Differential Scoring Method


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Differential Scoring Method Comparison

The PGA Tour Adjusted Scoring Average
Compared to
GRI's Differential Scoring Average^©

One of professional golf's highest honors, The Vardon Trophy, is awarded to the player with the lowest adjusted scoring average of the year. The award is based on an average of the adjusted scores a player accumulates from all the stroke-play events within the "official season" of the Tour. (See: PGA Tour Methods for Calculating the Adjusted Scoring Average)

The need to have an adjusted scoring average was sparked from an acknowledgment that there are numerous variables affecting a players score from week-to-week and even round-by-round. The major variables are:

The players performance
The differing par values of courses
The course condition and setup
The events played on multiple courses
The weather conditions
The quality or strength of the field
The size of the field

A non-adjusted scoring average that fails to take any of these variables into account might favor a player who avoids events with higher par values, extreme weather conditions, or may reward a player who fails to qualify for the top events against better competition.

To that end, the Tour uses the following method to adjust for those factors.

"Scoring Average is a weighted avg. which takes the stroke avg. of the field into account. It is computed by adding a player's total strokes to an adjustment, and dividing by the total rounds played. The adjustment is computed by determining the stroke avg. of the field for each round played. This avg. is subtracted from par to create an adjustment for each round. A player accumulates these adjustments for each round he plays in."

A cursory examination of the method describe above and detailed here seems to adequately adjust for those variables.

However, a closer examination of the PGA Tour Adjusted Scoring method reveals 2 major flaws.

FLAW #1

The first flaw relates to the Tour's use of the par value of a course in its calculations. Par values vary from event to event and the use of a par value in an adjusted score calculation can create aberrations in adjusted scoring average calculations.

A comparison of data from two actual 2004 events, illustrates how the PAR VALUE flaw in the Tour ASA methods skew results.

Week 18 - The 2004 Wachovia Championship - Joey Sindelar won the event at 11 under par in a playoff. 36 of the top 60 players were in the competition. The field averaged .368 strokes over par for 4 rounds of the event.

Week 19 - The 2004 EDS Byron Nelson - Sergio Garcia won the event with at 10 under par in a playoff. 34 of the top 60 players were in the competition. The field averaged .343 strokes over par for the 4 rounds of the event.

In a cursory examination of the results of the two events, it might be concluded that Garcia and Sindelar performed almost equally... perhaps Sindelar holding an approximate 1-stroke advantage for the 4 day event, or about .25 of a stroke per round advantage.

WRONG! . According to the PGA Tour Adjusted Scoring Average formula, Garcia outperformed Sindelar by more than 7 strokes for the event and 1.77 strokes per round. Why? Because Wachovia was played at par 72 while the EDS was played at par 70 and the PGA Tour adds its adjustment to the course par value.

The actual data from the two events is shown in EXAMPLE A below.

Example A - PGA Tour Adjusted Scoring Average (ASA) Error

	Wachovia Championship - Sindelar				EDS Byron Nelson - Garcia

Round	1	2	3	4	1	2	3	4
Players	156	154	72	72	156	153	80	80
Tot. Strokes	11293	11198	5170	5194	10912	10868	5531	5680
Field Average	72.39	72.71	71.81	72.14	69.95	71.03	69.14	71.00
Par	72	72	72	72	70	70	70	70
Adjustment	-0.39	-0.71	0.19	-0.14	0.05	-1.03	0.86	-1.00

	Wachovia 4 round adjustment			-1.05	EDS 4 round adjustment			-1.12
	Sindelar's 4 round total			277	Garcia's 4 round total			270
	Sindelar's adjusted total			275.95	Garcia's adjusted total			268.88
	Rounds Played			4	Rounds Played			4
	Sindelar's ASA:			68.99	Garcia's ASA:			67.22

If the PGA Tour's objective is to "even out" discrepancies caused by variations in par value of different courses, it obviously failed in the above real case scenario.

According to the Tour's adjusted scoring method, the 7 players who tied for 34th at the EDS with 3-under 277 totals, had a better scoring average than Joey Sindelar's winning total at the Wachovia Championship.

A more recent example of the Tour's ASA failing to represent a players relative results comes from a comparison of the 2005 Mercedes Championship and 2005 Sony Open in Hawaii.

Stuart Appleby won the Mercedes (par 73 course) with a 21-under total of 271. After week-1, Appleby led the Tours ASA with an adjusted average of 70.53. Appleby did not participate in week-2 at the Sony-Hawaii (par 70 course) which Vijay Singh won with an 11-under, 269 total.

After week-2, Appleby was #2 in the non-adjusted scoring average at 67.75. However, in the Tour's Adjusted Scoring Average, Appleby had dropped all the way down to a tie for 71st. Ranked ahead of Appleby were players such as Duffy Waldorf who shot 4-over par, 284, and finished tied for 64th at the Sony (his first event of the year). Even Kevin Stadler, and 13 other players WHO MISSED THE CUT at the Sony (+3, 143), had a better ASA (70.17) than Appleby's 70.53.

Flaw #1 - The Solution: Remove PAR From the Calculation by Using the Scoring Differential Method

It takes only a slight change in the calculations above to fix the error caused by the current formula. The change would be to use a scoring differential method instead of an adjustment to par.

In the scoring differential method the field scoring average is calculated exactly as before. The difference in this method is that a comparison is made between the PLAYERS actual scores to the FIELDS scoring average. The par value of the course is not a factor.

The actual data from the same two events from the ASA example above (Wachovia and EDS), is used in the differential method example below.

Example C - GRI's Differential Scoring Method (DIF)

	Wachovia Championship - Sindelar				EDS Byron Nelson - Garcia

Round	1	2	3	4	1	2	3	4
Number of Players	156	154	72	72	156	153	80	80
Total Strokes	11293	11198	5170	5194	10912	10868	5531	5680
Field Average	72.39	72.71	71.81	72.14	69.95	71.03	69.14	71.00
Player's Score	69	69	70	69	66	68	65	71
Player's Differential	-3.39	-3.71	-1.81	-3.14	-3.95	-3.03	-4.14	0.00

	Sindelar's 4 round differential			-12.05	Garcia's 4 round differential			-11.12
	Rounds Played			4	Rounds Played			4
	Sindelar's average DIF			-3.01	Garcia's average DIF			-2.78

It is GRI's position that the differential calculations shown above more accurately reflect the similar performance of the two players in those two real events.

FLAW #2

The second major flaw is due to the way the PGA Tour calculates scoring averages in events played on multiple courses. The current ASA method of calculation can result in players shooting the exact same score over 4 or 5 rounds, in the same event, to have differing adjusted scoring averages.

A comparison of data from the 2005 Buick Invitational illustrates how the MULTIPLE COURSE flaw in the Tour ASA methods skew results.

2005 Buick Invitational - Luke Donald , Charles Howell III and Tom Lehman tied for 2nd place in the event with identical scores of 275. One would think that all three would have the same adjusted scoring average for the event.

WRONG! . According to the PGA Tour Adjusted Scoring Average formula, Lehman outperformed Donald and Howell by more than 1.5 strokes for the event and .383 strokes per round. Why? Because the first two rounds of the Buick is played over 2 courses... the North and the South at Torrey Pines. Lehman played round 1 on the North Course... while Donald and Howell played round 1 on the South.

The PGA TOUR adjusts a players score on a round-by-round basis on a course-by-course basis. What it means is Donalds' and Howell's round 1 scores were compared ONLY with the players who played on the South Course in Round 1. Lehman's round 1 North course score was compared only with round 1 North course scores. The reverse was true as each player switched courses for play in round 2.

The problem arises due to the fact that the scoring averages for both the North and South courses varied from day to day. Both courses played a bit more difficult in round 2. Since the players scoring averages are based only against the players playing on a course on a particular day... the adjusted scoring averages are different.

The following example (using only Donald and Lehman) illustrates the comparison between Lehman and Donald for the 2005 Buick Invitational uses the actual scoring data from the event. (NOTE the differing adjustments for round 1 and 2... rounds 3 & 4 are constant as all players played the South course. )

Example C - PGA Tour Adjusted Scoring Average (ASA) Error

	Buick Invitational - Luke Donald				Buick Invitational - Tom Lehman

Round	1	2	3	4	1	2	3	4
Course	South	North	South	South	North	South	South	South
Par	72	72	72	72	72	72	72	72
Players	78	73	81	81	78	75	81	81
Tot. Strokes	5649	5059	5920	5917	5426	5527	5920	5917
Field Average	72.423	69.301	73.086	73.049	69.564	73.693	73.086	73.049
Players Scores	68	67	67	73	62	67	73	73
Adjustment	-0.423	2.699	-1.086	-1.049	2.436	-1.693	-1.086	-1.049

	PGA 4 round adjustment			0.140	PGA 4 round adjustment			-1.393
	Donalds' 4 round score			275	Lehman's 4 round score			275
	Donalds' adjusted score			275.140	Lehman's adjusted score			273.607
	Rounds Played			4	Rounds Played			4
	Donalds' ASA:			68.785	Lehman's ASA:			68.402

Note: The PGA's ASA adjustment on the above event was .137 and (1.379) vs the .0140 and (1.393) we calculate.

Flaw #2 - The Solution: Combine Scores played on a specific course... regardless on which day the course is played.

Using the example above combining the scoring averages from the round's 1 & 2 North course together and separately combining the scoring averages from rounds 1 & 2 on the South Course together would yield an adjusted scoring average of 68.595 for Donald, Howell and Lehman.

As the PGA Tour acknowledged that each performed equally by paying all three the same $358,400 in prize money, we believe they should also acknowledge they scored the same, adjusted or otherwise.

Conclusion

Reviewing the major variables discussed at the beginning of this article at least 5, and arguably all have been accounted for or are not a factor using the differential method. Below is a comparison of the Tour's current Adjusted Scoring Average (ASA) method vs. the Differential (DIF) method in accounting for those variables.

		DIF	ASA
•	The players performance Both the current method and the differential method account for the players performance as they compare actual results of the player against the field	Yes	Yes
•	The differing par values of courses The differential method removes a comparison of player results to par from the calculation, while it is a key element of the current adjusted scoring method.	Yes	NO
•	The course condition and setup As both methods are calculated on a round by round basis and against the field competing, they both adjust for these variables. In a single round, all the players (usually) play the same course and thus are faced with the similar course conditions and setup.	Yes	Yes
•	The events played on multiple courses The ASA adjustment allows for 2 players playing the same event and scoing the same to have differing ASA's. The DIF method makes a round-by-round exception for multiple course events which guarantees the players will have the same adjustment.	Yes	NO
•	The weather conditions As both methods are calculated on a round by round basis they both account for varying weather conditions that may change from day to day. However, neither method can account for changing conditions within a single day.	Yes	Yes
•	The quality or strength of the field While neither method adjusts for the strength of field directly, the statistical data indicates that the strength of field is not a significant factor one way or the other. In addition, the very nature of the Tour "self-adjusts" for this factor. Example: Players with better scoring averages are more likely to rank higher in earnings and world and Tour rankings, thus be invited to play in more of the top events against the tougher fields.	???	???
•	The size of the field & no-cut events Neither method adjusts for the size of the field or no-cut events directly. The statistical data for both methods does indicates a bias in favor of players finishing high in events with larger fields, but against players finishing low in the same events. In the "short field" or no-cut events, the reverse is true.	???	???

While no formula is perfect in adjusting for every factor that could affect a players scoring average, the objective is to remove as many of the variables as possible. The key to the DIF method is the realization that the par value of a course being played in any particular week is insignificant and thus should NOT be used in creating an adjusted scoring average.

Arriving at a final Differentially Adjusted Score

Another difference in the methods is that the Differential Method does not create an actual adjusted score, instead it creates a statistic that would likely run in the 2.00 to 3.00 range for the leader. The current Adjusted Scoring Average "looks" more like a number that a golf fan can relate to as it usually runs in the 68.00 to 69.00 range.

To overcome this, the Differential Method results are subtracted from a value of 71.50. This number was selected by comparing the average par value of all courses played over the past 10 years. During that period the average par value for all courses played in a stroke play event during the year has hovered within .25 of 71.5. (trending lower) The 2004 average par value for all courses used in stroke play events is 71.36.

It is important to note that the actual number chosen to subtract the differential from does not matter. It could be 71, 72 or any other number; the statistical difference between the players would not change.

Through the end of 2004, Vijay Singh winner of the Tour Adjusted Scoring Average , had an ASA of 69.19. Singh's average differential at year end was -2.54 or a scored adjusted 68.96. While the application of the differential to 71.5 creates a result that appears similar to the current PGA Tour system, it does NOT skew the results as it is applied equally to all players.

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