The Americans have lost five successive Ryder Cups on European soil since triumphing at the Belfry in 1993, but were convincing winners in Minnesota two years ago and boast 31 major titles among their team as well as the top three in the world rankings.
Jim Furyk added Woods, Phil Mickelson and the red-hot Bryson DeChambeau as captain’s picks earlier this week, with his final selection to be made on Monday (Sept 10).
The Ryder Cup starts on September 28 at Le Golf National just outside Paris, only the second time the three-day matchplay showdown will be played in continental Europe.
“It’s obvious that the one thing that has been missing over the years is for our team to go over to Europe and win,” said five-time major champion Mickelson.
“I’m very excited about the team this year. We have some incredible players, great leadership and a really special opportunity to do something that we haven’t done in a long time.”
Francesco Molinari ended a run of five straight American major victories by becoming the first Italian to win one of golf’s four biggest tournaments at the British Open in July, but Brooks Koepka restored order at the PGA Championship.
The 28-year-old Koepka will be a force to be reckoned with at the Ryder Cup, having claimed three major titles in less than two years to move to the brink of taking the world-number-one spot from Dustin Johnson.
He will also be more accustomed to conditions at Le Golf National than many of his teammates, having built his professional career in Europe.
With five rookies qualifying automatically for his team, European captain Thomas Bjorn is keen to avoid a repeat of Hazeltine two years ago, when a side featuring six debutants were well-beaten 17-11.
The Dane opted for experience when he named Sergio Garcia as a wildcard despite the Spaniard’s recent poor form, alongside Ian Poulter, Paul Casey and Henrik Stenson.
That took the average age of the European team to 34, two years older than a US side whose figures were boosted by the selection of 48-year-old Mickelson.
“All four bring loads of experience, points and know-how to win and lose and they will bring plenty of heart,” said Bjorn.
But turning to players based on reputation rather than form has provided mixed results for Ryder Cup skippers in the past.
Raymond Floyd took three points, including the decisive singles rubber against Jose Maria Olazabal, as a 51-year-old captain’s pick for the USA in 1993 at the Belfry, while European talisman Colin Montgomerie played a starring role in 2004.
But Darren Clarke paid for his loyalty to the experienced pair of Martin Kaymer and Lee Westwood last time out, as they managed just one point from seven matches between them.
The Albatros course at Le Golf National will provide the players with a far sterner test than Hazeltine did two years ago, with a formidable closing stretch of holes defended by water at every turn.
The water-guarded par-three 16th could bring the end of many matches, while games that do reach the 18th will see players facing one of the most daunting tee shots on the European Tour, with a lake down the left-hand side and thick rough on the right.
The wide fairways and fast greens of 2016 played perfectly into the strengths of the Americans, but they will have to adapt to conquer Europe this time around.
“There’s a lot that can happen on 15, 16, 17, 18,” Furyk said on a visit to the course in July. “It’s an amazing amphitheatre.”