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).
Probability That Sam Wins the Match

Sam’s’ Average Net Score Advantage
Probability Sam Wins the Match

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?    


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
For a 1-stroke advantage,
                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,, 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