What turns the tables for a victory?

Many of us who play golf often have had friends who know our games tell us during a good round that we're playing way over our heads. "You can't keep it up," they might mutter under their breath. "You're going to fall into your old habits." And mostly they are right. We do eventually discover through some calamity on the golf course that we aren't destined to win the club championship or the state amateur.

To varying degrees, most pros play over their heads every week to win on the PGA Tour. Of the 2011 PGA Tour winners, no one personified this truth more than Harrison Frazar, who got his first tour victory when he won the FedEx St. Jude Classic in June after 355 PGA Tour starts.

Frazar was 4.6 strokes per round better when he won the St. Jude than in tournaments before and after his win. Unlike Luke Donald, who played just 0.7 strokes per round better to win the Children's Miracle Network Hospitals Classic, Frazar couldn't have won in Memphis unless he played over his head.

As a highly skilled player with 14 years on the PGA Tour and millions of dollars in earnings, it's not fair to call Frazar's win a fluke. But when you compare his strokes gained per round improvement -- which includes putting, short game and long game -- with those of Donald and Webb Simpson in their wins, you understand why those two players had remarkably consistent seasons and why the St. Jude title was Frazar's only top 10 of the year. Donald and Simpson could play close to their normal games and still win, a rare feat on the PGA Tour unless your name is Tiger Woods.

Though he was only 39 -- far from over the hill in golf years -- Frazar had suffered for a decade with back, hip and elbow problems, a combination that had brought him to the brink of quitting the game. The former Texas Longhhorn, who had toyed with a full-time career in the golf course design business before turning pro in 1996, was telling anyone who would listen that 2011 was likely his last year on the tour.

The Dallas native had started the 2011 season on a major medical exemption after shoulder surgery in August 2010. Coming into the week of the St. Jude Classic, he had missed the cut in six of his first nine events. And despite a tie for 14th at the HP Byron Nelson Championship the week before the St. Jude, no one except perhaps Frazar, his caddie and his family would have believed that he could have shot 64-67 on the weekend to get into a playoff, where he beat Robert Karlsson on the third extra hole.

"I think it just shows you how sometimes when you let your guard down or you let your expectations soften, you can free yourself up," Frazar said after the playoff. "But if you would have asked me three weeks ago if I thought I would be sitting here right now, I would have told you absolutely not."

Winning on the PGA Tour is certainly not a crapshoot, but at times it can seem exactly like winning the lottery.

"If you have a field of 156 players, a handful of them are going to play lights-out relative to how they normally play," says Richard Rendleman, a visiting professor in Dartmouth's Tuck School of Business. "It doesn't mean that they are necessarily playing better or that they have gotten better, but just because of random variation or what you might call luck, there is going to be somebody who is going to have four good rounds in a row.

"If you have a 156 guys flipping coins, some are going to hit four heads in a row and that's like playing better than normal four days in a row."

For the past eight years, Rendleman has been studying the art of winning on the PGA Tour. With Robert A. Connolly, a UNC Chapel Hill business professor, he published "Skill, Luck, and Streaky Play on the PGA Tour" in 2008 in the Journal of the American Statistical Association. In the paper, they argue that PGA Tour players cannot win tournaments without experiencing some good luck.

In a subsequent work that studied Woods' career from 1998 to 2009, they found that at Tiger's peak in 2000, he could have placed in the top four in every tournament that he entered without experiencing any good luck.

"Tiger was the only player who could have won tournaments in the modern era without experiencing some good luck in his scoring," Rendleman said. "That doesn't mean that Tiger would win every time, but just that he was the only player who could have won playing just his normal game, which is what he would shoot after adjusting for the relative difficulty of the golf course."

In 2011, Frazar might have been the most surprising winner due to the number of strokes that he gained per round, but he finished near the bottom on the ranking of amazing shots per round, or what Rendleman and his colleague from Columbia Business School, Mark Broadie, reluctantly call shots gained from luck.

At the St. Jude, Frazar didn't gain many shots from long putts or hole-outs from off the green. He didn't have the kind of good fortune that Rocco Mediate had a year earlier at the Frys.Com Open when he gained 1.8 strokes from his long game due to four hole-outs from the fairway. Mediate gained 2.4 strokes overall.

Last season, the amazing shots king was Steve Stricker, who won the Memorial with four hole-outs from off the green, including a hole-in-one on a par 3. He gained 1.6 strokes just from those amazing shots.

Broadie is the pioneer of the strokes-gained approach to PGA Tour statistics, which uses
data to make it easier to pinpoint a golfer's strengths and weaknesses by measuring the quality of shots in units relative to the field. In 2011, the PGA Tour began using his putts-gained stat, which takes into account the distance each putt starts from the hole and then compares the number of putts taken to the average of other PGA Tour golfers from that distance. The result shows the number of putts gained or lost relative to the field. Long considered by his peers as a great putter, Donald led the category in its inaugural year.

"Most of the past PGA Tour stats are pretty simple in that they involve counting how many putts you take or how many fairways you hit," said Broadie, who is working with the PGA Tour to implement more strokes-gained stats. "But they don't take into [account] if you miss a fairway or a green by one yard or 20 yards. Strokes gained gives you a much better measure of a quality of a shot."

Broadie points to sand saves as one of the most misleading stat categories administered by the PGA Tour. Presently, the stat combines sand shots and putting to determine a sand saves percentage. The strokes gained approach separates the putting from the sand shot.

Broadie, who updated the data with Rendleman for the most surprising winner and the winner with the most help from amazing shots for ESPN.com, was surprised to discover superstars Adam Scott, Phil Mickelson and Dustin Johnson so high on the list of surprising winners, yet he found the most comforting aspect of the surprising-winner table to be Donald at the bottom of the list.

"It makes sense," Broadie said. "He was so consistently good throughout the year."

Players are taking notice of the strokes-gained statistic for measuring the strengths and weaknesses of their games. Pat Goss, Donald's teacher, has consulted with Broadie to hone in on every aspect of his student's game. Though it's not yet an official PGA Tour stat, Broadie had Donald improving from a rank of six in 2010 to No. 1 in total strokes gained, which is very similar to the tour's adjusted-scoring average, except it only takes into account rounds measured from ShotLink, excluding the majors and WGC events.

According to Broadie, Donald improved by about three-quarters of a stroke, making his greatest stride in his long game, improving from 53rd in 2010 to 7th in 2011. Over the past two years, Donald's putting has been bulletproof. If strokes-gained putting had been an official stat in 2010, he would have led the stat two years running.

"The importance of putting and the short game is one of the biggest misconceptions about the game. I think the long game is way more important than people give it credit," said Broadie, who defines the long game as any shot longer than 100 yards. "About two-thirds of scoring differences come from the long game and the other third comes from the short game and putting.

"I think this would be a surprise to a lot of people who have had it drilled into them that it's all about putting or getting up and down around the greens. But throughout the course of the year, the best players tend to be the ones with the best long games. If you're Tiger Woods and you're good at all three, you're going to stay on top as he did for a lot of years. But even for Tiger, it was his long game that separated him from the pack."

At the St. Jude, nearly 40 percent of Frazar's strokes gained came from his long game with nearly 50 percent coming from his putting. The other 10 percent came from his short game. Sure, he was a surprise winner, but he also played some good golf and a win is a win.

In Kapalua this week, 28 of last year's winners will be teeing it up Friday on the Plantation course. In the infancy of the season, many of their games will be rusty. No matter how well they play, everyone will need a little luck to earn the winner's check come Monday. Frazar will probably need to play way over his head to beat Simpson, but in a small field like this, anything can happen.

Farrell Evans covers golf for ESPN and can be contacted at evans.espn@gmail.com.