How Will the World Handicap System Affect Your Index?

A player’s Handicap Index is based his adjusted scores and the Course and Slope Ratings.  The USGA Course Rating is based on a model which predicts the better half of scores of the 288 competitors in the U.S. Amateur Championships.  The Bogey Rating is equivalent to the average of the better half of a bogey golfer’s scores under normal playing conditions.[1]  Under the World Handicap System (WHS) that will become effective January 1, 2020, however, a player’s Handicap Index will be based on the better 40 percent of a player’s differentials (i.e., best 8 of 20).  The size of any reduction in a player’s Handicap Index depends on whether the Course and Slope Ratings are changed to reflect the drop in the number of best scores used—i.e., the current Course Rating is an estimate of the performance of a scratch handicap when his best 10 scores are used and not his best 8 scores.

It is unlikely the Scratch and Slope Ratings will be changed to reflect the changes under the WHS.   The cost of changing USGA models and the Course and Slope Ratings at courses is prohibitive.   So what will be the effect on a player’s Index given the Course and Slope Ratings stay the same? Any change in the Slope Rating due to the WHS is negligible and is neglected here.[2]  The change in a player's Index will be determined by the standard deviation of the distribution of his scoring differentials

Assuming a normal distribution, the average of a player’s ten best differentials is .8∙σ below his mean differential. The average a player’s 8 best differentials is .95∙σ  below his mean differential.   A player's Handicap Index  under the current system is:

     Current Index = (Mean Differential - .8∙σ)∙.96 (.96 is termed the Bonus for Excellence)

Under the WHS, the Bonus for Excellence is eliminated.   The player's WHS Handicap Index is:

     WHS Handicap Index = Mean Differential -.95∙σ  

The change in the player's Index when the WHS is implemented is:

    WHS Index Change = WHS Index - Current Index  =  .04 Mean Differential -.18∙σ   


 The change in Handicap Index will depend upon a player's mean differential and standard deviation.  If a player had a mean differential of 10 and a standard deviation of 3.5, his Handicap Index would decrease by 0.23  As shown in the Table below, the impact on a player's Handicap Index would be small or negligible.  Given all of the other complexities of the WHS (Daily Handicap Index, Playing Condition Calculation based on weather conditions,  limits on Handicap Index reductions,  and changes in Equitable Stroke Control) a player may not notice a change in his Index nor understand the cause for the change if he did notice.  

Estimated Change in Handicap Index Under the World Handicap System

Mean Differential	Standard Deviation	Change in Index
0	3.0	-0.54
10	3.5	-0.23
20	4.0	-0.01
30	4.5	+0.39

A typical player’s reaction to all of this might be “Whatever.”  There are other changes in the offing--e.g., playing handicap, reduction for exceptional performance. These changes will be examined in future posts.

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[1] Stroud, R.G., Riccio L.J.,” Mathematical Underpinnings of the slope handicap system,” Science and Golf, E & FN Spon,  London, 1990, pp. 141-146.

[2]  The decrease in the Course Rating based on 8 out of 20 differentials is likely to be small.  To estimate the revised Course Rating assume a player’s differentials are normally distributed with a standard deviation of σ.   The average of a player’s ten best differentials will be approximately .8∙σ below his mean differential.  The average of a player’s eight best differentials will be approximately .95∙σ below his mean differential.  So to keep a “scratch player” a “scratch player” the Course Rating should drop by .15 ∙σ.   Assume the distribution of a scratch player’s differential has a standard deviation of 2.5.  In that case, the new Course Rating should be 0.4 strokes (.375 strokes rounded up)
Similarly, if the average Bogey player has a standard deviation of 3.5 strokes, the Bogey Rating should be reduced by 0.5 strokes.
The men’s revised Slope Ratings will then be:

              Revised Slope Rating = 5.381 ∙ ((Old Bogey Rating -0.5) – (Old Course Rating -0.4))
                                                     = Old Slope Rating – 5.381∙(-0.1)
                                                     = Old Slope Rating -1.0 (rounded up)

[2] The decrease in the Course Rating based on 8 out of 20 differentials is likely to be small.  To estimate the revised Course Rating assume a player’s differentials are normally distributed with a standard deviation of σ.   The average of a player’s ten best differentials will be approximately .8∙σ below his mean differential.  The average of a player’s eight best differentials will be approximately .95∙σ below his mean differential.  So to keep a “scratch player” a “scratch player” the Course Rating should drop by .15 ∙σ.   Assume the distribution of a scratch player’s differential has a standard deviation of 3.0.  In that case, the new Course Rating should be 0.5 strokes (.45 strokes rounded up)

Similarly, if the average Bogey player has a standard deviation of 4.0 strokes, the Bogey Rating should be reduced by 0.6 strokes.

The men’s revised Slope Ratings will then be:

              Revised Slope Rating = 5.381 ∙ ((Old Bogey Rating -0.6) – (Old Course Rating -0.5))

                                                     = Old Slope Rating – 5.381∙(-0.1)

                                                     = Old Slope Rating -1.0 (rounded up)