JERSEY CITY, N.J. — The bull’s-eye at the Barclays tournament this week will reside yet again on the back of Tiger Woods, the No. 1 player in the FedEx Cup rankings after the PGA Tour’s regular season concluded last weekend. And lurking from the deep, deep depths will be Portland’s Ben Crane.

As the 125th and last player to sneak into the FedEx Cup, golf’s monthlong playoff system, Crane is golf’s Mr. Irrelevant, barely off the bubble for inclusion. His odds to win at Liberty National golf club, according to Bovada Las Vegas, are 200-1. But he is embracing the underdog distinction with unusual aplomb.

On Tuesday, he spent 30 minutes on the course filming a one-minute music video spoof titled “Bubble Boy.” The vocals were sung by musician Mat Kearney, a close friend. The choreography included Crane tossing inflatable balls in the air and posing like, yes, a crane.

Earlier in the day, when he was practicing, he noticed two golf carts drive past lugging portable toilets.

“I’m all the way across the fairway and I yell, ‘Stop!’” Crane said. “’I’ve got to get a picture with you.’”

He later posted a picture on Twitter of himself in the driver’s seat, along with a self-deprecating note: “This is the cart I get for being the 125th-ranked player in the FedEx Cup.”

Crane, 37, said Wednesday: “I’m like, this is too good. I could have fun with this.”

With a $10 million grand prize on the line, and all of the PGA Tour’s most recognizable names in the field, the FedEx Cup is generally a tense and competitive stretch of weeks. No Cup winner has risen from further down the final regular-season FedEx rankings than 19. This year’s No. 1 player, Woods has won twice from that position since 2007.

Only the top 100 players advance to next week’s Deutsche Bank Championship in Boston, and then that number gets whittled to 70 for the BMW Championship. Finally, only the top 30 players compete in the Tour Championship in Atlanta.

In other words, it is a large hill to climb for Crane.

“There’s nothing really to lose,” said Jason Bohn, who held the 125th ranking at the start of the Cup last season.

“You’re like, ‘Hey, might as well try everything I’ve got,’” Bohn said. “If it works, great. If not, I get to sit for a couple weeks.”

There are a few examples of players rising from oblivion to make things interesting — bracket busters, if you will. In 2009 here, Heath Slocum outdueled Woods, Ernie Els, Padraig Harrington and Steve Stricker to win the Barclays, despite entering the tournament as the 124th-ranked player. He finished eighth in the final rankings.

Then Bill Haas, ranked 25th out of 30 entering the final week, won the Tour Championship and the FedEx Cup in 2011. He said he would not necessarily want to go through anything like that again.

“I don’t want to be that far down and have to have that many things go my way,” Haas said. “You would rather play your way to Atlanta, and you might as well be as high up as you can.”

Bohn said Liberty National was not a course that especially favors risky or aggressive play, perhaps limiting Crane. The course layout has been modified slightly since the Barclays was last played here in 2009, after players criticized the club’s tight landing zones and unforgiving rough.

With its sweeping views of New York Harbor, though, Crane does not have to look far for inspiration. The Statue of Liberty, a symbol of opportunity, sits less than 1,000 yards from the 18th green.

“I’ve got an opportunity with this format,” Crane said. “If I play well, at the right time, it could be my best year ever. That’s the volatility of the FedEx Cup and the opportunity it presents in front of us.”

On Sunday, Crane was at Piedmont Triad Airport in Greensboro, N.C., with two tickets in his hand: one to head home to Dallas, the other bound for New York.

“It was like I’m either going home, season’s over, or I’m going to the playoffs with a chance to win $10 million,” Crane said. “It’s crazy.”

Crane has made the FedEx Cup field six seasons in a row, never starting lower than 65th. He has battled back issues this year and finished in the top 10 of only two tournaments, the Houston Open and the Players Championship. He missed the cut at the Wyndham Championship last week.

“It’s been one of the most trying years I’ve ever had,” Crane said. “But with that comes a great opportunity to learn. I’m trying to grow because of it. I’ll tell you what, tough times really help you press into the issues and evaluate and carefully change direction.”

He is certainly playing up his role as this week’s biggest long shot, bouncing around the practice area Wednesday to show colleagues his video. Crane said he felt like a 16 seed in the NCAA basketball tournament, hoping to make a run.

“But in order to be a Cinderella, you can’t lose in the first round,” Crane said. “If I play well, yeah, I think I could get a little bandwagon thing going.”

On the air: The Barclays

• Golf Channel: First- and second-round coverage, Thursday-Friday, noon

• CBS: Third round, Saturday, noon; Friday, Sunday, 11 a.m.

More coverage, C2