If Tiger Woods is on the range at a PGA Tour event, as he will be Thursday morning at Congressional Country Club prior to the first round of the AT&T National, there will almost certainly be a buttoned-to-the-top, shades-wearing, dapper-looking figure with him. He will tote a video camera. He might pantomime a swing. He will almost certainly tell a joke.

And there’s every chance that a golf fan, leaning against the railing, would have a better chance of recognizing Sean Foley, swing coach, than the PGA Tour player teeing it up next to Woods.

“The scrutiny, it’s part of the job,” Foley said.

Woods’s golf swing is as analyzed as any athletic motion on the planet, broken down as often as Tim Tebow’s throwing mechanics, more than Stephen Strasburg’s windup or Usain Bolt’s stride. In winning 14 major championships, he has helped make his previous teachers, Butch Harmon and Hank Haney, golf celebrities. Foley, with whom Woods began working late in the 2010 season, is the latest to rise to prominence, being credited or blamed with Woods’s every success or failure.

But in any given week on any given range, Foley — or Harmon or David Leadbetter or Pete Cowan or on and on — could be spotted, working with a noted pupil, in the days and hours leading up to a tournament. Woods’s swing changes — one under Harmon, one under Haney, and the latest with Foley — are the most well-documented in history, but the reality is a cottage industry long ago developed around pro golfers and their swings.

“If you look at the world rankings or whatever,” said Nick Watney, counted as a member of Harmon’s stable, “everybody has a coach.”

This isn’t an entirely new phenomenon, because men such as Jim Flick and the late Harvey Penick instructed pros more than half a century ago. But with one notable exception — Masters champ Bubba Watson — instructors appear ubiquitous now. Watney said he sees Harmon, who lives near him in Las Vegas, nearly every day. Marc Leishman, an Australian who is the most recent winner on the PGA Tour, has used the same coach for a decade. That Denis McDade, that coach, lives in Australia isn’t a problem.

“If I called him now,” Leishman said, “he can be here Friday.”

Such is the dependence, for so many top players, on their coaches. When Jack Nicklaus was in the prime of his career, he said he would have a few lessons with his teacher, Jack Grout, at the beginning of the year, just to reset himself. But he then preferred to be on his own.

“I needed to be able to fix things on the golf course,” he said. No longer. Being on their own is an anomaly to most top players, regardless of talent or personality.

“Different players learn in different ways,” Foley said. “That’s one thing we have to realize as coaches, 100 percent.”

Six years ago, Foley was waiting tables and teaching golf in Toronto. “I had a bunch of crazy jobs,” he said. None might be as crazy as the one he has now.

“He knows a lot about a lot,” is how Woods described the native of Ontario last spring. Foley and his primary students — Woods, Hunter Mahan and England’s Justin Rose, all winners on tour this year — have received plenty of attention over the past year. Foley, then, has talked a lot about his theories and interests. He reads books, he said, delving into the coaching styles of John Wooden and Phil Jackson and Scotty Bowman. He studies how different students react to different scenarios, and adjusts.

“You think about how university students are taught,” he said Wednesday. “Sitting in a lecture hall, not everybody’s an auditory learner. Smart kids can get B’s and C’s in that setting. But take different kids one-on-one, and you discover what might work.”

Take his three current clients. Mahan is “through-the-roof visual,” and he responds well to video. Rose, by contrast, likes to joke and chat on the range, and he learns more by listening. “I wouldn’t really get much out of video with him,” Foley said. Woods “likes to get into his own mind. The way I work with Rosey would never work with Tiger.”

But with all of them, Foley falls back on another area of his expertise: science. A familiar scene on PGA Tour ranges is of a coach with a computer seemingly hovering above the ground. A product known as TrackMan can track, via radar, the speed and flight path of any shot. Foley will often take video of his player’s swing on his phone, then store it in a file with the data from the radar.

“It’s not pseudo-science,” he said. “It’s straight physics, geometry and biomechanics. When I show them, they can’t really argue.”

So when Woods wanted to overhaul his swing in 2010 — knee injuries suffered in 2008 cost him nine months, and his knee still wasn’t fully healed — he turned to Foley to engineer the process.

“I didn’t want to play the way I did because it hurt, and it hurt a lot,” Woods said. “Was I good at it? Yeah, I was good at it. But I couldn’t go down that road, and there’s no way I could have had longevity in the game if I would have done that.

“Four knee surgeries later, here we are. I finally have a swing that it doesn’t hurt, and I am still generating power.”

The swing is the one Foley and Woods built together, the one Woods will use this week at Congressional Country Club. The two statistics that best reflect how players are hitting the ball when taking a full swing are total driving (a combination of driving distance and driving accuracy) and ball-striking (a combination of total driving and greens hit in regulation). Woods is second in total driving and tied for second, with Mahan, in ball-striking.

“Eventually, I get to a point where the full game becomes very natural feeling, and I can repeat it day after day,” Woods said. “And [then] I can dedicate most of my time to my short game again.”

That, then, is what the golf world is waiting for, for the full swing and the sharp short game to merge at a major. But most of the process of teaching and changing swings happens without the world watching. Still, many of the goals are the same: make changes that might not be seen in the short-term, but will help a player over months and years. So part of a coach’s job is selling that process.

“It’s can be very difficult,” said Matt Killen, who coaches J.B. Holmes and Josh Teater, both in the AT&T National field, among others. “Most of the guys are really, really good players already. For them to go out on the limb and change things, they have to have faith that it’s going to work, and they have to have confidence in the person that’s helping them make the changes.”

That faith is built not only on the range, but at dinners and in phone calls. And what is left unsaid can be just as important as what is.

“These guys were really good before they could spell ‘physics,’” Foley said. “There’s an inner genius going on there. I think, as teachers, people think if we’re talking, people are learning. That’s just not true.”

What is true: On the range at Congressional this weekend, a coach will be talking, a player will be listening, a swing will be tweaked, and an industry will churn on.