Pop quiz! Place your books under your desk, and keep your eyes on your own paper.
G = fs - fe - 1 is:
A) Coca-Cola's secret formula
B) An unpleasant reminder of college calculus
C) A golf equation that could change the way you
practice and play—and save you several strokes per round
If you circled "C," you're correct—and you may soon be circling more birdies on your card, too.
The formula is the key component in ongoing research by Mark Broadie, a professor at Columbia Business School in New York City who, when not teaching courses with names like "Computational Finance," spent much of the last decade logging 70,000 shots hit by players of all levels and ages, from Tour pros to 100-shooters.
Broadie, a 4-handicap, set out merely to analyze the games of a range of players, but he stumbled on powerful evidence that golfers lose more strokes in the long game—defined as shots of 100 yards or more—than the short game.
Sacrilege? Conventional golf wisdom says so. It could be etched in granite: Drive for show, putt for dough. After all, about 60 percent of the typical weekend player's shots occur within 100 yards of the hole. But Broadie, a former club champion at Pelham (N.Y.) Country Club (where he recorded much of his data), calls that number misleading.
"If you toss out gimme putts, that number is more like 45 percent," says Broadie, 53. "The Golfmetrics database"—the software program he used to crunch his numbers—"makes it clear that, while the short game is important, weekend players have more room to improve in the long game."
While less earth-shattering than E=mc2, the formula that unlocked Broadie's findings is inspired in its own right—and almost as difficult to explain. In the equation G = fs - fe - 1, the G stands for strokes gained. Broadie's equation gives any shot—from an ace to a whiff—a precise mathematical value relative to a scratch golfer's average score on a given hole.
Every swing either gains stroke value (good shots where G has a positive value) or loses stroke value (think Charles Barkley) compared to scratch. The closer a swing gets you to the hole without finding trouble, the higher the value.
Let's say you're on a par-5 on which the typical scratch player takes exactly 5 strokes to hole out. You uncork your drive to a spot in the fairway from where Mr. Scratch averages 3.7 strokes to finish, so your tee shot gained .3 strokes relative to scratch—that is, your G is +.3.
Had you instead sliced your drive into the woods, and the scratch average for holing out from there is 4.6, then your wayward tee shot loses .6 against scratch. (Got it? Maybe not, but the PGA Tour does. Impressed by Broadie's formula, the Tour is planning to adopt a new "strokes gained" statistic in 2011.)
With a credible system in place to precisely quantify any shot's value, Broadie crunched his numbers and found that players of all levels were losing more strokes in the long game than the short game. Three of his key findings:
1. The long game gets short shrift
Of the 15 shots that a typical 90-shooter loses relative to a scratch golfer, he gives away nine of them while outside 100 yards, against six from inside 100 yards.
Why? Location, location, location! There's more real estate which means more trouble. "Trees, water, O.B.—there are more landmines to step on outside of 100 yards than when you're nearer the green," Broadie says.
2. 'Awful' shots are more awful than you think
Tops, chunks, shanks, clanks. We all know awful shots add up on the scorecard. Broadie was surprised to learn how quickly they add up. "In a typical 90-shooter's round, about six strokes are lost due to awful and doubly-awful shots," he says. His system defines as "awful" any shot that loses about one shot against par. In the long game, an awful shot is a swing that advances the ball less than 80 yards, that results in a penalty, or that forces a recovery shot.
A swing can be ugly—say, a topped drive that trundles 150 yards down the fairway—but not statistically awful. A total whiff loses exactly one shot. There are "doubly awful" shots that lose about two shots against par, such as shots hit OB with a stroke-and-distance penalty. (You heard right: A whiff may be embarrassing, but statistically a drive O.B. is twice as awful.)
Awful and doubly-awful shots can happen anywhere—a stubbed chip, for example— but for both pros and everyday players, more than twice as many occur in the long game than the short game.
The good news? "A fast way for everyday players to save strokes is to reduce the number of awful shots," he says. "Some of it can be done simply with better course management, without a swing change."
3. If you don't drive for show, you can't putt for dough
There's a direct correlation between longer, straighter driving and lower scores. "This is a reality check for those looking to reach the next level," Broadie says. "If your typical drive is 220 yards, you're shooting in the 100s or 90s, and maybe the 80s. But you're not in the 70s. No matter how good your short game is, there's a scoring ceiling that relates to distance. You need length and accuracy off the tee to give your short game the chance to post good numbers."
Broadie adds that the short game is important to scoring—just not as important as we think. "You should definitely practice chipping and putting," he says. "But what really separates the pros from average golfers is hitting it a lot straighter and farther. So working on your full swing, and on avoiding those awful shots, is a great way to save strokes."