## Tuesday, January 15, 2013

### The USGA’s “Bonus for Excellence” Ruse

The United States Golf Association (USGA) states the “bonus for excellence is an incentive for players to improve their game that is built into the USGA Handicap System.  It is the term used to describe the small percentage below perfect equity (emphasis added) that is used to calculate a Handicap Index.”[1]  The bonus for excellence (BFE) is currently set at .96.

Dean Knuth, former Senior Director of Handicapping for the USGA, described another purpose of the BFE when he wrote in Golf Digest:

“Historically, the USGA wanted to reward the accomplishments of better players…For a six-stroke difference in handicaps the better player gains a one-shot advantage (due to the BFE) and should win 60 percent of the matches.”[2]

The argument of this paper is that the BFE is neither an effective incentive to improve nor a reward for superior performance and should be eliminated from the USGA Handicap System.

To demonstrate the ineffectiveness of the BFE, we examine matches between a scratch player and players of various ability.  As a measure of ability we use the average of a player’s ten best differentials (ATBD).  Table 1 presents the perfect equity handicap(PE), as defined by the USGA, and the handicap using the BFE(BE) for players with ATBDs varying from 35.0 to 0.0.  If a player’s ATBD is 35.0 (Slope Rating = 113), the BFE reduces his handicap by one-stroke. This is termed the Bonus for Excellence Penalty shown in column 4 of Table 1.   Assume the player improves to the point where his ATBD is 15.0.  The BFE reduces this player’s handicap by one-stroke. In essence, even though he has improved dramatically, he is no better off in his match against a scratch player.  In both cases, he is getting one less stroke than the USGA considers perfect equity.

Table 1

Bonus for Excellence Penalty (Slope Rating = 113)

 Avg. of 10 Best Differentials(ATBD) Perfect Equity Handicap(PE) Bonus for Excellence Handicap(BE) Bonus for Excellence Penalty 35.0 35 34 -1 30.0 30 29 -1 25.0 25 24 -1 20.0 20 19 -1 15.0 15 14 -1 12.0 12 12 0 10.0 10 10 0 5.0 5 5 0 0.0 0 0 0

Table 1 also shows improvement does not improve his competitive position among his fellow high-handicappers.  The difference between the PE and BE is the same for all players with ATBDs between 35.0 and 13.0—i.e., approximately 59 percent of players with a USGA index.[3]

Table 1 also reveals that Knuth’s assertion that the BFE provides the better player with a one-shot advantage when handicaps differ by 6-strokes is in error.  Without the BFE, a 35-handicap would receive 20 strokes from a 15-handicap player.  This is the same number of strokes he receives when the BFE is applied.  Knuth would be roughly correct under the old system when the BFE was .85.[4]  The BFE was changed from .85 to .96 in 1976, however, some 32 years before Golf Digest published Knuth’s remarks.

The incentive effect for players with indexes of 12.0 and below is also negligible.  Those with integer ATBDs between 0.0 and 12.0 will have identical PE and BE handicaps.[5]  So the only real incentive created by the BFE is for a player to become less than a 12.0 index.   For a great number of players this is a difficult, if not an impossible task. Therefore, the BFE cannot be considered an incentive for most golfers.  It is just a penalty assessed to the high-handicap player in competition against low-handicap players.

In some cases, the BFE is actually a disincentive for improvement.  Table 2 shows the difference between the PE and BE for a course with a Slope Rating of 130.  The BFE penalty does not systematically decrease as a player’s ATBD decreases. For example, as a player improves his ATBD from 35.0 to 30.0 he is at an even greater disadvantage with the scratch player. He now must play at two strokes below his PE handicap rather than one.

Table 2

Bonus for Excellence Penalty (Slope Rating =130)

 Average of 10 Best Differentials Perfect Equity Handicap(PE) Handicap With Bonus for Excellence(BE) Bonus for Excellence Penalty BFE Penalty When  Applied to PE 35.0 40 39 1 2 30.0 35 33 2 1 25.0 29 28 1 1 20.0 23 22 1 1 15.0 17 17 0 1 10.0 12 11 1 0 5.0 6 6 0 0 0.0 0 0 0 0

The peculiar pattern in BFE penalties is caused by applying the BFE to a player’s ATBD rather than to his handicap.  A systematically decreasing BFE penalty could be constructed by calculating a player’s handicap as the integer value of the product of his perfect equity handicap and the BFE (see Table 2, Column 5).[6]  This would involve changing the method for calculating a player’s index and recalibrating all handicap conversion tables.  This would require a great deal effort with only a negligible impact on the equity of competition and is not recommended.

The total elimination of the BFE, however, is recommended on several grounds.  First, there is no theoretical or empirical justification for its existence.  To argue it provides an incentive to improve is a ruse, and not a very clever one.  Second, it isn’t even an effective reward for the good player.  It is not uncommon for a player with a single digit ATBD to get a 1-stroke BFE reduction, while his high-handicap competitor does not.[7]  Third, no other sport gives a built-in edge to the better player.  (Did Secretariat carry less weight than his rivals?  Do the Charlotte Bobcats spot the Miami Heat 4 points?).  The USGA should be about ensuring equitable competition and not about giving an edge to a group of players it deems more worthy.

The BFE is an anachronism left over from an era when rigorous thought was not always applied in formulating the handicap system.  It is time—actually in 2016 when the USGA Handicap System is revised—for the BFE to go the way of the stymie.

[1] The USGA Handicap System, 2012-2015, USGA, Far Hills, NJ, p. 77.
[2] Knuth, Dean, ”Handicaps,” Golf Digest, September 2008  as reprinted at www.popeofslope.com.
[3] Men’s USGA Handicap Index Statistics, www.usga.org/articles_resources?Men-s-USGA-Handicap-Indexes.
[4] We say roughly correct because of differences caused by rounding.  A scratch player gains a 1-stroke advantage against a 4-handicap (i.e., only a for 4 stroke difference) who is reduced to a 3-handicap by the BFE.  A 4- handicap and a 10-handicap (i.e., a 6 stroke difference) remain at parity as both are reduced 1-stoke by the BFE. (Note: These calculations assume the players had integer ATBDs and a Slope Rating of 113).
[5] The BFE does shift the breakpoint between handicaps.  For example, without the BFE players with ATBDs between 7.5 and 7.8 are 8-handicaps (Slope Rating =113). When the BFE is applied, these players become 7-handicaps. The beneficiary is the player with a 7.9 ATBD who will now get a stroke from the players with an ATBD between 7.5 and 7.8. In this case, the BFE rewarded the player with less ability.
[6] This would be similar to the procedure for calculating a player’s handicap in four-ball stroke play (i.e., the percentage allowance is applied to a player’s handicap).
[7] There are cases where a player with an ATBD less that 10.0 would receive a BFE reduction from his perfect equity handicap.  For example, assume a course with a Slope Rating of 80.  Players with ATBDs of 1.0, 2.0, 3.0, 4.0, 6.0, 7.0, and 9.0 do not get a BFE reduction in handicap.  Players with ATBDs of 5.0 and 8.0 do get a BFE reduction of 1- stroke.  Players with ATBDs of 19.0 and 20.0 would not get a BFE reduction.  Better players are less likely to get a reduction, but the sporadic nature of the reduction is another argument for abolishing the BFE.