## Thursday, December 19, 2013

### A Sandbagger's Guide to Winning

It takes a great deal of effort to manipulate a handicap.  A player has to generate artificially high scores in rounds that are not in competition. This post examines a sandbagger’s winning percentage as a function of how “many strokes he has in the bag” – i.e., the difference between his manipulated handicap and his true handicap.
Let’s assume Tom and Sam play golf together.  The winner of a match is the player with the lower net score.  Sam has worked his handicap so that his average net score is 1-stroke less than Tom’s.  This does not mean Sam wins every time.  The random nature of scoring lets Tom win when he has an exceptionally good round, or Sam has a bad round.  The probability that Sam wins will depend on the standard deviation of scoring for each player.  For simplicity, it is assumed that each player has a standard deviation of three strokes (i.e., 68 percent of all scores will be between ±3 strokes of the player’s average score).  The probability that Sam wins a match is presented in Table below for various levels of sandbagging.  (Note: The methodology for calculating the probabilities is shown in the Appendix).
Table
Probability That Sam Wins the Match

 Sam’s’ Average Net Score Advantage Probability Sam Wins the Match -1 .59 -2 .68 -3 .76 -4 .82

The best long-term strategy for the sandbagger would be to have only a 1-stroke advantage.  He wins, on average, six out of ten matches.  Tom may not realize he is at a disadvantage since having four wins and six loses is not unreasonable record.  For just a little handicap manipulation (1-stroke), Sam gets an annuity as long as Tom does not figure out the game is rigged.
Tom, however, is not a complete idiot and realizes if his net score was 1-stroke lower he would do better.  He can do this by a) decreasing his average gross score in competition by 1-stroke while maintaining his current handicap, or b) artificially increasing his handicap by 1-stroke while maintaining his average gross score in competition.  Option b) is the easier of the two and the one most often chosen.   In essence, sandbaggers beget sandbaggers.
Sadly, many players do not look at their USGA Handicap as a measure of performance—How good am I?—but as weapon in their arsenal to beat their opponents.    The best evidence of this is watching players post their score.  Are players more jubilant when their trend handicap goes down or up?

Appendix

Suppose there are two scores, X1 and X2 drawn randomly from the normal distributions N(µ1, σ12) and N(µ2, σ22).  We want to find the probability that X1 < X2.
Now X1- X2 is normally distributed with mean,
µ = u1 – u2
and variance,
σ2 = σ12 + σ22
Hence, the variable (X1- X2 -µ)/σ is distributed normally with a mean of zero and a variance of 1 (i.e., the standard normal distribution N(0,1).
And so, the probability that X1 is less than X2, is the cumulative probability up to -µ /σ.   In our example, the standard deviation of scoring for each player is 3.  Therefore,
σ = (32 +32)½   = 4.24
µ = -1
The probability that X1 is less than X2 is
= f(1/4.24)  = f(.24) = .59

## Wednesday, December 4, 2013

### The USGA's War on Sandbagging, Part VI: The War Ends in a Wimper

(The United States Golf Association (USGA) has made various attempts to control players who manipulate their handicaps in order to do well in tournaments.  The name for such manipulation is “sandbagging.” If the USGA’s effort can be characterized as a war, then it is not winning.  A series of five posts examines the history and effectiveness of the USGA’s war plan.  Part I details the flaws of the USGA’s earliest attempt at controlling sandbagging.  Part II examines a proposed policy that increased the penalties for alleged sandbagging. Part III argues the current handicap system may actually encourage sandbagging.  Part IV explains why the USGA could be losing the effort to win the hearts and minds of local golfers.  Part V examines the flaws in the USGA's current war strategy. Part VI asks if the USGA's efforts are counterproductive and suggests it may be time for the USGA to withdraw from the battlefield.)

The USGA’s War on Sandbagging is over.  Section 10-3 (Reduction of Handicap Index Based on Exceptional Tournament Scores) is still part of the Handicap System, but it is merely symbolic.   Sec. 10-3 gives the appearance the USGA has an effective instrument for controlling sandbagging.  In reality, the current incarnation of Sec. 10-3 is a failure.  Here are some reasons why Sec. 10-3 is ineffective or inequitable:
1.       Tournament Formats – Many important tournaments are partner events.  They often include formats (e.g., scramble, foursome) where a score cannot be posted (i.e., Sec. 10-3 has no effect).  In four-ball formats, it is easy for the serious sandbagger to take a high score on a hole when his partner is in good position.   This eliminates being caught by the strictures of Sec. 10-3.
2.       Inequity – As discussed in Part V[1], Sec. 10-3 applies to scores and not to whether a player actually won anything.  It is possible a player can receive a reduced index, be labeled a sandbagger, yet never place high in a tournament.  This defect was addressed by Dean Knuth, the USGA director of Handicapping responsible for the implementation of Sec. 10-3.  He developed what he termed the Tournament Point System.  Under this system, a player can receive a reduced index based on where he places in tournaments, and not on his scores.[2]   While not without its own problems, the Tournament Point System does correct for this major deficiency of Sec. 10-3.
3.       Non-Uniform Application – There are no strict guidelines on what determines a Tournament Score for posting purposes.  The USGA argues a tournament score should be reserved for significant events. [3] This leads to a variety of interpretations.  At one club, a holiday two-best ball-of-four was considered a tournament score.  At another club, even the member-guest was not considered a major event.  A lack of uniformity leads to disparate results for the same scoring performance which is antithesis of what a good handicap system should be.
4.       Anomalies – Sec. 10-3 can lead to some strange results.  Assume Player A and Player B only play rounds together from the same tees.  Player B never posts a score lower that Player A.  Under Sec. 10-3, however, it is possible for Player B to have the lower Course Handicap.  This stems from measuring exceptional performance by the difference of the T-score differentials and a player’s current index, and not the player’s index at the time of the tournament.   This makes it possible for a player to receive a reduced index not for exceptional performance, but for having a higher index some time later. (For example assume a player had two T-score differentials of 10.0 that were made when he was a 12.0 index.  Months later, for a variety of legitimate reasons, his index goes to 14.0.  The player’s index would now be reduced by 1.0 under Section   10.3.)
5.       Can’t See the Forest for the Trees – By focusing on major events, the sandbagger is free to ply his trade throughout the year (and at one major event) without the possibility of receiving a reduced index.  Without an “R” index, even the biggest handicap scoundrel receives the implicit imprimatur of the USGA. [4] Handicap Committees have traditionally been loath to reduce a player’s index on its own.  Most committees are only too happy to rely on Sec. 10-3 for identifying sandbaggers.  In essence, Committees are relying on an enforcement mechanism that does not work.

The USGA knows its war on sandbagging is over.  When asked how many players receive a reduced index, the USGA replied:

“We do not have such statistics.  However, it is a very small number compared to the total number of players in the system”[5] (How the USGA knows it is a very small number without statistics is left unsaid).

The absence of statistics implies the USGA does not have any on-going evaluation of Sec. 10-3. Apparently, the USGA is not concerned about the effectiveness of Sec. 10-3 or whether it discriminates against players by club, association, sex, frequency of tournament participation or handicap level.  Sec. 10-3 will remain part the Handicap System since bureaucracies do not readily admit to their mistakes.  Rather than having the war on sandbagging end with a bang by the removal of Sec. 10-3, the war will end on a whimper.   Sec. 10-3 will simply be allowed to wither through benign neglect.

[1] The USGA’s War on Sandbagging, Part V: Problems With the Current Strategy, www.ongolfhandicaps.com, November 14, 2013.
[2] Newport, John Paul, “Fighting Back Against Sandbaggers,” Wall Street Journal, July 2, 2011.
[3] Hovde, Scott, Posting a Score As a Tournament Score, www.USGA.Org, 12/17/2012.
[4] When a player receives a reduced index through Sec. 10.3, it is identified with an “R.”
[5] E-mail to the author from Annie Pollock, Coordinator, Handicap and Course Rating Administration, 11/21/2013

## Thursday, November 14, 2013

### The USGA War on Sandbagging - Part V: Problems With the Current Strategy

(The United States Golf Association (USGA) has made various attempts to control players who manipulate their handicaps in order to do well in tournaments.  The name for such manipulation is “sandbagging.” If the USGA’s effort can be characterized as a war, then it is not winning.  A series of five posts examines the history and effectiveness of the USGA’s war plan.  Part I details the flaws of the USGA’s earliest attempt at controlling sandbagging.  Part II examines a proposed policy that increased the penalties for alleged sandbagging. Part III argues the current handicap system may actually encourage sandbagging.  Part IV explains why the USGA could be losing the effort to win the hearts and minds of local golfers.  Part V examines the flaws in the USGA's current war strategy. Part VI asks if the USGA's efforts are counterproductive and suggests it may be time for the USGA to withdraw from the battlefield.)

The Reduction in Index for Exceptional Tournament Scores (RIETS) has been part of the USGA’s never-ending quest to snag sandbaggers.  The USGA’s effort has been plagued with flaws.  In its earliest form, the RIETS gave a player a good chance to receive an index reduction if he played in a sufficient number of tournaments.[1]
The USGA reacted to this problem by making the reduction in index a function of the number of tournaments a player entered. While this greatly reduced the probability a player would receive a reduction by chance, it also made the RIETS less penal and less effective as an instrument for controlling sandbagging.[2]   The focus here, however, is not on the efficacy of the RIETS, but on conceptual problems with the current RIETS.  A conceptual problem exists when the RIETS assigns reduced indexes that are not consistent with the general premises of the USGA Handicap System.
Two such problems are identified here along with a remedy for correcting the inconsistencies inherent in the present RIETS.

1. My Partner Always Kills Me, But I Get the Lower Handicap! - A general premise of the USGA Handicap System is that a player with the lower scores should have the lower index.  This is not always the case under the RIETS.  Let’s look at an example:

Two players, A and B, always play together from the same tees.  Player A’s adjusted score has always been higher than Player B’s in every round they have played.  This month, however, Player A finds his USGA index is lower than Player B’s.  How can this happen?
Answer: Player A has a handicap index of 14.0, while Player B’s index is 9.4.  Player A has two tournament differentials that average 5.0.  Player B has two tournament differentials that average 4.0.  Player A has his index reduced by 8.1 giving him a reduced index of 5.9.  Player B’s index is reduced by 2.6 giving him a reduced index of 6.8.  On most courses, Player A would have to give Player B one stroke.

Under the old RIETS, the penalty for exceptional performance was a function of how well you played in tournaments.[3]  Under the latest RIETS, the penalty is a function of how well you played relative to your current index.  One argument in support of the USGA’s latest approach is that a player should receive a greater penalty for shooting a lower net score.   For example, assume that Player A had a 14.0 Index while player B had a 12.0 index.   Further assume for simplicity that they play a course with a slope rating of 113 and a course rating of 71.  If both players have two tournament scores of 75, Player A would have scored a net 61, while Player B scored net 63.  Player A would have a reduced index of 4.8, while Player B would receive a reduced index of 5.2.  The USGA is essentially adding an additional penalty to the higher handicapped player.
The USGA could argue that the additional penalty is assessed because the tournament scores of the higher handicapped player are less likely due to chance and there is a greater chance of sandbagging being involved.  The USGA has not made this argument, but if it did, it does not have much merit.  You might as well argue that the winner of the Powerball lottery must have cheated since the probability of winning is so low.
Other evidence speaks against the penalties being based on the probability of occurrence.  The Appendix presents the marginal increase in the index reduction for an increase in AVDIFF (the average of the best two tournament differentials below the player’s handicap index).  The marginal increase becomes smaller as the AVDIFF increases.  For example, as the AVDIFF goes from 4.5 to 5.0, a player is hit with an increased index reduction of .8.  But as the AVDIFF goes from 11.5 to 12.0 the increase in index reduction is only .5.  If the USGA were penalizing performance on the base of probability, the marginal increase in the index reduction should go up and not down.[4]

The Worse I Play, the Lower My Index! - Another curious element of the current the RIETS is that the worse a player scores, the lower his index goes. Let’s take as an example a player who has two tournament differentials that average 2.9.  Table 1 shows his reduced index for various handicap indexes and 10-19 T-Scores.

Table 1
Reduced Index for Various Handicap Indexes

 Handicap Index Reduced Index 14.0 4.6 13.0 5.0 12.0 5.5 11.0 6.2 10.0 7.0 9.0 8.0 8.0 8.0

If the player had a 12.0 handicap index and 10-19 T-Scores, he would receive a reduced index of 5.5.  If he plays poorly and his index rises to 13.0, his reduced index would be lowered to 5.0.   His index has decreased because he is in a slump.  The RIETS, however, makes no distinction between a player’s index at the time of his two T-Scores and at some time later.  This violates the basic tenet that a player’s handicap should be based on his potential.  His potential can be measured either by his tournament scores or his calculated index.  To increase the penalty because a player is not playing well seems outside the bounds of rational handicap policy.

Remedy - One remedy for making the RIETS more rational is to eliminate the Handicap Reduction Table and go back to simple formulae.  Table 2 below shows the reduced index for various levels of T-Scores under the proposed remedy.[5]

Table 2
Reduced Index for Various Numbers of T-Scores

 Number of T-Scores Reduced Index 2 3.0 + Average of Two Lowest T-Score Differentials 3 3.5 + Average of Two Lowest T-Score Differentials 4 4.0 + Average of Two Lowest T-Score Differentials 5-9 4.5 +Average of Two Lowest T-Score  Differentials 10-19 5.0 + Average of Two Lowest T-Score Differentials 20-29 5.5 + Average of Two Lowest T-Score Differentials 30-39 6.0 + Average of Two Lowest T-Score Differentials >39 6.5 + Average of Two Lowest T-Score Differentials

The Reduced Index would be the player’s USGA Handicap Index provided that it is at least one less than his USGA Handicap Index based on the Formula in Section 10-2 of the Handicap System manual.
Let’s see how this formula would work on the problems raised in this post.  First, there was the problem of a player with the lower gross scores having the higher index.   Player A had a 14.0 index and two tournament differentials averaging 5.0.  Under the proposed RIETS, his reduced index would be 8.  Player B had an index of 9.4 and two tournament differentials averaging 4.0.  Player B’s reduced index would be 7.0.  That is, the player with the better tournament performance has the lower index.  This outcome is consistent with the premise that lower scores should receive lower indexes.
Second, the problem of a player’s index rising as he played worse is eliminated. This problem no longer exists since the reduced index is no longer a function of the player’s index, but only of his tournament scores.[6]
The proposed RIETS is not quite as penal as the current RIETS.  A player with a 13.0 index and two T-Score differentials averaging 3.0 would receive a reduced index of 3.8 under the current REITS.  Under the proposed RIETS he would receive a reduced index of 6.0.  Change, however, should not be made on the basis of which procedure is more penal, but which is more equitable.[7]  While the current penalty is short of “cruel and unusual,” the conceptual problems identified here strongly argue that the RIETS should be re-examined by the USGA Handicap Procedure Committee.  As discussed in the next post, however, a strong case can be made for simply eliminating the REITS

Appendix

Marginal Increase in Handicap Reduction for Increase in AVDIFF (Average of best two T-Scores below Handicap Index)[8]

 Number of Eligible Tournament Scores AVDIFF 2 3 4 5-9 10-19 20-29 30-39 >39 3.0 to 3.4 3.5 to 3.9 4.0 to 4.4 4.5 to 4.9 .8 5.0 to 5.4 .8 .9 5.5 to 5.9 .8 .8 .9 6.0 to 6.4 .7 .8 .9 .9 6.5 to 6.9 .7 .8 .9 1.0 1.0 7.0 to 7.4 .7 .7 .8 .9 1.0 1.1 7.5 to 7.9 .7 .7 .8 .9 .9 1.0 1.1 8,0 to 8.4 .6 .7 .7 .8 .9 1.0 1.0 1.2 8.5 to 8.9 .6 .7 .7 .7 .9 .9 1.0 1.1 9.0 to 9.4 .7 .7 .7 .8 .8 .9 1.0 1.1 9.5 to 9.9 .6 .6 .7 .7 .8 .8 .9 1.0 10.0 to 10.4 .5 .6 .7 .7 .7 .9 .9 1.0 10.5 to 10.9 .6 .5 .6 .7 .7 .7 .8 .8 11.0 to 11.4 .6 .7 .6 .6 .7 .8 .8 .9 11.5 to 11.9 .6 .6 .6 .7 .7 .7 .8 .7 12.0 to 12.4 .5 .6 .6 .6 .6 .7 .7 .8 12.5 to 12.9 .6 .5 .6 .6 .7 .6 .7 .8 13.0 to 13.4 .5 .6 .6 .6 .6 .7 .7 .7 13.5 to 13.9 .6 .6 .5 .6 .6 .6 .7 .7 14.0 or more .5 .5 .6 .6 .6 .6 .6 .7

[1] See “The USGA’s War on Sandbagging – Part I The War Begins,” www. ongolfhandicaps.com, 9/9/2013.
[2] Assume a player is a 14.0 index and plays a course with a course rating of 70.9 and a slope rating of 128.  Further assume he has played in 30 tournaments.  If he shot two rounds of net 63 in the Member-Guest, he would not receive a reduction in index for his performance.  Under the old system (1991), the player would receive a reduction in index of 2.3.
[3] In its most general form, the formula for a player’s reduced index was:
Reduced Index = AVGTD + Constant
Where,
AVGTD = Average of Two Lowest Tournament Differentials
As can be seen, the Reduced Index is not a function of a player’s index.
[4] The Appendix raises the question if there is any theory behind the numbers in the USGA Handicap Reduction Table. The marginal increases do not continuously decrease.  It is difficult to conceive of any mathematical function that would behave in such a fashion.
[5] The formula is derived by setting the index reduction equal to 1.0 at the initial break point for a particular number of tournaments.  For example, the index reduction for a player with two tournaments would be:
Index Reduction = 1+ (AVDIFF - 4.0)
Now,
AVDIFF = Index - Average of Two Lowest T-Score Differentials
The reduced index is:
Reduced Index = Index - Index Reduction
Substituting, the reduced index formula simplifies to:
Reduced Index = 3.0 + Average of Two Lowest T-Score Differentials
[6] This remedy also minimizes the breakpoint problem where small changes in a player’s index can lead to relatively larger changes in the player’s reduced index.  For example, under the current RIETS, a player with two T-Scores and an AVDIFF of 8.4 receives a reduction of 6.8.  A player with an AVDIFF of 8.5 receives a reduction of 7.4.
[7] It would not be difficult to make the formulae more penal if that was warranted.
[8] The USGA Handicap System 2002-2005, United States Golf Association, Far Hills NJ, 2002, p. 54. Note: The Handicap Reduction Table should more properly be termed the Index Reduction Table since that is what it does