Jan. 15, 2001 CHAPEL HILL -- When two golfers play one another and employ the U.S. Golf Association's handicap system -- designed to give players an equal chance of winning despite different skill levels -- the better golfer enjoys a 60 percent to 70 percent chance of winning.
That's the conclusion that a University of North Carolina at Chapel Hill statistician and colleagues have drawn after carefully studying the mathematics of golf handicaps.
"We're not the first to suspect or to claim that the current USGA system is biased in favor of the better of two golfers, but we are the first to look closely at the variability in a golfer's scores and to analytically consider its impact on the handicap system," said Dr. Lawrence L. Kupper. "Based on our analysis, we recommend modifications that will make two-person golf matches more equitable. That way, each golfer will have roughly a 50-50 chance of winning." Kupper, Alumni Distinguished professor of biostatistics in the UNC-CH School of Public Health, has been an avid golfer for almost 40 years. Besides playing competitively, he has also organized and run tournaments at the university's Finley Golf Course and has headed Finley's golf association. A research and teaching award-winning fellow of the American Statistical Association, the mathematician focuses on environmental biostatistics.
A report on his unique golf study will appear in the February 2001 issue of Chance, a publication of the American Statistical Association. Co-authors of the report are Dr. Leonard B. Hearne, a former postdoctoral fellow in biostatistics now at American University; Dr. Sandra L. Martin, associate professor of maternal and child health at UNC-CH; and former biostatistics graduate student Jeffrey Griffin.
Kupper's group used theoretical statistical arguments, coupled with detailed analysis of score data, to demonstrate that the current USGA handicap system contains a bias.
"The reason for this bias is that the USGA system uses only the lowest 10 of a golfer's last 20 adjusted scores for handicap purposes," he said. "Since poorer golfers are less consistent than better golfers, which we demonstrated using real data, this means that the poorer golfer gets a handicap that is less representative of how he typically plays than does the better golfer. So, if my handicap is six and yours is 18, I could give you 12 strokes and still win roughly two out of three matches.
"Generally, the more inconsistent a golfer is, the more his handicap is overly optimistic about his average golfing ability."
The researchers collected and analyzed scores from 130 golfers at Finley Golf Course for 1997 and from 60 golfers in 1994. That work confirmed the widely expected inconsistency of poor players relative to good players.
Kupper and colleagues recommend using all of a golfer's most recent 20 scores to generate an accurate handicap or using all but the two lowest and two highest scores to eliminate unusually good and bad rounds. Both the UNC-CH team and the USGA ignore the possible effect of "sandbagging," where some players are inclined to turn in only poorer scores to boost their official handicaps.
"Since the current USGA handicap system probably will continue to be used, tournaments would be more equitable if competitors are 'flighted,' or grouped, so that players with roughly the same handicaps compete against one another," Kupper said. "That would make handicap tournaments more equitable."
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