Saturday, December 26, 2015

What's "Age" Got to Do With It?

A Member/Guest tournament has a condition that if a player’s combined age and handicap equals 90 or higher, he can play the forward tees.   The Tournament Committee explains the inclusion of age as a determinant of the tees played is intended to increase participation from an increasingly older membership.  (This begs the question of why the tee prize for participants is a quasi-walking golf bag.)  

This attempt at affirmative action for the elderly is misguided for two reasons.  First, it is “tacky.”  In a Member/Guest, do you really want to inquire about your partner’s age?  And how would you vet the age of a player?   Require a photo-id like he is checking into a Motel 6? 

Second, to ensure equitable competition, golfers should be measured by their ability (i.e., their Index) and not some extraneous attribute.  An example should demonstrate why age is an inappropriate criterion:

Assume Lance and his twin Larry are 16-handicaps from both the back and forward tees—there is only a small difference between the two Slope Ratings.  Since they are both 75, they qualify to play the forward tees. There is a one stroke difference in the Course Ratings so each would be assigned a 15 handicap for the tournament.  Since the event consists of a series of nine hole matches, Lance and Larry would each be assigned an 8 handicap for each match (15/2 = 7.5 which is rounded to 8).

Twins Justin and Jim are a couple of years younger than Lance and Larry, but are also 16 handicaps.  They too would play the back tees as 8 handicaps for their match.   Both teams are of equal ability and handicap, yet Lance and Larry would have the advantage of playing from the forward tees.   This would not be fair on its face.  (Justin and Jim could be assigned ½-stroke, but that presents other problems in equity, ease of administration, and user friendliness not discussed here.)

Competitions between players from different sets of tees are inherently inequitable.  The handicap adjustment under Sec. 3-5 , Players Competing from Different Tees, may not be equitable even for singles stroke play, and there is no evidence  its makes for equitable competition in four-ball.[1]  To obtain the best chance for a fair competition, all matches within a flight should be played from the same set of tees.  This would eliminate the need to invoke Sec. 3-5, increase equity, and ease the burden on tournament administrators. 

If there is a playoff among flight winners for an overall championship, it too should be conducted from one set of tees.  If three sets of tees are used, for example, the middle set could be selected for the playoff.  This would minimize grumbling from those who might otherwise have to give a stroke and distance to their less skilled opponents.




[1]  The theoretical problems with Sec. 3-5 are discussed in “The Problems with Section 3-5,” www.ongolfhandicaps.com, March 4, 2014.  A small empirical study reports Sec. 3-5 did not correct for the difference in tees.  In this case, the players competing from the back tees were at a disadvantage--see “Is Your Tournament Equitable,” www.ongolfhandicap.com, October 22, 2012.

Wednesday, December 2, 2015

Eliminating the Blind Draw-Continued

In commenting on a previous post (“Eliminating the Blind Draw,“ October 31, 2012), an astute reader suggested an alternative method:

My club had been messing around with options to handle this problem until I suggested that we should try using the second best score as the score of the third player. For example, in Stableford Scoring if Player A gets 2 points, Player B gets 2 points, and Player C gets 1 point, then the team gets 6 points.
This has now been accepted by all the informal groups in the club as results seem to suggest that teams of 3 win a prize in proportion to the number of teams of 3 or 4 entered. The number of prizes is in proportion to the size of the field.  I would be interested to know if you thought there was any mathematical support for this.

Let’s look at a simplified example to get a preliminary judgment of equity.  Assume only four scores are possible (3 = net birdie, 2 = net par, 1 = net bogey, and 0 = net double bogey or worse).  Further assume the probability of each score is the same (i.e., 1/4).  The question is whether the expected second best score of the threesome is greater, equal, or less than the expected score of a fourth player.  Column 4 of Table 1 shows the probability of each outcome for the threesome.[1]

Table 1
Probability of Outcomes

(1)
 Highest
(2)
 Second Best
(3)
 Third Best
(4)
Probability 
3
3
3
1/64
3
3
2
3/64
3
3
1
3/64
3
3
0
3/64
3
2
2
3/64
3
2
1
6/64
3
2
0
6/64
3
1
1
3/64
3
1
0
6/64
3
0
0
3/64
2
2
2
1/64
2
2
1
3/64
2
2
0
3/64
2
1
1
3/64
2
1
0
6/64
2
0
0
3/64
1
1
1
1/64
1
1
0
3/64
1
0
0
3/64
0
0
0
1/64

The expected second best score is the sum of the value of each score multiplied by the probability of each score occurring:

                Expected Second Best = 3·(10/64) +2·(22/64) + 1·(22/64) + 0·(10/64) =  96/64 = 1.5

The expected score of the fourth player is:

                Expected Score of the Fourth Player = 3·(1/4) + 2·(1/4) + 1·(1/4) + 0·(1/4) = 1.5

Under all of the assumptions made, using the second best score would be equitable.  This result is not surprising.  The expected second best score is also the expected average score of any player.   (It would not be equitable under a modified Stableford System where the difference between hole scores is not constant.  For example, assume a net birdie is now worth 5 points while all the points for the other scores remain the same.   The expected second best score would be 1.81.  The expected score of the fourth player would be 2.00.) 

To get a more realistic estimate of any advantage, the number of possible hole scores is expanded as shown in Table 2.  Since not all hole scores are equally likely, however, Table 2 presents reasonable probability estimates for an easy course (Course Rating less than par) and a more difficult course.

Table 2
Probability of Hole Scores (Stableford Points) for Easy and Difficult Courses



Course


Net Eagle(4)


Net Birdie(3)


Net Par(2)


Net Bogey(1)
Net Double Bogey or Worse(0)
Expected Score
Par = 72
Easy
.10
.30
.40
.15
.05
67.5
Difficult
.05
.20
.45
.20
.10
73.8

Using the same methodology presented in the simplified example, the expected score of the second best hole score of the threesome and the expected score of the fourth player can be estimated.  Those holes scores are shown in Table 3.

Table 3
Expected Holes Scores


Course

2nd  Best

Fourth Player
Threesome Advantage per Hole
Easy
2.27
2.25
0.02
Difficult
1.91
1.90
0.01

Table 3 shows a small edge for the threesome on both courses.   Given all of the uncertainties embedded in the model (e.g., probability assumptions, assumption that all players have identical scoring patterns and variances), such a small edge is not significant.  And given the random nature of team scoring, such a small edge would be hard to notice without a large number of trials.  If threesomes are winning in proportion to their numbers as the reader suggests, there is no reason to believe his method is not equitable. [2]

The one remaining problem is how prize money is distributed.  If first place wins the same amount regardless of team size, the threesomes have a big edge.  A threesome is just as likely to win, but only has to split the prize money three ways instead of four.  Since the reader was clever enough to devise an equitable competition, I am sure he has solved this problem too.



[1] The probability of an outcome is the probability of any one outcome multiplied by the number of ways that outcome can be achieved.  For example, the outcome 3,3,2 can be achieved in three ways—Player A gets a 2 and the other players get  3s, Player B gets a 2 and the other players get 3s, Player C gets a 2 and the other players get 3s).   The probability of any one outcome is 1/4·1/4·1/4 = 1/64.  Therefore, the probability a team has two 3s and a 2 is 3x1/64 =3/64. 

[2]  Probabilities for courses can be constructed where there is a significant difference in hole scores between the second best score and the score of the fourth player.  A course where net bogey and net double bogey are the likeliest scores will favor the foursome.  A course where net eagle and net birdie are the likeliest scores would favor the threesome.  Neither course is likely to exist in the real world. 

Thursday, November 12, 2015

The Golf Digest Handicap: Why Bother?

Golf Digest started offering a handicap service in 2013.  The question is “Why bother to offer or get a Golf Digest handicap?”  Golf Digest was once the flagship magazine of the golf community.  It has been listing badly as of late.  It is hard to be current when you only publish once a month.  Its time lapsed photography used for instruction seems antiquated in today’s internet and iphone world.  In an effort to be relevant, the editor’s decided Golf Digest should become hip – the magazine for millennials.  The magazine recently featured articles about the best looking girlfriends on Tour, the joy of playing shirtless, the thrill of having sex on the golf course, and a cover story on Paulina Gretsky—golf’s equivalent of a  Kardashian.  It appears Golf Digest has traded its dignity for stagnant circulation at best.

The Golf Digest handicap may be a gesture of atonement for its sophomoric behavior.   If public service was the motive, however, the Golf Digest handicap would have to have some value for there to be absolution. Unfortunately, the Golf Digest handicap is of little benefit to the player for the following reasons:

Not Universal – For a handicap system to be effective, competing players must use the same handicap system.  Golf Digest argues its handicap “allows golfers of all skill levels to compete against one another fairly.”  This assumes other players have a Golf Digest handicap which is very unlikely. If the other players have USGA handicaps, they would probably look upon your Golf Digest handicap like a cashier looks upon a $3 bill.[1] 
No Peer Review – An absolute necessity for a handicap system is peer review.  Peer review gives some assurance (maybe p=.85) a handicap is a true measure of a player’s potential. Peer review is absent from the Golf Digest handicap system. 
OversoldGolf Digest argues its handicap is “a way to determine where your game needs the most help.”  Handicap systems, however, can identify a bad golfer but not pinpoint why he is bad.  At best, the Golf Digest handicap can put you in a class of players (e.g. 20+ handicap) who usually have these deficiencies (e.g., sliced drives, inadequate short game).  Since players are typically aware of their weaknesses, it is unlikely the Golf Digest handicap will provide any new information.
Absence of Slope Rating – The Golf Digest Handicap was developed by Dean Knuth, former Director of Handicapping at the USGA, who was responsible for the adoption of the Slope System.  Knuth argues the Golf Digest handicap is fair and “portable.”  His statement goes against 30 years of arguments made by himself and the USGA proclaiming only the Slope System can make handicaps portable.   If you are a muni player (Slope Rating = 110) and Jerry Tarde, Managing Editor of Golf Digest, asks you to be his guest at Pine Valley (Slope Rating = 155), you will be at a serious disadvantage with your Golf Digest handicap. 
Measure of Progress – The Golf Digest handicap does let a player measure how his performance changes over time.  A player with a minimal knowledge of spreadsheets, however, can track a USGA handicap using actual Course and Slope Ratings.  If that is too difficult, the player can track his differential (Adjusted Score – USGA Course Rating) and get essentially the same information provided by the Golf Digest handicap. 

A better explanation than public service for the free handicap is Golf Digest’s desire to increase visits to its website.  Golf Digest has been giving away “free stuff” for years in hopes of stemming subscriber defections.  For example, it has tie-in sales where the magazine is given away if another product is purchased—e.g., a golf association membership or a large purchase at a golf store.  (Note: About 25 percent of Golf digest’s circulation is listed as “free or nominal rate distribution.”)  Now it is giving away a free handicap in hopes of harvesting the player’s e-mail address or having him click on an ad that appears on the posting sheet.
 
The Golf Digest handicap is aimed at the universe of players who 1) Are not serious enough about the game to get a USGA handicap,  2) Are serious enough to want to improve their game, and 3) Are aware of the existence of the Golf Digest handicap.  This should be a very small population indeed.   Golf Digest’s gambit should fail as both a marketing ploy and as a viable handicap.  To answer the title question of this post, neither the magazine nor the player should bother with the Golf Digest handicap.
 
Appendix
The USGA vs. Golf Digest Handicap

For legal reasons, Golf Digest could not use the USGA handicap formula.   The Golf Digest handicap differs from the USGA handicap in the following four ways:

1. The Course Rating is estimated solely as a function of yardage.
2. There is no Slope Rating.
3. Different equitable stroke control procedures.
4. The sample size of scores is smaller.

Each of these differences affects the difference between a USGA and Golf Digest handicap:

Course Rating formulae – The USGA’s course rating formula for men is:

                Course Rating(USGA) = Yardage/220 +40.9 + SOV
                                                 SOV= Scratch Obstacle Value
The Golf Digest formula for the Course Rating is:
                Course Rating(GD) = Yardage/200 +39

For all courses greater than 4200 yards, the Course Rating(GD) will be larger than the yardage component of the  Course Rating(USGA).  This difference could be a proxy for SOV which the Course Rating(GD) does not explicitly incorporate.  Instead, it could be assuming the SOV is an increasing function of yardage.
This adjustment for omitting the SOV may not be sufficient.  The table below shows the USGA and Golf Digest Course Ratings for a selection of courses in Southern California.  The USGA Course Rating is higher is 6 of the 7 cases.  Therefore, the Golf Digest Course Rating formula would, on average, yield a slightly higher handicap than the USGA Course Rating formula.    

Table
USGA and Golf Digest Course Ratings

Course(Tee)
Yardage
USGA Rating
Golf Digest Rating
Difference
Los Angeles CC(White)
6486
72.4
71.4
+1.0
Riviera(White)
6531
72.2
71.7
+0.5
Torrey Pines South(White)
6628
73.1
72.1
+1.0
PGA West Stadium(White)
6166
70.2
69.8
+0.4
Rancho La Quinta Jones(White)
5986
68.6
68.9
-0.3
Wilshire CC(Blue)
6265
70.7
70.3
+.04
Bel Air CC(White)
6235
71.0
70.2
+0.8

Absence of the Slope Rating – The Golf Digest Handicap system is the product of Dean Knuth.  Knuth was also the lead designer and proponent of the Slope System while he was at the USGA.   The Golf Digest handicap will have all of the same flaws Knuth noted in his arguments supporting the Slope System. Knuth may have believed the casual player mostly plays the same course so “portability” is not all that important.  In many cases, this is not an unreasonable assumption.
Different Equitable Stroke Control(ESC)l Procedures – The Golf Digest handicap system limits a player to a net double bogey.  The USGA sets limits on hole scores depending a a player’s handicap.  Sometimes the Golf Digest ESC is more penal, and at other times the USGA ESC is more penal.  Take a 15 handicap for example.  The USGA allows him a maximum of 7 strokes on a par 5.  If he strokes, on this hole, however, Golf Digest allows 8 strokes.  On a par three, the USGA allows a 7strokes, while if the player doesn’t stroke Golf digest only allows 5 strokes.  The differences in strokes would probably even out, so the two  ESCs should not result in significantly different adjusted scores.
Differing Sample Sizes – The USGA takes the average of the ten best differentials out of the last 20 and then multiplies by .96 (the Bonus for Excellence).  Golf Digest takes the average of a player’s second, third, and fourth-best scores out of the last ten.  Without submitting the proof, the average computed by both methods will be similar. 

In summary, the Golf Digest handicap is a reasonable estimate of a player’s USGA handicap except for the omission of the Slope Rating.  If a player plays most often at the same course, the Slope Rating loses importance and the two handicap systems yield approximately the same result. 





[1] The differences between the Golf Digest and United States Golf Association handicaps are detailed in the Appendix.  In many instances, the Golf Digest handicap will approximate the USGA handicap.  It is not a replica, however, and cannot be considered equivalent for any serious competition.  

Monday, October 12, 2015

The Cost and Pricing of Golf Handicaps

Golf Associations provide a variety of services paid primarily by membership dues.  A partial list of those services would include 1) handicap administration, 2) course rating and measurements, 3) golf publications, 4) member tournaments, and 5) sometimes ownership of a golf course.   Most of the services are of little or no value to the average golfer.  The only service that is a necessity is the player’s handicap.  Golf associations, however, do not sell the handicap service separately.  Instead they follow the cable industry model and bundle all of the services for one price—You say you never watch the Hallmark Channel?  Too bad.

Associations have another advantage in that they are monopolies.  There are other organizations that sell handicap services (Myscorecard, for example), but these handicaps are generally not accepted at club tournaments.  This monopoly power lets the golf association charge higher than the free market prices for handicaps as well as bundle unwanted services.  Table 1 presents the percentage of membership dues spent on the handicap service for a sample of state golf associations.  These numbers were extracted from Income Tax Form 990 filed by each organization.  These are only rough estimates since each association accounts for costs and revenue differently.  The consistency of the percentages, however, indicates roughly 10 percent of membership dues are spent on the handicap service.

Table 1
Handicap Costs as a Percentage of Membership Dues (2013)1

Association
Membership Dues
Handicap Cost
Percentage
Colorado State Golf Association
$1,346,753
$125,141
9.3
Northern California Golf Assoc.
$6,404,947
$331,832
5.2
Oregon Golf Association
$1,380,620
$113,345
8.2
Southern California Golf Assoc.
$4,813,105
$481,260
10.0
Washington State Golf Assoc.
$1,942,900
$164,352
8.5

What does an association do with the excess revenue it collects?  Most associations would argue the money is invested for the good of the game—e.g., association golf courses, junior golf, scholarships.  These may be good endeavors, but why should a person wanting a handicap be forced to donate to the charities the association wants to support?

In truth, most of the charitable donations made by associations are small.  The Florida State Golf Association, for example, with annual revenue close to $5 million gave only $26,000 in college scholarships. More likely, bureaucracies follow the commandment “Pay thy own self first” and direct discretionary income to management salaries.  As shown in Table 2, the wages of the key executive at each association increases with the size of the membership.  With more dues there is more money to divert to staff salaries. When benefits are also included, the disparity in the compensation between the small and large associations is even more apparent.  At a membership cost of $40, for example, it takes over eight thousand members to pay the total compensation of the Executive Director of the Southern California Golf Association.[1]  It would only take slightly over 3000 members to cover the total compensation of the Executive Director of the Oregon Golf Association.  

Table 2
Reportable Compensation of Key Employees (2013)*

Association
Key Employee
Total Wages
Colorado State Golf Association
Edward Mate
$131,887
Florida State Golf Association
Jim Demick
$246,750
Northern California Golf Assoc.
Lyn Nelson
$247,640
Oregon Golf Association
Barbara Trammell
$128,890
Southern California Golf Assoc.
Kevin Heaney
$239,971
Texas Golf Association
Rob Addington
$373,177
                * Does not include retirement, deferred compensation, and nontaxable benefits.

A counter explanation of the correlation between association size and salaries is large corporations pay their chief executive officers more than small corporations so the varying salary levels at associations should be expected.  The difference is large corporations have billions of dollars at stake and face stiff competition.   Golf associations face no such threat.  They own a monopoly that is almost impossible to challenge.  The executive director of a golf association does not have to make decisions that could make or break the association.  He or she only has to keep the governing board happy.  This can usually be accomplished by giving board members a blue blazer and outings on the better courses in the state.  The skills needed to run large or small associations are basically the same.  That leaves the size of an association as the best explanation of salary level.

For most players, the cost of a membership in an association is a negligible part of their golf budget.  The demand for membership will not be very sensitive to price for these players.  The price may be too high, however, for the casual player whose golf budget is limited—the type of player that needs to be reached if the game is to expand.  Will associations lower the cost of handicaps to attract this player?  If a cafeteria plan was adopted where players could choose “handicap only,” the revenue base of associations would be cut dramatically.  This would mean a reduction in salaries and personnel. The adoption of such a plan is unlikely since bureaucracies are genetically predisposed to follow another basic commandment, “Do not kill the goose that lays the golden eggs.”      






[1] In 2013, the Executive director of the SCGA received $239,971 in base compensation, $51,170 in retirement and deferred compensation, and $4,158 in nontaxable benefits, for a total of $333,299.  Of course the big pay waits if you make it to the USGA.  The Executive Director of the USGA received $812,000 in total compensations.  When an executive goes from a state association to the USGA, he or she can expect a salary bump of around $200,000.