World Handicap System's Stroke Allocation Method: Part II

The World Handicap System (WHS) suggests the Stroke Index Allocation be determined by hole difficulty (Rules of Handicapping, Appendix E).  The WHS defines hole difficulty by the following equation.

              Hole Difficulty = Scratch Vale + Bogey Value – 2 x Par

As discussed in a previous post (USGA Covers-Up for the World Handicap System, February 12, 2021), the WHS has never defined how Scratch and Bogey Values are determined.  Nor has the USGA produced research indicating the accuracy of its methods in predicting difficulty as indicated by actual scores.  It has also been demonstrated that regional golf associations have made errors in implementing the WHS method (see World Handicap System’s Stroke Allocation Method: Part 1, January 25, 2021).  All of this indicates the WHS method is suspect and its validity questionable.

This post presents a preliminary analysis of the WHS method.  Because of the small sample size any conclusion cannot be definitive.  There is evidence the WHS procedure produces inaccurate and inconsistent results.  At a minimum, the WHS should review its recommendation with an eye to eliminating Appendix E in its entirety.

A sample of 41 rounds from two courses was used to assess the accuracy of hole difficulty estimates.  The players had course handicaps from 3 to 24.  The average handicap was approximately 14.  This is also approximately the average handicap of a scratch player and a bogey player.  Therefore, course difficulty determined from the sample was the average score on a hole minus par.  The rankings of the holes by using the sample were compared with that provided by the Southern California Golf Association (SCGA) using the WHS method.  The rankings are compared in the table below.

Table

Hole Difficulty

Course 1		Course 2
Sample	SCGA	Sample	SCGA
Front
9	9	8	8
5	5	9	9
6	7	4	1
1	1	6	7
2	3	2	6
3	6	3	4
7	8	7	3
8	4	1	2
4	2	5	5
Back
18	11	15	12
11	16	18	11
10	15	12	15
15	18	17	18
17	10	14	16
16	17	16	17
14	13	13	14
12	14	11	13
13	12	10	10

 

Most of the rankings on Course 1 are within two placements of one another.  The exceptions are holes 2 and 16.  At Course 2, holes 2, 4, and 11 differ by three or more placements.  The larger differences could be explained by either sample error or problems with the WHS method. 

While the exact WHS methodology is unknown, it appears to be largely a function of the yardage of the approach shot.  For example, the USGA assumes a scratch player drives the ball 250 yards at sea level and can hit a fairway shot 220 yards. On a 400-yard hole, the scratch player would have a 150-yard approach shot.  On a 500-yard hole, he would have a 30-yard approach shot.  The bogey player is assumed to drive the ball 200 yards and can hit a fairway shot 170 yards.  At the 400-yard hole he would have a 30-yard approach but would lie two.  On the 500-yard hole he would have a 130-yard approach. Let’s see if this explains any of the discrepancies in hole rankings.

Course 1, Hole 2:  The Sample rated this hole as the 5^th hardest on the front nine.  The SCGA rated it as the 9^th hardest.  As shown in the Appendix, the ratings by the SCGA are highly correlated with yardage—as it should be.  Hole 2 is only 125 yards.  Under the USGA’s assumptions, this is shorter than the approach shot the bogey player will have on any par 4 or par 5 on the front nine.  This is probably why the SGA rated it as the easiest.  The Sample ranking suggests the SCGA underestimated the obstacle value.  The tee shot on this hole is all carry over water.  The bailout area on the left of the green leaves a treacherous pitch to a hard green sloped toward the water.  The Sample ranking seems to be the better placement. 

Course 1, Hole 16:  The Sample rates this hole as the 6^th most difficult on the back nine.  The SCGA rated it as the 2^nd most difficult.  If the bogey player his a 200-yard drive, he would have a 152-yard approach shot (the effective distance is probably longer since the hole plays uphill.)  This is the longest approach shot (or par 3 tee shot) he would have on the back nine except for holes 11 and 15.  This would explain the SCGA’s high difficulty ranking.  The Sample ranks holes 18 and 17 above hole 16.  Both 18 and 17 both present obstacles (e.g., carry over water) that bring high scores into play.  Hole 16 does not have similar obstacles.  This indicates the SCGA d rating does not properly weight the obstacle value of a hole.  The Sample gives a more realistic estimate of hole difficulty.

Course 2, Hole 2:  This is a par 5 hole the SCGA ranks as the 8^th most difficult on the front nine.  The hole is only 442 yards.  The WHS assume the scratch player can reach the hole in two shots.  The bogey player should have a 72-yard approach shot.  It is no wonder the SCGA rated it so easy.  The Sample ranks this hole as 5^th hardest on the front nine.  The green is sloped toward the water on the right so holding the green is difficult for anything except a short iron.   A deep bunker on the left precludes playing it safe. Again, it looks like the SCGA has underestimated the obstacle value for this hole.

Course 2, Hole 4:  The Sample ranking is 3^rd most difficult.  The SCGA outs it at 6^th.   Since Sample ranking between the 3^rd and 6^th place is only 0.12 strokes, the difference in rankings could be due to sample error.

Course 2, Hole 11:  The SCGA ranks this hole as the 2^nd most difficult on the back nine, while the Sample ranking is 8^th.  The SCGA also ranks this hole as more difficult than the longer hole 15. SCGA must see obstacle values that are not experienced by the player.

The WHS rankings are also inconsistent.  The most difficult hole on Course 2 is Hole 12 with a difficulty rating of 1.29.  This is a par 5 with a yardage of 518 yards.  The other par 5 (Hole 17) on the back nine is ranked the easiest (difficulty rating of 0.67) and given the stroke allocation of 18. The only obvious difference between the two holes is Hole 12 is 25-yards longer.  Apparently, the SCGA believes this is the toughest 25 yards in golf.

In conclusion the WHS hole ranking procedure yields inaccurate, inconsistent, and curious stroke allocations.  There is no reason for the WHS to get into the stroke allocation business.  The mechanical tools given to the Ratings Committee are not adequate—whatever they may be.  Rating Committees do not have knowledge of the nuances of a hole that can make it more difficult.  Stroke allocations should be data driven and made by the Handicap Committee.  Given the electronic scoring being used at many courses, rating holes by difficulty would not be the laborious process it once was.  It is highly recommended that Appendix E of the Rules of Handicapping eliminate it current formula for stroke allocations.  

  

Appendix A 

Table A-1

Par 3 Difficulty Rating

Course 1			Course 2
Hole	Diff.	Yardage	Hole	Diff	Yardage
15	1.08	169	16	0.94	146
17	0.74	137	6	0.89	156
4	0.61	145	14	0.74	155
2	0.54	125	3	0.48	134
12	0.30	120

 

Table A-2

Par 4 Difficulty Rating 

Course 1			Course 2
Hole	Diff.	Yardage	Hole	Diff	Yardage
11	1.59	394	8	1.33	361
9	1.52	355	9	1.30	358
5	1.48	395	1	1.23	350
7	1.28	363	7	1.18	349
16	1.22	352	11	1.18	349
1	1.07	352	15	1.10	364
6	0.88	312	18	1.03	342
13	0.60	295	13	0.67	324
			10	0.38	280
			5	0.20	276

 

Table A-3

Par 5 Difficulty Rating

Course 1			Course 2
Hole	Diff.	Yardage	Hole	Diff	Yardage
3	0.90	498	12	1.29	518
8	0.87	507	17	0.67	493
18	0.80	486	4	0.50	473
10	0.77	493	2	0.27	442
14	0.59	488