Tuesday, July 21, 2020

World Handicap System Penalizes the Honest Player

Handicap golf has always been abused by players manipulating the system to gain a higher handicap than deserved.  The USGA tried a precision strike against such players with it “Reduction of Handicap Index Based on Exceptional Tournament Scores (Sec. 10-3).” Players who had two exceptional scores could have their Handicap Index reduced.   The USGA’s effort, however, was ineffective as any penalty could be easily avoided by the astute sandbagger.  The USGA, apparently admitting defeat on its war on sandbaggers, eliminated this section with the adoption of the World Handicap System (WHS).

The WHS took a different approach.  Instead of concentrating on tournament scores, it decided to penalize all exceptional scores whether in or out of competition (Rule 5-9 of the WHS).  This was carpet bombing without regard to civilian casualties and hoping a sandbagger might be among the injured.

Before assessing whether Rule 5-9 serves any legitimate purpose, it is important to understand how it works.  As an example, assume a player has a 16.0 Handicap Index.  For simplicity further assume par on the course is 72 and the Slope Rating is 130.  This gives the player a course handicap of 18.  Now assume the player shots an 81 for a scoring differential of 7.8.  The difference between his current Handicap Index and his exceptional differential is 8.2 (16.0 – 7.8).  Since the difference is greater than 7.0, the player is subject to an exceptional score reduction. 

Under Rule 5.9, a reduction of -1.0 is applied to each of the player’s most recent score differentials.[1]   Even though the WHS consider the players 81 an exceptional score, for handicap purposes he is credited with an even more exceptional score of 79.8 (i.e., a scoring differential of 6.8).   This is like radar catching you speeding at 65 mph and the officer writing you up for 70 mph.  The WHS has not published any defense of this unusual punishment,

The actual effect on a player’s handicap will depend upon the distribution and placement of his eight best differentials.  Assume the player had the following 8 low differentials in his file before the exceptional score: 11.0, 14.0, 15.0, 16.0, 16.0, 17.0,18.0, 21.0.  The table below shows the player’s Course Handicap would be reduced by three strokes under Section 5-9 and one stroke if the Section was not applied.  In general, the reduction with Sec.5-9 will initially be one or two strokes below what player’s handicap would be without Section 5-9. 


Handicap With and Without Rule 5.9 Penalty 


With Penalty

Without Penalty

Low Differential



Total of Next 7 Differentials



Handicap Index



Course Handicap




The question never answered by the WHS is why an exceptional round out competition should be penalized?  Here are three possible reasons the USGA might put forward:

1.       Scoundrel Theory -The USGA assumes an exceptional score indicates the player is a scoundrel and deserving of punishment.  Assuming a normal distribution of scoring differentials, a player with  standard deviation of 3.0  would have a 1 in 333 chance of making his exceptional score or better.   While such exceptional scores would be rare, they are not evidence of cheating beyond a reasonable doubt.  It would be like assuming the winner of the Powerball Lottery must have cheated since the odds against winning are astronomical.   It is also clear from the USGA’s own research that high-handicap players are forty-two times more likely to have the exceptional score discussed above than a low-handicap player.[2]  Therefore, Rule 5-9 continues the USGA tradition of discriminating against the high-handicap player.

2.       WHS Failure -Another defense of Rule 5-9 would be an exceptional round proves a player’s current Handicap Index is not a good estimate of his potential and therefore the reduction is justified.  The penalty, however, is reduced overtime as new differentials are not reduced by -1.   If a player enters three scores a week, the penalty will disappear within 7 weeks.  Unlike the Reduction in Index Based on Exceptional Tournament Scores which could last a year, a Rule 5-9 only lasts a short period.  Which raises the question, if an exceptional score indicates a player’s Index should be lower, why is the penalty of such short duration?

3.       Anti-sandbagger Tool -The USGA could argue Rule 5-9 is another weapon in its war on sandbaggers.  This is not a convincing defense of the Section since it will have no impact on sandbaggers.   The unethical player knows enough to dump a shot in the lake coming in to avoid any penalty.  The only one affected is the honest player who is excited to post a low score.  Unfortunately, he is collateral damage of an unwise policy created by the technocrats at the USGA and R&A. 

Rule 5-9 can have a consequence that is not good for the game.   If a player is having a hot round, he should not have to be worried about a Rule 5.9 penalty. The handicap system should encourage those to go as low as they can.  If his playing partners give him a three-footer to speed up play, should he insist on putting to protect against a penalty. If he misses, he might be viewed as a sandbagger.  Better to take the penalty than hurt his reputation he may reason.  A player should not be put in such a predicament.

So how did Rule 5-9 make into the WHS?    The WHS is not the result research, but of compromise among committee members.  The sections on the treatment of exceptional scores are similar to the old Golf Australia Handicap System.  Under that system, a reduction for an exceptional score was imposed at the discretion of the player’s club.  That seemed fair, but the WHS did not want to give primary authority to clubs.  The WHS first delivers a few penalty whacks and then allows the club to override if it feels the WHS was unjust.  Historically, clubs are hesitant to act for or against members.  If a member had a great round not in competition, the club’s inertia would lead it to take no action.   If the Rule 5-9 penalty were imposed, a club would take the position that this is the result of the WHS and without convincing evidence otherwise it must stand. 

In its effort to make it look like it is tough on sandbaggers, the WHS has only imposed collateral damage on the honest player.   Thankfully, the damage is short lived, but has a lasting consequence on the game.  The WHS states the player has the responsibility to make the best score possible on each hole.[3]   Rule 5-9, however, discourages a player to live up to this responsibility and that is too bad.

[1] If the difference between a player’s Handicap Index and his scoring differential is between 7.0 and 9.9, the player receives a score reduction of -1.  Differences greater than 9.9 receive a score reduction of -2.  There are also other sanctions placed upon the player for having an exceptional round. If the player’s low index is now 13.4,  under the “soft cap” procedure, a player receives only 50 percent of any increase above in his Handicap Index over 16.4 See Rule 5-8 of the Rules of Handicapping).  For example, if his differentials compute to an 18.0 Handicap Index, the soft cap procedure would reduce his Index to 17.2.   The “hard cap” limits in increase to five strokes over his Low Handicap Index or 18.4

[2] The USGA Handicap System 2016-2017, Appendix E. A 0-4.9 Index player has a one in 8795 chance of having a net handicap differential of 8.00 or better.  The 30.0 Index player has a one in 209 chance.

[3] Rules of Handicapping, Appendix A, USGA, p. 79.

Saturday, July 4, 2020

Eliminating the Blind Draw with Mr. Par

This blog has previously examined ways to eliminate the blind draw (Eliminating the Blind Draw,” October 22, 2019) when threesomes competed against foursomes. The post concluded giving the threesome a phantom player who always scores par (Mr. Par) led to equitable competition if the Course Rating and Par were not too far apart.  Since the publication of the post, the World Handicap System has made par and not the Course Rating the target score of the handicap system.  This eliminates the caveat about par and the Course Rating mentioned in the previous post.

The previous post was based on theory and urged playing groups to provide actual tournament results to verify the equity of using Mr. Par.  One group, playing two-bests balls of four, has used Mr. Par over the season.  The question addressed here is whether actual tournament results match up with what theory suggests?

What does theory suggest?  Let’s assume you are the captain of a threesome and have the choice of selecting a handicap player at random or taking Mr. Par.  You realize the handicap player will only have a net score below par twenty percent of the time.[1]  If the game was aggregate four- ball, Mr. Par would be the clear choice.  In two-best balls of four, however, the handicap player may contribute some net birdies while Mr. Par will not. If you take the handicap player, the standard deviation of the team score will be higher than with Mr. Par.   That means you will have a better chance of coming in first, but also a better chance of coming in last.  Since you are not risk averse, you opt for the handicap player.  Let’s look at the data to see if you made the right choice.

Empirical Test - A group plays two-best balls of four format and assign Mr. Par to the threesome.  At the end of the season, the mean score and standard deviations of threesomes and foursomes are computed (Team scores are presented in the Appendix):

              M3 = Mean team score of threesome relative to par = -12.09

              S3 = Standard deviation of threesomes scores = 3.49

              N3 = Sample size of threesomes = 23

              M4 = Means team score of foursomes relative to par = -12.67

              S4 = Standard deviation of foursome scores = 4.77

              N4 = Sample size of foursomes = 101

The null hypothesis is that the difference in the true means of each distribution (threesomes and foursomes) is zero.  The alternative hypothesis is the difference is not zero.  These hypotheses constitute a two tailed test.  The null hypothesis will be rejected if the absolute difference between the sample means is too large. 

The standard error of the sampling distribution is given by:

              SE = sqrt((S32/N3) + (S442/N4)) = 0.87

The t statistic is then: 

              t = (M4 – M3)/SE = (-12.09 – (-12.67))/ .87 = 0.67

The t-Distribution Calculator for 51 degrees of freedom shows the probability of the t-value less than -.067 and greater than 0.67 is 0.50.[2]  Therefore, the null hypothesis that the difference between the two means (threesomes and foursomes) is zero cannot be rejected.

If the threesome could deduct one stroke from its score, the t statistic would be 0.48 ((12.67-13.09)/0.87)).  The probability of a t-value less than -.48 and greater than 0.48 is .68.  Due to the small sample size it would be difficult to choose between giving a threesome zero or minus one stroke on statistical grounds.  It is clear, however, that either of these two options would be equitable.

Other Considerations – The smaller standard deviation for threesomes indicate it is more difficult for a threesome to go low. A look at the winners of competitions bears this out.   The data shows 14 competitions where threesomes competed against foursome.  The table below presents the probability of each type winning assuming threesomes and foursomes had an equal chance.


Probability of Winning


The table shows the threesomes are expected to win four times and foursomes 10 times.  Threesome had two outright firsts and one tie for first.  Had threesomes been given an additional stroke, they would have had three wins which is close to what was predicted.  As expected, threesomes do not go as low as foursomes, but they also do not go as high.  Threesomes only had one tie for last. 

Whether the threesome captain made a good choice in selecting the handicap player depends in part on the payoff structure.[3]  If the payoff structure pays a winning team the same regardless of its composition, a threesome’s smaller chance of winning is offset by a 33 percent larger payoff per player.  Even if the payoffs are per player, a threesome with Mr. Par may have a better chance of being in the money even though they do not win.  The examination of expected payoffs is beyond the scope of this study, but a cursory review indicates if payoffs are per man, neither threesomes nor foursomes have a significant advantage.  

In formatting a competition, there should be no team that realizes it has little or no chance before teeing off (e.g., a team of three low handicappers and Mr. Par in a two-best ball of four game).  If in the game under consideration, the handicaps among teams are evenly spread, threesomes with Mr. Par (possibly with a stroke deduction) and foursomes should have an equitable competition.  Importantly, this conclusion should hold for all courses regardless of the Course Rating



Team Scores

Three -10 -10-10  -4-15-14
Three   -9    -14-14
Three   -7      
Four-16 -13 -8-11-11-5-8 
Four-10 -13 -7-9-10-3  
Four     -8-7-3 



Three-13 -16 -14-19-14 -12-17
Three-10 -14 -14 -11   
Three    -9     
Four -10-11-9-12-14 -14-11-14
Four -8-9-7 -14 -14 -12
Four   -7 -11 -11  
Four   -4   -10 

[1] Under the USGA Handicap System (UHS), a player had a net score below the Course Rating about 20-25 percent of the time.  Under the World Handicap System (WHS), a player’s eight best score are used in calculating his Index instead of his ten best in the under the UHS.  This lowering of a player’s Index under the WHS is offset by the elimination of the Bonus for Excellence (.96).  The WHS now makes “par” the standard of performance and not the Course Rating.  Therefore, a player will have a net score of par or better approximately twenty percent of the time.

[2] The degrees of freedom is estimated by:

              DF = (S32/N3 + S42/N4)2/ ((S32/N3)2/(N3 -1)) +( (S42/N4)2/(N4 -1)) = 57

[3] Weather is also a factor.   If the weather is bad, most players will have net scores over par, which would make the consistent Mr. Par a better choice.