By Henry Young, CNN

(CNN) -- He's said it before but this time people were sitting up and taking notice.

This time, as Tiger Woods charged up the leaderboard at the Players Championship, a long overdue 80th PGA Tour victory really did look within reach.

The 14-time major champion hit eight birdies in his first 12 holes Saturday, carding his best ever score at TPC Sawgrass and briefly flirting with the lead.

He maintained that form in the final round, showing flashes of the man that won the Players in 2001 and 2013, coming within four shots of leader Webb Simpson.

But as the clamor grew in the galleries and the golf world drew breath, it wasn't to be.

"I played so well this weekend; unfortunately, I just didn't cash in," said Woods, who finished tied for 11th, seven shots behind eventual winner Simpson.

"There's no way I would have predicted I would be at this point at the beginning of the year. But now I feel like I've got my playing feels back and I'm playing tournament golf.

"I'm not that far off from winning golf tournaments."

Jordan Spieth, his playing partner Sunday, said: "He'll win sometime soon enough. He's certainly playing well enough to do so."

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Simpson's revival

That the headlines will focus on a man who ended up outside the top 10 underlines the fact Woods remains golf's biggest draw.

Look beyond the grand narrative, though, and Simpson was completing a career resurrection of his own.

It's been six years since the 32-year-old's crowning achievement, the 2012 US Open title, and five since the last of his four previous PGA Tour wins.

The American has had to reinvent himself in the wake of the 2016 ban on anchor putting, forsaking the style he'd honed all his life and plummeting down the rankings as a result.

He's also endured personal tragedy, recently losing his father and best friend Sam aged 74 following a battle with Parkinson's disease and Lewy Body Dementia.

"It's been a long time. We did it," said an emotional Simpson after his first Tour win in 108 starts. "It's hard to put into words what this week has been like.

"I thought before [my father] passed that maybe the golf course would be the hardest place to be ... but I think it's my favorite place to be. That was where we had most of our memories."

Simpson's overall score of 18 under was the lowest at the Players Championship since 2003, and his six consecutive birdies on Friday equaled a tournament record.

Precision was the key to his Mother's Day victory, having been last in the field for driving distance but first for driving accuracy.

Simpson has adapted his putting style in the aftermath of the ban and uses a longer than normal putter with the shaft running up his left forearm as he addresses the ball.

Former Masters champion Adam Scott, who was also affected by the ban, joked: "I hope he doesn't putt to well with that thing up his arm or they'll ban that, too."

Also finishing alongside Woods on 11 under was fellow American Justin Thomas, who leapfrogged Dustin Johnson to become world No. 1 for the first time.

Thomas is the 21st player to hold the top spot since the rankings began in 1986, and at 25 the fourth youngest behind Woods, Jordan Spieth and Rory McIlroy.

"I want to have it for a really long time," he told reporters.

Americans now hold all four major championship titles, as well as the unofficial fifth major, The Players.

The last time US golf held such sway? The 'Tiger Slam' of 2000-01, when Woods won all five of t