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Watch a golf tournament on television, and you'll hear the announcers explain why Tiger Woods or Justin Rose or Ernie Els is in the lead. "He's tops in the field this week in fairways hit," they might say. Or perhaps they'll point to his stellar driving distance, or his amazingly low number of putts per round, or his excellent birdie conversion rate. But none of those statistics—the ones we're told separate the champions from the also-rans—truly reflects why golfers win and lose. At worst, they're actively misleading, giving us the wrong impression of why the best players in the game succeed.
For example, a common measure of a player's driving accuracy is the percentage of times he reaches the fairway on his first stroke. The PGA Tour's current leader in driving accuracy, Omar Uresti, has hit the fairway on 76 percent of his tee shots. But even if a golfer cracks his drive into the fairway 76 percent of the time, you can't assume that he had a good driving day. What if his misses were so atrocious that they went into the deep rough, inflating his scorecard with a bunch of recovery shots? That's the weakness of the driving accuracy stat: In recording errant drives, it doesn't distinguish between a shot that trickles just off the fairway and one that hits an unsuspecting fan in the butt.
The pros are aware of the holes in the standard stats. When I talked to players at the AT&T National, the stat that came most under fire was greens in regulation. GIR presumes to measure the accuracy of a golfer's iron play—reaching a green in regulation means landing the ball on the green in three strokes on a par 5, two strokes on a par 4, and one stroke on a par 3. Michael Letzig, a lanky, affable pro from Missouri, recalled a shot that he hit on a long par 3 that landed five feet away from the hole—except the ball was on the fringe. That counts as a missed green. If you go by GIR, Letzig's shot was worse than one that landed on the putting surface, 100 feet from the cup.
Mark Broadie, a professor at the Graduate School of Business at Columbia and an avid golfer, understood the fundamental problem with golf statistics: They don't factor in distance and location. Professor Broadie spends most of his time studying the financial markets. He knew that he could take the same mathematical tools that he uses to value an unusual security and apply them to golf. But first he needed the data. Around 10 years ago, he started keeping track of the rounds that he played with his friends and colleagues. He didn't just record standard stats such as his total number of putts and the number of fairways he hit. He created something that, with the PGA Tour's ShotLink not yet in existence, nobody had thought to construct: a database that allowed him to enter the precise coordinates of every shot that he and his golf buddies struck.
Broadie's collection has since grown to include more than 65,000 shots from golfers as young as 8 and as old as their 70s, with rounds as low as 61 and as high as 150. Thanks to his golf shot database, Broadie was able to do away with the old-fashioned, simplistic stats we hear about on TV and figure out how the game is truly played. Just as baseball's statistical pioneers overthrew the tyranny of ERA and RBI by developing more meaningful metrics, Broadie saved golf from GIR with a concept called "shot value."
The foundation of shot value is the idea that, once you have a huge database of golf shots, it's possible to set a benchmark for performance from every position on the course. Broadie uses the scratch golfer (someone who shoots par) as his benchmark. Using the data he collected, he determined how many strokes it would take a scratch golfer, on average, to get the ball in the hole from every inch of turf—everywhere from the first tee to the bunker that guards the 18th green.
Imagine that you are standing in the fairway with a 150-foot approach shot to the green. You look down, and instead of a yardage marker, you see a stake with the number 2.5. That's the average number of strokes it takes a scratch golfer to hole out from that spot. Picture these same sorts of markers everywhere. The tee box on a difficult par 4 may say 4.6. A 60-yard sand shot may have a 2.7 marker, and so on.
Once you have a benchmark "fractional par" value for every point on a course, you can figure out the value of every single shot. In a paper presented at the World Scientific Congress of Golf (PDF), Broadie gives the example of a 140-yard par 3 that plays, for the scratch golfer, like a par 3.2. Let's say a golfer hits his tee shot to within 14 feet, moving from a location where it takes an average of 3.2 strokes to hole out to a spot where it takes an average of 1.8 strokes to finish. The simple arithmetic to determine the value of the shot: 3.2 - 1.8 - 1 (for the stroke that was taken) = 0.4. The superb approach shot has given our fictional golfer a four-tenths of a stroke advantage over a scratch golfer.
Like all revolutionary concepts, shot value takes a few moments to get your head around. Perhaps the easiest place to grasp it is the green. Let's return to that 14-foot putt for birdie on the par 3. According to Broadie's research, a scratch golfer makes 14 footers about 20 percent of the time, gets home in two about 80 percent of the time, and rarely three putts. That gives the 14-foot putt a fractional par of 1.8—if you sink the putt, you pick up eight-tenths of a shot. If you just miss it, you lose two-tenths of a stroke.
While we write down our golf scores in whole numbers, Broadie's concept of shot value reinforces that a golfer loses or gains fractional advantages on every swing. This aligns with what it's like to be on an actual golf course. Every hole has certain places where it's great to land your ball—a spot where there's a good angle to the green, or an easy uphill putt—and other spots where you're "in jail," or out of bounds, or blocked by a tree. Hitting a shot to a good position is obviously more valuable than hitting it to a bad position. What shot value does is tell you exactly how much more valuable.
The beauty of shot value is that you can add it up. How many strokes is a golfer gaining or losing due to his approach shots? How about his putting? It's simply a matter of tallying individual shot values and comparing the results to the player's peers'.
In order to see shot value in action, Broadie analyzed for me how Tiger Woods won the 2008 Arnold Palmer Invitational at the Bay Hill Club. Tiger was at the height of his powers during this tournament—a golfing superhero who looked nothing like the all-too-mortal duffer who finished a breath out of last place at Firestone last week. The victorywas capped by this famous highlight:
Tiger is standing over a 24-foot putt for birdie. If he misses, he will enter a playoff against Bart Bryant. If he makes it, he will win his fifth consecutive tournament and tie Ben Hogan on the all-time wins list. As Tiger reads the break, the announcers unleash a series of statistical insights. "Probably means nothing right now, but he is 0 for 21 this week on putts over 20 feet," says color analyst Johnny Miller.
Tiger strokes the putt. The ball slides toward the hole … rolling, rolling … it's in! Tiger throws his hat onto the turf, then does a double fist pump. "Hello, Ben Hogan!" shouts play-by-play man Dan Hicks. Bart Bryant shakes his head in the scorer's booth. The crowd walks to the clubhouse, marveling at another example of Tiger's greatness in the clutch—he'd saved his best putt of the week for the 72nd hole.
Tiger's putt was undeniably clutch, but it was merely one of 270 shots that he hit during the tournament. Shot value tells us that it wasn't that lone act of skill on the last hole that earned Tiger the first-place check. Rather, the victory was achieved thanks to a series of small things he did to put himself in a position to sink that long putt. But what were these small things?
Broadie took all of the ShotLink data collected at the Arnold Palmer and figured out the shot value of each stroke. Let's go back to Tiger's tourney-winning 24-foot putt. Broadie's data shows us that an average pro golfer hits about 24 putts of longer than 22 feet in a standard four-round tournament. It's typical to sink two of these long putts per tournament. (Yes, that's right—the best golfers in the world make just two long putts per 72 holes.) Until that putt on the 72nd hole at Bay Hill, Tiger's long putting had been below average: As Johnny Miller indicated, he'd had 21 putts from longer than 22 feet, and he'd missed them all. If Tiger could have been even an average long putter, then he wouldn't have needed those 18th green heroics.
To figure out where Tiger gained on the field, Broadie compared his shot value measures with those of his four closest competitors: Bart Bryant, who finished second, and Cliff Kresge, Vijay Singh, and Sean O'Hair, who tied for third. Tiger beat them by 2.5 strokes—where did those strokes come from?
Tiger made his name on the PGA Tour with long drives, but at Bay Hill his driving cost him 2.4 strokes to Bryant and Co. throughout the four days of play. (Indeed, just like last week at Firestone, Tiger's driving was disastrous in the early rounds.) He also lost 2.8 strokes on approach shots from 100-150 yards out. His layup shots were also slightly subpar, dropping him another eight-tenths of a stroke. That puts him six strokes down.
But now we reach one of the strongest parts of Tiger's game: He excelled at approach shots from 150-250 yards out, allowing him to pick up an amazing eight strokes on his closest competitors. This matches the highlights of his play. On Saturday, he hit a 4-iron around a stand of trees to within two feet of the hole. And on the last hole of the tourney, Tiger summoned what he called "the best swing I made all week" to land a 5-iron from 177 yards on the green and set up the winning putt. (Even with all of his 2010 struggles, Tiger remains the world's best on long approach shots. As I wrote last month, "His remarkable ball striking from this range is what keeps him in tournaments when other departments of his game are lagging.")
Thanks to his superb long approach shots, Tiger is now two shots up as we turn to the short game. Broadie defines the short game as all shots from 100 yards and in, excluding bunker shots close to the green. Tiger loses two strokes in this department. This fits with the lowlights of Tiger's play, as when he hit a pitching wedge that flew the green and chunked a sand wedge that landed well short of the putting surface. Tiger's touch closer to the green was more assured. He gained four-tenths of a stroke from the sand.
As we finally get to putting, Tiger is fractionally ahead by 0.4 strokes. Even after that clinching putt on Sunday, his below-average long putting cost him four-tenths of a stroke. He also lost another stroke due to his relatively poor performance on putts between three and six feet. He's now one behind his nearest competitors.
Where Tiger pulls away once and for all is midrange putting. He was deadly from seven to 21 feet, gaining 3.5 strokes. Even more remarkable is that he achieved this advantage despite three-putting from inside seven feet on the 10th greenon Sunday.
In Broadie's final analysis, then, it was Tiger's long approach shots and midrange putting that "won" the tournament. So, it is ultimately fair to say that Tiger's win at Bay Hill can be partly attributed to his clutch putting—clutch putting on every single one of the 34 putts he took between seven and 21 feet. That last putt he rolled in from 24 feet just brought him closer to being an average golfer. And where did he pick up the most ground on his competitors? It wasn't on the green; it was far away from the hole, with an iron in his hands.
Broadie's analysis helps us answer a question that it's never really been possible to solve before: How do you accurately compare one player with another? Sure, there's always the final score at the end of 72 holes. But imagine if the kind of analysis that Broadie did at Bay Hill were applied to an entire PGA season. Instead of a confusing, aggregated stat like, say, "total driving," you could have a figure that truly shows who gains the most from their driving skill. You could then use this figure to make better predictions about whether a course would favor a player's strengths. You could also do what Broadie has done: challenge the conventional wisdom of golf that putting is the pre-eminent skill, the dividing line between greatness and failure.
In my next piece, I'll take a closer look at putting and the researchers who are trying to bring mathematical rigor to golf's most mystical skill.
Next: The Putter
To hear Michael Agger, Josh Levin, Mike Pesca, and Hanna Rosin discuss Agger's "Moneygolf" series, click the arrow on the audio player below and fast-forward to the 16:35 mark:
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