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This one's a par 4
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Pope Of Slope

The Numbers Game

Is any sport more numbers-crunchy than golf? For many of us, playing is only half the fun. Keeping track, filling in all those enticing little rectangles on a pristine scorecard with hole scores, fairways hit, greens in regulation, putts - that's really why we play the game.

It's no accident that one of golf's best-known teachers, Dave Pelz, used to be a rocket scientist, or that former United States Golf Association handicap czar Dean Knuth scored 800 on his math SAT. It should come as no surprise, then, that all four members of a Florida State Golf Association course-rating team that re-rated West Palm Beach Country Club last fall are retired engineers.

Course raters figure out a course's difficulty and translate it into numbers that players can plug into the handicap system, which is only slightly less intricate than advanced trigonometry.

For these guys, though, this is heaven.

"What we did for a living," said Brian Robideau, "was quantitate things." Like fellow course raters Jack Guthrie and Mallory Privett, Robideau is retired from Pratt & Whitney. The other member of the team, Herb Andrew, was with Chicago Bridge and Iron.

The numbers course raters come up with are used to help golfers determine whether the course they've selected for this weekend is appropriate for their ability, or if they're more likely to be eaten by a shark in a water hazard than to break 100.

The numbers are also used to help determine how many handicap strokes you're going to give me when we play. Handicapping is a math junkie's Grand Slam, with addition, subtraction, multiplication and division.

History is unclear on who first said, "I want three strokes a side," but the idea changed the game forever. In virtually every other sport, if you're better than me, then I need to practice more. But golf sought to create a way to level the playing field. Why? To make it possible to bet, that's why.

Early handicaps were based on how much worse you were than the best player at your club. That system fell apart once you tried to play against someone from another club.

It also didn't take into account that my home course might be harder than yours. Course Ratings - numbers which approximate the score a scratch player should be able to make on a course - attempted to solve this problem, but they had a flaw. USGA researchers found that as courses got harder, scores made by less-skilled players ("bogey golfers") increased at a higher rate than scores made by scratch players.

The man credited with devising the Slope system that cured this problem is Dean Knuth, the USGA's former senior director of handicapping. Through a class assignment while he was pursuing a master's degree in computer systems technology from the Naval Postgraduate School in Monterey, Calif., in 1975, Knuth (Kuh-NOOTH) became involved in course rating.

In 1979 the USGA asked him to come on board, and in 1981 he became director of handicapping. Almost 20 years later, all the regional golf associations in the U.S. - plus most countries in Europe and Asia - use Slope.

The system earned Knuth a nickname, the "Pope of Slope." Knuth left the USGA for private business in 1997 and now works for defense contractor Litton/PRC, uses it as his Web site address (www.popeofslope.com).

When he was in the Navy, Knuth, 53, developed a submarine detection tactic to use against the Soviets. Compared to detecting submarines, how hard could improving handicapping be? You'd be surprised. Consider the following sentence from Knuth's USGA paper, "A two-parameter golf course rating system":

"The solution method used was the classic multiplication of both sides of an overdetermined system Ax=b by the transpose of A."

I have no idea what "A" or "b" stands for. "X" is what I often score on difficult holes, but I doubt that's what Knuth had in mind. I do know that I am more likely to be eaten by a shark in a water hazard than ever to understand it.

Fortunately, however, I don't have to understand it. "Computers do the calculations," Knuth says, "and the average golfer doesn't have to know the details."

As long as I can keep filling my scorecards with numbers, that's OK with me. There's room in the game for us "bogey mathematicians," too.

Inside the numbers

A guide to handicapping and course rating:

Why Slope?

The system of adjusting a golfer's handicap to the course being played is called Slope. It is based on a study of the scores of golfers of various ability levels playing on courses of varying difficulty. A graph of these scores would show lines that slope upward from left to right. The more difficult the course, the steeper the slope.

What does it all mean?

Course Ratings and Slope Ratings are essential parts of golf's handicapping system. Here are some key terms and formulas golfers should know if they are going to use the system.

Course Rating: A measure of the difficulty of courses for a scratch player. Such a player would be expected to shoot 67 on a course rated near 67, or 75 on a course rated near 75.

Slope Rating: A measure of the relative difficulty of courses for players who are not scratch golfers. It takes into account the fact that increased difficulty affects such players more than it affects scratch golfers. The lowest USGA Slope Rating is 55. The highest is 155. The "standard" Slope Rating is 113.

Handicap differential: The first step in figuring your Handicap Index. You determine one for each round you play. Take your total score and subtract the Course Rating. Take the result, multiply it by 113 (the USGA's "average" Slope Rating) and divide it by the Slope Rating. Round the result to the nearest 10th.

Do the math: Bill shoots 92 from the white tees, which have a Course Rating of 69.9 and a Slope Rating of 121. His handicap differential for that round is 20.6 (92-69.9x113/121).

Handicap Index: Average the better half of your 20 most recent handicap differentials and multiply by 96 percent. Delete all digits after 10ths.

Do the math: From your most recent 20 rounds, 96 percent of the average of your 10 best handicap differentials is, say, 10.76. Your Handicap Index is 10.7.

Course Handicap: This is the number of strokes you should receive when playing a particular course. It's based on your Index, but you'll get more strokes on a course with a higher Slope Rating, fewer on one with a lower Slope Rating. To figure your Course Handicap, take your Handicap Index, multiply it by the Slope Rating of the course you will be playing and divide the total by 113. Round the answer to the nearest whole number.

Do the math: Bill, who has a Handicap Index of 9.0, will be playing a match from tees with a Slope Rating of 147. He multiplies his Index by 147 and gets 1,323, then divides that total by 113 and gets 11.7. So his Course Handicap for this match will be 12. If the match were to be played from tees with a 100 Slope Rating, Bill's Course Handicap would be 8 (9x100, divided by 113, equals 7.9). If you don't like to do math most courses have Course Handicap tables.

Do you have a handicap?

Probably not.

The U.S. Golf Association says only about 4.5 million of the nation's 26.4 million golfers have an official Handicap Index.

If you did, what would it be?

Probably lower than you'd guess. It's a common misconception that your handicap is the average number of strokes you shoot over par. Your handicap is based on your best scores and takes into account the difficulty of the courses you play.

How does your handicap stack up against the national average?

The USGA says the average Handicap Index for men is 16.1. For women, it's 28.9.

What are Course Ratings and Slope Ratings?

They're measurements of the difficulty of a golf course. Ratings measure how tough a course is for expert players. Slopes measure how tough it is for the rest of us.

Why do we need them?

They're used in figuring handicaps. Without them, a handicap established at an easy course would be inaccurate at a difficult one.

What kind of math nerd came up with this stuff?

One who scored 800 on his math SAT and later went on to become a Navy engineer and devise a submarine tracking system.

Tough courses

Palm Beach County and Treasure Coast courses with the highest Course Ratings from the championship tees:
Trump International 75.9
West Palm Beach
Ibis (Legend) 75.5
West Palm Beach
PGA National 75.3
(Champion)
P. B. Gardens
Pine Tree 75.3
Boynton Beach
Boca Rio 75.2
Boca Raton
Legacy 75.2
Port St. Lucie
- Palm Beach County and Treasure Coast courses with the highest Slope Ratings from the middle tees:
Harbour Ridge (River) 144
Palm City
Trump International 135
West Palm Beach
Bear Lakes (Lakes) 133
West Palm Beach
Hunters Run (South) 133
Boynton Beach
Old Marsh 133
Palm Beach Gardens
PGA National (Champion)133
Palm Beach Gardens

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