Wednesday, July 24, 2013

One Set of Stroke Allocations is Enough: A Note on Designing Scorecards

            In a perfect world a scorecard would have a place for your name, 18 numbered squares where you would record your score, yardage for each hole, par, and a set of stroke allocations specifying where handicap strokes are to be taken.  The course and slope rating should be on the card, but I would put them on the non-scoring side of the card.  The less I am reminded of the USGA Slope System during a round, the better for my piece of mind. 

            It would also be nice to ban all advertising from the card.  I can at least tolerate this clutter, however, in the pollyannish belief that advertising lowers my green fees.

            This is not a perfect world, however, and growing number of scorecards have taken on the look of a random number table as different handicap stroke allocations are assigned to each set of tees.  The problem has been exacerbated by the trend toward more tees to accommodate players of varying abilities. 

            To add these additional rows of numbers for stroke allocations, some courses have simply increased the size of the scorecard.  Now you need origami lessons to fold that big sucker to fit in your back pocket.  Of course the scorecard is not designed to fit in your pocket, but rather to rest comfortably on the steering wheel of an electric cart, but that is another complaint.

            Another approach for adding the numbers has been to reduce the size of type to that used in newspapers to list the winners of the Malaysian Four Ball Championship and obituaries of lesser luminaries.  To read this scorecard requires squinting which is just another reminder of advancing age.  If I wanted such a constant reminder, of course, I would have stuck to pick-up basketball games.

            A last technique shrinks the space for writing your score and any information relative to wagers you might have placed.  This reflects the misplaced priorities of the designer who believes the scorecard is more important than the score.

            Why are some courses including stroke allocations for each set of tees?  In an unscientific sample, most of the perpetrators thought they were doing the right thing.  The more numbers, they believed, the more accuracy and hence more equity in competition.  Unfortunately, they were as wrong as they were well intentioned.

            The first thing you have to understand about stroke allocations is that there is no adequate theory demonstrating that one method is better than any other.  In fact, the USGA recommended methodology for allocating handicap strokes is almost universally ignored.  The USGA argues holes should be ranked by the difference in average scores between a group of good golfers (handicaps less than 8) and not so good golfers (handicap range of 20 to 28).  This method, the USGA argues "will maximize, on average, the number of halved holes in a match." [1] The USGA never states why a useful criterion is the number of halved holes.  Does it make any difference if I win one hole and my opponent wins one hole, or if we halve both holes?

            The more common way of allocating strokes is to rank holes by the difficulty of making par.  The number 1 stroke hole is then the toughest hole on the course and so on.  But the offending courses have taken this to extremes.  A small difference in hole rankings among sets of tees is all the justification needed for different stroke allocations.  No attempt at measuring the statistical significance of the difference in ranking or the impact on the equity of competition is made.

            Let me argue that it makes little difference in match play where strokes are given or taken.  (There are obviously rare situations where this hypothesis does not hold, but they are so uncommon as not to harm the general premise.)  As an exercise, you should produce a stroke allocation you believe is best for you.  Then play a match with your "desired" stroke holes.  Compare the results with the outcome of the match as if it were played by the stroke allocation on the card.  Over the long-run, you should not see a significant difference in your won and lost record using either allocation.

            But this thesis does not rely solely on anecdotal evidence.  To test the impact of stroke allocation on the equity of competition a computer simulation of matches was used.  Scores from one course with two sets of tees (white and blue) and stroke allocations were used.  It was found that if you won your match with a white tee allocation, there was a 95 percent change you would have won with the blue tee allocation.  This small difference should be expected due to the random nature of scoring.

            A simulation was also run with an inverse allocation of the white tee allocation (i.e., the first stroke hole becomes the eighteenth stroke hole). Winners under the white tee allocation won or tied 97 percent of their matches under the inverse allocation.  Even though this inverse allocation seems so foreign, it produces essentially the same winners as the more orthodox stroke allocation.  And if you want to use the USGA's peculiar criterion, all three allocations yielded about the same number of halved holes. 

            I hope this small research effort is convincing evidence that "one stroke allocation is enough."  The scorecard should be a work of art reflecting the beauty and simplicity of the game itself.  Superfluous stroke allocations represent visual clutter and unnecessary complication.  They add nothing to the equity of competition and should be eliminated.


[1] Decision 9-4a/1, USGA Handicap System, 2012-2015,  p. 74.

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