## Monday, July 27, 2015

### Estimating a Player’s Index under Various Handicap Systems

There is no doubt handicap systems differ from country to country.  The question is “How big are those differences?”  To examine this question, the scoring records of six United States players were selected.    Using these scores, an estimate of a player’s Index was made for 5 of 6 major handicap systems—data limitations prevented using the sixth system.  The term “Index” is used throughout even though it is peculiar to the United States Golf Association (USGA) System.  Index as used here represents each system’s measurement of a player’s ability. The broad outlines of each handicap system and the assumptions made in estimating the player’s index are detailed below:

USGA Handicap System – Both competitive and non-competitive rounds are allowed.  Scores are not adjusted based on playing conditions.  A player’s handicap differential is his gross adjusted score minus the course rating multiplied by the ratio of 113/Slope Rating.   The maximum score a player can take on a hole is determined by his handicap (e.g., a handicap between 10 and 19 is allowed to take a 7).  A player’s Index is the average of his ten best differentials multiplied by .96 and truncated to one decimal.

Council of National Golf Unions (CONGU) – Only rounds made in competition are used.  The USGA’s Slope Rating system is not used.  Course Rating can be adjusted based on the scores of players.  For various levels of Indices, a buffer zone is defined (e.g., 0 to 2 strokes above the Course Rating).  If a player’s net score falls within the buffer zone, his Index is not changed.  If his net score is above the buffer zone, 0.1 is added to his Index.  If his net score is below the Course Rating by n-strokes, his Index is reduced by n times the adjustment factor for his Index level (e.g., the adjustment factor is 0.2 for players with an Index between 5.5 and 12.4).
In estimating a player’s CONGU Index, the USGA Course Rating rounded to the nearest integer was used.  It was assumed the rounds were played under normal conditions so there was no adjustment to the Course Rating.  A player’s CONGU Index was assumed to be his USGA Index on the date of the oldest of his 20 scores.  The player’s handicap was his CONGU Index rounded to the nearest integer.   Starting with his oldest score, the player’s net score was calculated.  If the net score triggered an adjustment, the player’s Index was changed and a new handicap calculated.  This procedure was used for all 20 scores.

Australia – All rounds played under the Rules of Golf are used.  Australia uses the USGA Course and Slope Rating System but rounds the Course Rating to the nearest integer.  The maximum score that can be taken on a hole is a net double bogey.  For handicap purposes, a Daily Course Rating (DCR) is estimated.   A player’s differential is based on his Stableford score and is calculated as follows:
Course Par plus Handicap minus (Stableford Points minus 36) = A
A minus the DCR = B
B multiplied by 113 = C
C divided by the Slope Rating = D
D (rounded to one decimal place) = Differential

The Australian Index is based on the average of a player’s 8 best differentials out of 20 multiplied by .93.  It is assumed rounds were played under normal conditions and differences in posted scores adjusted for stroke control are minimal.  Australia’s differential calculation is approximately the same as in the USGA system.   Therefore, the estimate of the Australian Index was found by using USGA differentials, taking the average of the eight best differentials, multiplying by .93, and truncating the result to the first decimal.

South Africa – All rounds played under the Rules of Golf are used.  Currently, South Africa has not adopted the Slope Rating system.  The Course Rating is expressed as an integer.  Maximum score on any hole is 2 over par except where a player has two handicap strokes on a hole in which case the maximum score allowed is 3 over par for that hole.  The differential is the player’s adjusted gross score minus the Course Rating.   A player’s Index is the average of his 10 best differentials out of 20 multiplied by .96.  If a player has two exceptional scores (i.e., a net score of 3 or more below the Course Rating), his Index is based on his best eight scores.
In estimating the South African Index, it was assumed the South African Course Rating was the USGA Course Rating rounded to the nearest integer.   Differences in posted scores due to differences in stroke control were assumed to be minimal.

Argentina – Only scores from competitions are used.  Argentina has a Course Rating system loosely based on the USGA’s system.   There is no Slope Rating.  There is no equitable stroke control.  The handicap differential is the player’s gross score minus the Course Rating.  A player’s Index is the average of a player’s 8 best scores out his last 16 scores multiplied .87.
In estimating the Argentina Index, it is assumed the USGA Course Rating is equivalent to the Argentina Course Rating.  Differences due to different stroke control procedures were assumed to be minimal.

European Golf Association (EGA) – The EGA has adopted the USGA Course and Slope Rating System.   A player’s Index is based primarily on rounds in competition.   A player’s handicap is his Index multiplied by 113/Slope Rating + Course Rating – Par rounded to the nearest integer.  The Index adjustment process is similar to the CONGU system.   A score below a player’s Stableford buffer zone leads to a .1 increase in a player’s Index.  A Stableford score n-points above the buffer zone leads to a decrease of n times the adjustment factor for his Index level (e.g., .2 for a player with an Index between 4.5 and 11.4).  Based on score in the competition the buffer zone can be shifted up or down.  Because par is not known and the uncertainty in converting stroke play scores to Stableford scores, the player’s EGA Index is not estimated.

The estimated Index for a selection of players is shown in the Table below.  The Australian Index is usually the lowest since it is based on a player’s 8 best scores as opposed to his 10 best in the USGA system.   South Africa is typically the highest Index since differentials are not adjusted by the Slope Rating.  If all scores were at a course with a Slope Rating of 125, for example, the South African Index would be approximately 11 percent higher than the USGA Index.

Table
Estimate of Player Index by Major Handicap System

 System Player 1 Player 2 Player 3 Player 4 Player 5 Paler 6 USGA 7.3 12.9 9.9 4.4 6.4 19.0 CONGU 8.3 14.2 9.2 5.2 6.7 19.6 Australia 6.6 11.9 9.2 3.7 6.0 18.1 South Africa 8.5 14.7 11.8 4.8 7.2 20.5 Argentina 7.5 12.9 10.3 4.4 7.2 19.0 EGA NA NA NA NA NA NA

In general, the USGA Index is within ±1 of the Index in the other systems.  Such discrepancies, while not negligible, do not create significant inequities.  One remedy would be a Worldwide Handicap System (WHS). But there are less expensive remedies available.  Australians could have their Index increased when playing in the United States.  South Africans playing in the United States would not be permitted to use the Slope Rating to calculate their handicap since the Slope Rating was not used to calculate their Index.  These ad hoc solutions for what is social golf make more economic sense than spending millions on a WHS to correct a rare and minor injustice.