The USGA's War On Sandbagging - Part I, The War Begins

(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 six 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 United States Golf Association (USGA) first introduced the "reduction of handicap index for exceptional tournament scores" into its handicap system as Sec. 10-3 in 1992.  This was an opening salvo in the war against sandbagging. Under the new handicapping procedure, a player could have his index reduced if his tournament performance is significantly better than his current index would indicate.  The reduction is based on the lowest two tournament scores over the past year.[1]  The index reduction is clearly intended to restrict the prevalence of sandbagging -- players having handicaps much higher than their ability would dictate.  It is possible, however, that this new system could also penalize the ethical player who plays in many tournaments. A system that does not clearly distinguish between the ethical player and the sandbagger is worse than no system at all.

            What is the probability the ethical player is penalized under Sec. 10-3?  We start with the assumption that a player's differentials (adjusted score minus the course rating times 113 over the slope rating) are distributed normally.[2]  The player’s mean differential is X with a standard deviation of s.  A player's expected current index is then:

                          Current Index   = .96(X - .8s)

(The .96 is the bonus for excellence adjustment in the USGA handicapping system.  In the normal distribution, the average of the better half of all scores is approximately the mean minus .8 of the player’s standard deviation.)

            For an index reduction to be imposed two conditions must be met.  First, the player's second lowest tournament differential must be at least 3.0 lower than his current index.  Second, for players with six or more tournament rounds, the difference between the average of the two lowest tournament differentials and the player’s current index must be at least 5.5 to trigger an index reduction.

            To estimate the probability of an index reduction, we simplify the problem by estimating the probability of two tournament differentials being at least 5.5 below a player's current index. 

In equation form:

                                    CI - TD   > 5.5

Where,

                                            CI   = Current Index

                                           TD   = Tournament Differential

Then,

                                           TD   < .96 (X - .8 s) - 5.5

In the standard normal distribution, the distance (measured in standard deviations) to the nearest TD meeting the condition of the equation above is:

                                               D   = {X - ( 96 (X - .8s) - 5.5}/s = .04X/s + .77 + 5.5/s

Where,

                                               D  = Number of standard deviations from the mean 

                                                       differential to the nearest tournament differential 

                                                       meeting the inequality condition.

The probability of receiving an index reduction is inversely proportional to the value of the D. That is, the larger the value of D, the lower the probability of receiving a handicap index reduction.[3]       

            The probability of a player having a differential at least 5.5 below his current index is a function of his average differential, X, and the standard deviation of the distribution of differentials, s.  In a small sample of players, standard deviations were found ranging from 3.5 to 5.5.  It was also observed that standard deviations typically increase with a player's index.  Scheid has reported standard deviations of approximately 4.0.[4]  The probability of having an exceptional round (defined here as 5.5 below your current index) is shown in Table 1 below for players of different average differentials and for a range of standard deviations.

Table 1

Probability of an Exceptional Round 

Standard Deviation	Ave. Differential = 0	Ave. Differential = 20
3.5	.0096	.0051
4.5	.0233	.0150
5.5	.0384	.0274

            The probability of having an exceptional round on any one day is quite low.  If you play in enough tournaments, however, the probability of having two such rounds and incurring an index reduction is not negligible.  Table 2 presents those probabilities under our assumptions of the mean and standard deviation of the distribution of scoring differentials.[5]

            Table 2 indicates that a player has a good chance to receive an index reduction if he plays in a sufficient number of tournaments.  A player with an average differential of 20 and a standard deviation of 4.5 (a typical bogey golfer), for example, is estimated to have a 23 percent chance of a reduction if he plays in 60 tournaments.  It is likely that the USGA did not design this system for such heavy tournament participation.  Some clubs, however, are designating weekly couples events, intra-club matches, and bi-monthly club tournaments as "tournaments." By including minor weekly tournaments, the number of tournaments entered in one year can easily rise to above 60 tournaments per year.  In this case, a player can be penalized not because he is a sandbagger, but because he participated.

Table 2

Probability of Two Exceptional Rounds in N Tournaments 

Number of Tournaments(N)	Average Differential = 0			Average Differential = 20
	Standard Deviation			Standard Deviation
	3.5	4.5	5.5	3.5	4.5	5.5
10	.00	.02	.05	.00	.01	.03
20	.02	.08	.18	.00	.04	.10
30	.03	.15	.32	.01	.07	.20
40	.06	.24	.46	.02	.12	.30
50	.08	.32	.58	.03	.17	.40
60	.11	.41	.68	.04	.23	.49
70	.15	.48	.76	.05	.28	.57
80	.18	.56	.82	.06	.34	.65

            Almost all of the index reductions due to the random nature of scoring will be small.  In most cases it will only be one stroke.  The inability to distinguish between the ethical player and the sandbagger, however, may weaken the credibility of the index reduction procedure.[6]  To correct this deficiency the USGA could either: 1) increase the exceptional tournament performance limit for increased levels of play, or 2) narrow the definition of "tournament" to include only major events as measured by prize money, entry fee, or some other indication of importance.  The latter procedure is recommended, since the former allows the sandbagger to minimize his index reduction by competing in a large number of minor events.

             The problem with USGA policy is that it does not differentiate between a player who enters 6 tournaments and one who enters 40 tournaments a year.  When informed of this analysis, the USGA took the position that no problem was likely to exist.  Dean Knuth, USGA Director of Handicapping wrote:[7]

“The handicap reduction procedure was developed with the use of data from about one million golfers that use the USGA’s GHIN handicap service…The most active group of tournament players on GHIN are two Northern California women’s golf associations.  These most active tournament players average five tournament scores per year, and the top one percent average sixteen….For the present, we believe that taking the table to six t-scores is sufficient.”        

The war is off to an inauspicious start when the Commanding General does not recognize and obvious flaw.[8]  There was never any reporting on the success of  Sec. 10-3 (e.g., body counts of sandbaggers snared).  Sec. 10-3 was adopted to show the USGA was doing something, Whether that “something” was effective did not appear to be a concern. The USGA did try to improve the “reduction in index formula” over the years.  Unfortunately, those changes were also plagued with flaws as will be seen in Part II of the USGA’s War on Sandbagging-Shock and Awe.

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[1]USGA Handicap System, United States Golf Association, Far Hills, NJ, 1991, pp. 10-12.

[2]Scheid, F. J., "On the Normality and Independence of Golf Score, with Various Applications," in Science and Golf: The Proceedings of the First World Scientific Congress, Rutledge, Chapman, and Hall, London, 1990.

[3] Note that the higher handicap player has less chance to receive a reduction than the low handicap player if both have the same standard deviation in scoring.  This stems from the current index being based on differentials reduced by .96 while tournament differentials are not similarly affected.  It is not clear why the USGA included this bias against low handicap players in handicap system.

[4]Scheid, loc. cit.

[5]If we have N tournaments, the probability of having at least two exceptional tournaments is 1 minus the probability of having no exceptional tournaments and one exceptional tournament.  In equation form:

                        E = 1.0 - {(1 - p)N + N(1 - p)N-1(p)}

where,

                        E = Probability of at least 2 exceptional rounds in N tournaments

                        p = Probability of an exceptional round

[6]If clubs use different definitions of what is a "tournament," the equity of the handicap system among clubs would be lessened.  That is, some clubs may generate more index reductions simply because they designate more events as tournaments.

[7] Letter to author, February 19, 1992.

[8] It was only two years later, however, that the USGA had to correct the procedure by adding categories for up to 40 or more tournaments.  The change greatly reduced the probability of both the  ethical player and the sandbagger receiving an index reduction for exceptional tournament scores..