my "handicap index."

The Wall Street Journal writes for that general readership and we feel that by using the technical term we could be raising more questions than answering in readers' minds. (Note: When Carroll writes "that general readership" he implies there is more than one general readership. Apparently, he does not do a careful edit of his own writings.)

The first problem with the response is the term "Handicap Index" does not appear in the Rules of Golf as the editor states. (Perhaps his fact-checker was on vacation). The term Index is also not so arcane that it is use is restricted to the USGA.  If you enter any tournament, the tournament committee will ask for your Handicap Index and not your Handicap. Every player should know his or her Handicap Index which is the measure of a player's ability and is necessary to calculate his Course Handicap. 

The fact the editor has played with USGA officials is supposed to lend credibility to his argument, but only demonstrates an unbecoming degree of pomposity.   The editor is probably right that no one has asked for his handicap index in 50 years.  There are two possible reasons for this.  First, for the first 19 years of his playing career there was no Slope System and hence no Handicap Index. Second, his playing partners probably assumed the editor checked his Handicap Index and calculated his Course Handicap before coming to the first tee.

The editor's last defense is  WSJ readers lack the sophistication to understand the nuances of the handicap system.  That argument could be used if the article was about Bitcoin and blockchain technology.  Since the error in question appeared in the WSJ's golf column, it is probable most readers were golfers and familiar with the term Handicap Index. To dumb down the article was not necessary, but it was condescending.

The probable cause of the many errors in the golf columns is that the editors lack sufficient knowledge to do their job well.  Can you imagine Golfweek, Golf Digest, or Links getting mixed up about which hole was birdied?  If the WSJ is going to write about golf it should concentrate on what it knows best, the financial side. If it is merely going to report who won and regurgitate remarks from the press briefing, it is a waste of the WSJ's unique talent. 



     






Monday, July 10, 2017

Links Magazine’s Take on Who Should Pay for USGA National Championships

An article in Links Magazine (Schupak, Adam, “Pay to Play,” Summer 2017) asked who should pay the costs incurred in hosting a USGA National Championship?   The article argues the USGA should ease the burden on host clubs by increasing its subsidy to tournaments.  The argument however is not supported by cogent reasoning or empirical analysis.  There is no doubt the costs and revenues of USGA tournaments are in need of review.  This article does not provide that examination as explained below. 
    
The article focused on the costs incurred by the 2015 Men’s Mid-Amateur Championship held at the John’s Island Club in Florida.  It also mentioned a couple of other tournament, but did not describe those in depth.  Such a small sample size limits the credibility of the article’s position.  The article did state the 2013 Men’s Mid-Amateur cost the Country Club of Birmingham $300,000, but two years later John’s Island Club spent $650,000. The article is silent on what caused the $350,000 increase in costs.  It would have been important to review the contract between the USGA and John’s Island Club to determine which expenses were required by the USGA and which were optional expenses incurred at the Club’s discretion.

The article describes the current state of hosting costs:

The cost of running even one of the USGA’s 10 amateur championships has grown exponentially.  The starting price can be as modest as roughly $150,000 for the U.S. Women’s Mid-Amateur, balloons to $750,000 for the Walker Cup, and gets close to $1 million for the U.S. Amateur when a larger footprint for worldwide media an television compounds are factored in.

There is no reference to where these cost numbers come from.  This is a serious omission since the high costs are an essential part of the argument for increased USGA financial support.  If high costs are not documented, the article’s thesis cannot be proven.

The costs are purported to have risen exponentially, but the article only presents longitudinal data for the Gold Mountain Golf Club in Washington.  The cost of the Amateur Public Links was $150,000 in 2006.  Five years later the cost was $180,000 for the 2011 U.S. Junior Amateur.  That is only a 4 percent annual increase in current dollars and less than that in real dollars (i.e., costs adjusted for inflation).   The example from Gold Mountain was presented to demonstrate the escalating costs, but actually did just the opposite.

Now costs may have risen dramatically at other events or in years past 2011.  The article, however, presents no evidence to that effect or any explanation of why costs have exploded.  Has the USGA placed more requirements on the host club?  Or have host clubs increased the costs by trying to one-up previous host clubs?   These are important questions that go unanswered.

The article assumes the USGA places an inequitable burden on host clubs and suggests the USGA should pay more of the cost.   Mark Mulvoy, Chairman of the John’s Island Championship Committee makes the following argument:

Why does a non-profit (the USGA) have over $300 million in the bank?  Our members help fund educational programs and build museums and wings of hospitals.

Mulvoy’s complaint is not compelling.  The combined net worth of the members of the John’s Island Club dwarfs the USGA’s cash reserve. So why should the USGA subsidize the top 1 percent on the economic ladder?  It does not help matters that Mulvoy spent $100,000 on a “lavish gala” (as described in the local paper) for former Mid-Amateur champions in February 2016 when the tournament was still seven months away.   In the end, the John’s Island Club Mid-Amateur Committee only donated $7,500 to a junior golf organization.
   
Lacking any empirical evidence to support the article’s thesis, the author went to David Fay, former Executive Director of the USGA for support.  Fay came up with a platitudinous solution to a problem that may not exist.  Fay suggested the USGA should guarantee that no club that hosts one of its championships is ever put in a financial bind.  Fay’s proposal has two serious flaws.  First, if the USGA guarantees no financial harm it creates a moral hazard.  That is, clubs would not have an incentive to guard against risk because they would be protected from the consequences.  Second, Fay’s proposal would require the USGA to approve and monitor expenses.  If the USGA is to ensure host club is not put in dire financial straits, it must make sure the expenses are both reasonable (e.g., no strippers for the after-party) and legitimate (i.e., no charging the tournament account for steak when hot dogs are served).  This is essentially a forensic accounting exercise the USGA should avoid.

If the article’s thesis is correct and more USGA financial support is required, there should be a shortage of clubs vying to host tournaments.  This is not the case as the article concludes:

…Despite the watered down media exposure and fan interest, and overall lack of attention, top clubs continue to line up to host the USGA’s non-remunerative championships…

In essence, there does not appear to be a problem with the USGA’s current level of financial support.   This raises the question of why the article was written.  Was it to be a paean to the 2015 Mid-Amateur (Comments such as “even the Russian judge would give it a 9.9,” and”Sammy Schmitz made a stunning hole-in-one” were not essential to the article’s objective and should have been removed in editing)?  Was it to lay the blame on the USGA rather than on tournament director Mulvoy for the budget overrun?  Was it to cajole the USGA into increasing the subsidy to a future tournament where members of the Links editorial staff have an interest?  The answers to these questions are not known.  What is known is the article does not meet the high editorial standards associated with Links

Wednesday, May 10, 2017

Southern California Golf Association Errs Badly in Explanation of the Slope System


From time to time the USGA and regional golf associations publish articles explaining the USGA Slope System.  More often than not, the articles get it right.  On too many occasions, however, the articles demonstrate a lack of understanding of the Slope System.  Such articles tend to confuse rather than inform their readership.  The latest example comes from Fore Magazine, the publication of the Southern California Golf Association (SCGA).[1]  The article is entitled “Slippery Slope: Comparing Course Difficulty” and was written by Doug Sullivan, the Director of Course Rating for the SCGA.  The article contains three major errors.  First, the suggested criterion for measuring course difficulty is not adequate for many situations.  Second, the article incorrectly describes how the Slope Rating is determined.  Third, the article’s explanation of why a player gets more strokes is not consistent with the theory behind the Slope System. Each error is reviewed in turn
.
Error No. 1 – Misleading advice on measuring course difficulty
Sullivan follows in the footsteps of several other articles that claim the Course Rating is the dominant criterion for ranking courses by Course Difficulty.[2]  Sullivan is more adamant, however, and claims the Course Rating should be the sole criterion is measuring course difficulty.  He writes:

… Slope Ratings should not be used to compare the difficulty of different golf courses.  Instead a Course Rating is generally a better indicator in determining the difficulty of one course compared to another. 

To make the case for the Course Rating as the measure of difficulty, Sullivan creates a straw man.  He describes two courses.  Course A has a Course Rating of 68.5 and a Slope Rating of 130.  Course B has a Course Rating of 71.8 and a Slope Rating of 120.  Sullivan asks which course is more difficult.  Sullivan argues your answer should be “Course B because Course B has a higher Course Rating.”   Sullivan never defines a “difficulty.”  For the sake of argument, difficulty is defined here as the score a player needs to play to his handicap (i.e., Diff = Course Rating + Course Handicap).   Because of Sullivan’s fortuitous selection of ratings, a player’s Diff will always be higher on Course B.  Sullivan used this faux example as definitive proof the Slope Rating should not be used to compare the difficulty of courses.[3]
Sullivan concludes:

So the next time someone asks you which course you think is more difficult, compare the Course Ratings, not the Slope Ratings.  Not only will your answer be more accurate, but your friends will be more than a little impressed with your knowledge of SLOPE.    

Sullivan is wrong.  While the Course Rating may be the dominant factor in measuring difficulty, it is not the only factor.[4]  If the definition of difficulty shown above is accepted, then:

                            Diff = Course Rating + Index∙Slope Rating/113

If there is a large difference in Course Ratings (e.g., 3 strokes), the course with the highest Course Rating will also have the highest Diff.   If the difference in Course Ratings is small, then Diff will be influenced by the Slope Rating and the player’s Index.   To demonstrate how Sullivan is wrong, two fantasy courses are constructed.  Course A has a Course Rating of 70.0 and a Slope Rating of 69.0.  Course B has a Course Rating of 70.5 and a Slope Rating of 155.  The vast majority of players would score higher (i.e., have a higher Diff) on Course B since it has both a higher Course Rating and Slope Rating.  But what if a player’s Handicap Index was +4.0?  Course A would have a Diff of 67.6 while Course B would have a Diff of 65.0. This player would find Course A more difficult.  In essence, Course Difficulty for an individual player cannot be determined by simply comparing Course Ratings as Sullivan suggests.

Since Sullivan did not acknowledge the importance of Index and Slope Rating in determining difficulty, his knowledge of SLOPE should not impress his friends.  Moreover, though left unstated in Sullivan’s article, course difficulty will vary by a player’s characteristics (hooker, slicer, short hitter, etc.).  If you really want to determine which course is more difficult, you should play them and draw your own conclusion.  To try to determine the most difficult course solely by USGA Ratings that are prone to error will only yield answers of little reliability and even less consequence.

Error 2 – Incorrectly describing how the Slope Rating is determined
Sullivan demonstrates a lack of understanding behind the derivation of the Slope Rating when he writes:

This is the type of graph (shown below) that is created to compare scores of golfers of different abilities.  As you can see, scores increase as a player’s Course Handicap increases.  A line is created to connect as many scores as possible.  The steeper the line, the higher the Slope Rating.  The flatter the line, the lower the Slope Rating.  The concept of SLOPE simply refers to the slope of this line – that bit of trivia should help you make a few bucks on your next friendly bet.



Sullivan is simply wrong.  Since the advent of the Slope System, the slope of the line relating average scores to handicap is the same for all courses.  After all, that was the purpose of the Slope System. To be correct the horizontal axis in Sullivan’s graph should have been labeled Handicap Index and not Handicap.[5]   If you followed Sullivan’s advice and placed a bet—you lost!

Sullivan makes a technical error when he writes the “line (shown in the graph) is created to connect as many scores as possible.”  Connecting as many scores as possible is not the appropriate criterion for determining the slope.  The line is typically determined  by linear regression techniques where connecting the scores is definitely not a requirement.

Error No. 3 – Confusing the reader on how Course Handicaps are determined
In trying to explain how and why the Slope System assigns additional strokes, Sullivan writes:

In simple terms, SLOPE is designed to make sure a golfer receives more strokes when playing a more difficult course and fewer strokes when playing an easier golf course compared with the USGA Course Rating.

This sentence is so poorly constructed it is hard to discern what Sullivan means.  Since Sullivan has just proclaimed the Course Rating is the measure of difficulty, he seems to be saying a player should receive more strokes at the course with the higher Course Rating.  This would be incorrect.  The handicap player does not receive more strokes because the Course Rating is higher and the course more “difficult.”  Handicap strokes are given as a function of the difference between the Bogey Rating and the Course Rating at a course.  Even in Sullivan’s own example, most players will get more strokes at the course Sullivan has declared to be the easiest (Course A).

So why do articles such as Sullivan’s continue to be published?  It’s probably because neither the SCGA in this case nor the reader are sticklers about accuracy.  The SCGA is looking to fill its magazine and assume the Director of Course Rating must know what he is talking about.   And if he doesn’t, it doesn’t really matter.  SCGA members can be divided into three groups.  The first will pass on any article about the Slope System so the image of the SCGA will not be harmed.  The second group will assume the article must be accurate since it came from the experts at the SCGA.  The third group that recognizes the article as nonsense is a very small subgroup of the SCGA membership (i.e., approximately 1) that can easily be dismissed.  
  
     





[1]Sullivan, Doug, “Slippery Slope: Comparing Course Difficulty,” Southern California Golf Association’s Fore Magazine, Spring 2017, p. 94.
[2]Cowan, Jim. “An Explanation of Slope,” Northern California Golf Association website, ncga.org.  Metropolitan Golf Association, “How do the Course Rating and Slope numbers affect my Handicap Index?” mga.org.
[3] It is not clear why the authors of these articles have chosen peculiar Course and Slope Ratings to make their point.  Jim Cowan of the Northern California Golf Association, for example, used a course with a Course Rating of 72.8 and a Slope Rating of 114.  Since Course Ratings are highly correlated with Slope Ratings, it is very likely such a course does not exist.  Real courses could have been selected to demonstrate how difficulty is measured, but no author has taken that path.    
[4] Cowan, loc. cit.
[5] Stroud, R.C. and L.J. Riccio,  “Mathematical Underpinnings of the slope handicap,” Science and Golf, E & FN Spon, London, 1990, pp. 129-140.  Stroud shows the Perfect Valley Handicap as the label for the horizontal axis.  The Perfect Valley Handicap is a player’s Handicap Index. 

Wednesday, April 12, 2017

Another Inequitable Tournament and So It Goes...

This blog has documented many cases where a misunderstanding of the USGA Handicap Manual has led to inequitable results. The latest example comes from a tournament at a club in Southern California.  The tournament consisted of four different stroke play competitions of nine holes each: 1) Four-ball, 2) Total score of partners, 3) Scramble, and 4) Pinehurst. 
The Tournament Committee imposed a limit of 8 strokes between the handicaps of the partners.  The handicap of the higher handicapped player was reduced until the 8-stroke limit was reached.  This, however, is not what the USGA recommends:[1]
It is recommended that the Committee considers it a condition of four-ball stroke play competitions that the Course Handicap (after allowance) of the members of a side may not differ by more than eight strokes. A side with a large difference has an advantage over a side with a small Course Handicap difference. If a difference of more than eight strokes cannot be avoided, it is suggested that an additional 10 percent reduction be applied to the Course Handicap of each member of the advantaged side.[2]
Moreover, this recommendation is only for four-ball stroke play.  Its application to the other forms of competition, as was done in this tournament, is an egregious error.  To see the size of the error, assume Player A has an Index of 3.5 and Player B has an Index of 14.8.  The Table below presents the handicaps that were used in the Tournaments and those that would have been used if USGA guidelines had been followed. The USGA handicap calculations are shown in the Appendix.
Tournament and USGA Handicaps

Competition
Player A (3.5 Index)
Player B (14.8 Index)
Tournament
USGA
Tournament
USGA
Four Ball
4
4
11
13
Total Score
4
4
12
16
Scramble
1
1
2
2
Pinehurst
2
2
5
6

In Four-ball, Player B would play as a 7-handicap under USGA guidelines instead of a 6-handicap in the 9-hole competition. The competition used a modified Stableford scoring so that a net par was worth 2 points and a net birdie would be worth 4 points.[3]  It is likely the loss due to the Tournament handicap is in the 1 to 2 point range. (Note: The difference in Tournament handicaps after the allowance is 7-strokes and not the 8-strokes as recommended by the USGA.)
In the Total Score event, Player B would play as an 8-handicap rather than as a 6-handicap that was assigned by the Committee.  The loss due to the Tournament handicap is probably in the 2 to 4 point range.  If Player B bogeyed each hole where he had an additional stroke, he would gain 2 points.  If he made par on the two holes he would add 8 points instead of 4 for a net gain of 4 points.
The Scramble competition would not be affected since both the Tournament and USGA handicaps are the same.  Similarly, the handicaps are equal in a nine-hole Pinehurst competition.  The Tournament Pinehurst handicap of 3.5 is rounded to 4.0, the same as the USGA handicap.
The number of points lost by this team due to the Tournament Committee’s handicaps is in the range of 3 to 6 points.   Would this have affected the outcome?  Probably, since no team that had its handicap reduced by the 8-stroke rule came in the money.  The bigger problem, however, is the Tournament Committee that failed to follow USGA guidelines.   Players have an expectation a tournament will be run fairly.  In this case, that expectation was not met.

Appendix
USGA Handicaps
Four-BallPlayer A’s course handicap is 4. His handicap after the 90 percent allowance is still 4 (4x.9= 3.6 rounded up to 4.0).  Reducing his handicap by an additional 10 percent still leaves the player at a 4-handicap (4  - .1 x 4 = 3.6 rounded to 4.0).  Player B’s course handicap is 16.  His handicap after the allowance is 14.  After an additional 10 percent reduction, his handicap is 13 (14 - .1 x 14 = 12.6 which is rounded to 13).
Total Score of Partners – The USGA recommends players be assigned their full handicap.  Player A would be a 4-handicap and Player B a 16-handicap.
Scramble – The USGA recommends the team handicap should be 35 percent of Player A’s handicap and 15 percent of Player B’s handicap.  Player A would have a 1-handicap (.35 x 4 = 1.4 rounded to 1).  Player B would have a 2-handicap (.15 x 16 =2.4 rounded to 2.0).
Pinehurst –The USGA recommends the team handicap should be 60 percent of Player A’s handicap and 40 percent of Player B’s handicap. Player A’s handicap would have a 2-handicap (.6 x 4 = 2.4 rounded to 2).  Player B would have a 6-handicap (16 x .4 = 6.4 rounded to 6).




[1] The eight stroke limit stems from research done by Francis Scheid published in Golf Digest in June 1971.  Scheid never studied actual tournaments, but used scorecards from his home club to simulate matches.   In 1971 there was no Slope System and the bonus for excellence was .85 rather than .96 as it is today.  Nevertheless, the  8-stroke limit has been imposed in many four-ball events even though it has never been proven to lead to increased equity in studies of actual competitions. 
[2] USGA Handicap System, Sec. 9.4bii.  The USGA does not recommend the 8-stroke limit for Four-ball match play.  The USGA’s reasoning does not seem consistent.  If a large difference in handicap leads to low scores in Four-ball stroke play, it would seem that a large difference in handicap would also lead to low scores in Four-ball match play—i.e., the team with a large difference would always have an advantage.  The USGA has never explained why the 8-stroke limit should only apply to Four-ball stroke play.
[3] Modified Stableford scoring adds an element of serendipity in deciding the winner.  Under modified Stableford scoring, two players with the same handicap and gross score can have different point totals in the Four-ball competition.  It is not clear if the Tournament Committee purposefully wanted to add an element of chance to the scoring or simply made a mistake in selecting the modified Stableford scoring system.

Monday, August 22, 2016

Revising Rule 18-2: Ball at Rest Moved

No rule has caused so much consternation to the USGA and R&A as Rule 18-2.  Rule 18-2 states if a player causes a ball to move, the player incurs a penalty of one stroke.  In the end a rules official must determine what caused the ball to move, and there’s the rub.

The interpretation of Rule 18-2 caused what many describe as a fiasco at the 2016 U.S. Open.  Dustin Johnson’s ball moved on the 5th green, and it had to be determined what caused the ball to move.   Johnson declared he had not caused the ball to move.  On the 12th tee, Johnson was informed he may be assessed a one stroke penalty.  The question of the penalty became moot when Johnson won by four strokes. The USGA ruled that absent any other suspects (wind, gravity), Johnson was guilty.  The one stroke penalty only reduced Johnson's winning margin to three strokes.  If Johnson had tied with another player, would the USGA have assessed a penalty?   Probably not. The USGA looked bad enough without deciding the outcome of a major championship on the subjective judgment of a panel of rules officials.  The eighteen hole playoff would have been held on Monday.
The 2015 Open Championship encountered another problem with Rule 18-2.  Louie Oosthuizen addressed a tap-in putt, but a gust of wind started the ball moving and it did not stop until it was five feet away from the hole.  At that point, play was suspended, but too late to help Oosthuizen.  He had to play from the further distance.
The problem inherent in Rule 18-2 is that it does not make a distinction between a ball on or off the green.  With today’s fast greens, it is much more likely a ball can be moved by wind or gravity.  But whether wind, gravity, or the player is the culprit is still difficult to discern.  To bring more equity to the problem, a rule change (also suggested by others) could make a ball on the green not in play if has been addressed or marked.  It is only in play after the ball has been struck by a stroke. Under this rule change, if the ball moves for any reason other than a stroke, it must be replaced with no penalty.   This rule change meets the following requirements of a good rule.
Clarity – No need to call in an official if the ball moves on the green after it has been marked or addressed.  Simply replace it.  The adoption of this rule would eliminate many Decisions on when a penalty should be assessed. It does bifurcate the rule depending on whether the ball is on the green or elsewhere.   This is reasonable, however.  Through the green, a player could move his ball in an attempt to remove loose impediments around his ball. He should be penalized since the removal of the impediment would improve his lie.  On the green, however, the player is allowed to remove loose impediments without penalty.  In other words, the Rules already differentiate between a ball on the green and a ball through the green.
In determining whether a ball has moved a player is given some leeway in the rules.   If the ball moves by an amount not reasonably discernible to the naked eye, a player’s determination that the ball has not moved will be deemed conclusive, even if that determination is later shown to be incorrect through the use of sophisticated technology (Decision 18/4).[1]  The revised rule would eliminate this Decision, make the outcome independent of the leniency of the rules official  and minimize the number of call-ins from Rules Mavens who believe they detected ball movement.
 Fairness – The revised rule tends to minimize luck in determining tournament outcomes.  If the wind blows a ball that has been addressed or marked off the green or in the hole, the player would not be punished or rewarded for such random acts of nature.
Proportionality –The one stroke penalty for a player inadvertently moving his ball on the green appears to be disproportionate.  Currently, a player is assigned the same penalty for 1) dropping his marker on his ball and causing it to move or 2) hitting a ball into a water hazard.  The latter action is the result of a bad swing and/or judgment and should be penalized.   The first action is due to carelessness.   A player gains no advantage if he replaces his ball after inadvertently causing it to move on the green.  True, the current penalty of one stroke acts as a deterrent to such carelessness.  But any benefit from reducing the frequency of such behavior is more than offset by the elimination of disputes over what caused the ball to move.
Any change in the Rules needs to be seriously vetted.  There may be unintended consequences of having a ball on the green considered out-of-play.  Testimony should be taken from those most affected by Rule 18-2 (i.e., Tour Players).  USGA and PGA Tour officials responsible for making the call of when a ball has moved also need a voice.  Rules changes follow Newton’s First Law: A rule at rest tends to stay at rest.  Without a demand for change from players and officials, Rule 18-2 will be cut and pasted into the next edition of the Rules of Golf for the foreseeable future.  




[1] That same leeway test is not given when a player touches the ground in a hazard.  In the 2016 Women’s U.S Open, Anna Nordqvuist touched the sand with her club and was given a two-stroke penalty.  A strong argument could be made that the violation was not apparent to the naked eye.  No one noticed the small grain of sand take a tumble until Fox, using sophisticated technology, zoomed in on her address of the ball.  Should the USGA be consistent in its Rules and apply the same standards concerning sophisticated technology to ”ball moved” and “touching the ground?”  It is a debatable question, but one that has never been publically addressed by the USGA.

Thursday, July 7, 2016

Beating Your USGA Index or Beating Your USGA Handicap: Which is Easier?

There has always been some confusion about what the probabilities in Appendix E of the USGA Handicap System actually represent.  John Paul Newport of the Wall Street Journal, for example, wrote a player with a handicap between 13 and 21 will only play 3 strokes better than his handicap once in 43 rounds.[9]  Newport cites the website of Dean Knuth, former Senior Director of Handicapping at the USGA for his probability estimate.  Knuth cited the work of F.P.  Engel who defined the Net Differential as:[1]

         Net Differential = (Adj. Score – Handicap) - Course Rating

It appears Knuth used Engel's probabilities for a player with a 13-21 handicap.  These probabilities were for beating your Handicap by N strokes or better.

Some time later, the USGA changed the definition of Net Differential  to mean beating your Index, but the probabilities remained the same.  This change was made because either the USGA thought it expedient or did not understand that “beating your Index” and “beating your Handicap” were not the same thing. The USGA was informed of the problem, but chose to ignore it.

To demonstrate the difference, a player’s adjusted score under the two definitions of Net Differential is computed below:

Beat Your Handicap
1)      Net  Differential  = (Adj. Score – Course Rating)  - Handicap = -N  
2)      Adj. Score = -N + Course Rating + Handicap

Beat Your Index
3)      Net Differential = (Adj. Score – Course Rating)·(113/Slope Rating) – Index = -N
            4)  (Adj. Score-Course Rating)·(113/Slope Rating) - Handicap·(113/Slope Rating) = -N
            5)  Adj. Score = -N·(Slope Rating/113) + Course Rating + Handicap

Equations 2) and 5) show it takes the same score to beat your Handicap or Index (i.e., N = 0).  For other values of N, however, a player needs a lower score to beat his Index than he does to beat his Handicap if the Slope Rating is greater than 113.  For example, if the Slope Rating is 150 and N= 6, a player would have to score approximately 2 strokes lower to beat his Index by -6 than he would to beat his Handicap by -6.



[1] Knuth, D.L., F.J. Scheid, and F.P Engel, “Outlier identification procedure for reduction in handicap,”  Science and Golf II, E & F Spon, London, 1994, pp. 228-233.