The Pope and the Slippery Slope

Math ForumulasI recently noticed a posting on the bulletin board of the locker room at the Scottsdale club at which I play golf. Obviously posted by a higher handicap golfer, it heralded the claims of Dean Knuth, “The Pope of Slope”, that low handicap players retain a distinct advantage in head-to-head competition over higher handicap players. Although I have a lot of respect for the opinions of Dean Knuth, I took some issue with the article as printed in Golf Digest. Below is the original piece as taken from the bulletin board as well as my response. I then went into my database of golf matches and analyzed nearly one million head-to-head matches. I’ll present the empirical data upon request. What do you think?

Taken from Golf Digest June 2014 Issue

Another Reason to Ask for More Strokes

You would think that a golfer with a course handicap of 12 would have a decent chance of beating a scratch golfer, provided he was given his full 12 shots. But that golfer has only a 25 percent chance of winning, says Dean Knuth, former Director of the USGA’s Handicap Department. “The USGA set up its system to favor better players with a built-in bonus for excellence,” Knuth says. “It’s a philosophy that handicaps should be based on potential rather than average ability.” For every six strokes in handicap difference, the better player has a one-stroke advantage, Knuth says. So in a match between an 8 and a 14, the 8 handicapper has a 60 percent chance of winning. You might want to remember that before wagering.

But now (as Paul Harvey used to say), The Rest of the Story …

Dean Knuth is unquestionably one of the experts in the world of golf handicaps, however, he may be sugar-coating this one and allowing us middle to high handicappers to cry foul when there isn’t one.

The slight-of-word about handicaps being based on “potential” rather than “average” ability is a semantic dance with roots buried in the “USGA Handicap System”, but those roots are clouded and misunderstood. They are part and parcel of a circular argument that doesn’t make a lot of mathematical sense.

I suspect Mr. Knuth is alluding to the fact that for the purposes of handicap calculation, the differential for any given round is multiplied by 96% which the USGA calls its “Bonus for Excellence”, an “incentive for players to improve their golf game.” On the surface, it appears to favor the lower handicap players. But does it really?

I challenge you to go to the driving range and question one, ten or a thousand golfers as to why they’re practicing. I don’t believe any of them will respond they’re there because of the USGA’s “Bonus for Excellence”. They’re there because they lost two balls in a water hazard the previous day and they can’t afford to lose two more tomorrow. To suggest the “Bonus for Excellence” incents golfers to improve or for that matter that the USGA should concern itself with your level of motivation is delusion.

The “Bonus for Excellence” does tend to mitigate a statistical advantage that the higher handicap players have over the lower handicap players. Generally speaking, the higher the handicap, the greater the variability of scores. A scratch golfer’s net scores generally fall within a couple of strokes of par. A twenty handicap golfer’s net score will usually fall within four or five strokes of par – both over and UNDER. In other words, a twenty handicap golfer has a much higher probability of shooting a net 65 than a scratch golfer.

On any given day, in a head-to-head match, the scratch golfer may have a miniscule statistical edge over the high handicapper. However, it’s not the big edge Mr. Knuth suggests.

In a recent tournament at a nearby club, eighty-eight golfers competed where prizes were awarded to the best twenty-two net scores, i.e., 25% of the field. Slightly more than 20% of the field carried single-digit handicaps. If Mr. Knuth’s claims are valid, wouldn’t you expect the list of winners to carry more than 20% of the single-digit handicapper’s names? Alright, how about close to 20% of the winners come from the group of low handicappers? How would you explain only 10% of the winners being single-digit? The fact of the matter is that of the twenty-two prize winners, not a single one came from the single-digit list. With a closer look at the probabilities, this outcome was not unexpected.

No matter how you cut the math, here’s my conclusion. With all due respects to Mr. Knuth … If you come to me and ask for an extra stroke because your handicap is six strokes above mine, you’ll be talking to yourself. Play well.

Howard Jones

Handicap Committee Chair – Camelback Golf Club

Author: h. Alton Jones

writer/scientist/adventurer

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