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