Woods was on only one winning team, in 1999, and seemed to inhibit rather than inspire partners such as Mark O'Meara, Steve Stricker, Jim Furyk and most infamously Phil Mickelson in 2004 - when the pairing lost both of their opening day matches as the USA were routed.
"He's not got a great record in Ryder Cup; he didn't used to bond but he's changed his attitude now," noted three-time Europe captain Bernard Gallacher.
There was a time at the top of his game when Woods challenged reporters to recall Jack Nicklaus' Ryder Cup record.
His point was that we all knew Nicklaus had 18 majors, but not how he had performed in the biennial match-ups - which showed they were of less consequence.
Tiger is a different animal now, as the 2018 Ryder Cup approaches. And he is a winner once more after Sunday's Tour Championship triumph, his first in five years, which has capped one of the most remarkable sporting comebacks.
His legend is stronger than ever after recovering from four back operations and epic falls from grace - including the acute embarrassment of the mugshot that accompanied his reckless driving conviction only last year.
Woods is once again the supreme golfing athlete. Even at 42, he is an imposing physical presence and he is not shy of letting us know as we witnessed with the sleeveless top he wore en route to East Lake last Sunday.
His young team-mates will look up to him throughout this week and Furyk, the USA captain this time, will be looking to capitalise.
Le Golf National should suit Woods in his quest to improve a losing Ryder Cup record which currently stands at 13 wins, 17 losses and three halved matches.
The course puts a premium on accuracy off the tee. Drivers will be used sparingly and the key quality will be approach play and putting. These are potent weapons in the Woods armoury.
But he will also carry a target. He will be a prized scalp for the Europeans; a win against him and likely partner Bryson DeChambeau will feel like more than a single point to Thomas Bjorn's team.
"As far as Europe are concerned, that's something they will have to deal with," Gallacher added. "If I was a young player, I would want to play Tiger."
Rory McIlroy would surely want another crack at the former world number one after fading poorly in his company during the final round in Atlanta over the weekend. It is vital for Europe that there is no hangover for the Northern Irishman.
That was the sixth occasion in recent times he has found reverse gear having earned a place in the final group on a Sunday. It is a worrying trend for the four-time major winner, who needs a big Ryder Cup to salvage a frustrating season.
Justin Rose has been knocked from the top of the world rankings by Dustin Johnson but there are 10m reasons why he should not feel too upset after securing the FedEx Cup.
Fatigue is Rose's biggest enemy after a draining period which saw him climb to the top of the world rankings and secure the $10m PGA Tour bonus cheque.
Paul Casey and rookies Tommy Fleetwood and Jon Rahm had solid weeks at East Lake, and that will imbue them - and their captain - with confidence as they arrive in Paris.
Europe captain Bjorn will also have noted that American big guns Brooks Koepka, Patrick Reed, Bubba Watson and Phil Mickelson occupied the last four positions in the 30-man Tour Championship field.
In all 17 of the 24 on show this week competed in Atlanta and all of them will have to adapt quickly to the tighter fairways and slower greens that are expected to favour the home side this week.
This may prove the leveller given that the average world ranking of the Americans is 11 compared with 19 for Europe. For the first time the entire world's top 10 are competing at a Ryder Cup, indeed 17 out of the top 18 are here.
For the US, all bar Mickelson are in the top 17 in the world. Between them, they boast 31 major titles, with the line-up including the reigning US Open and PGA champion Koepka and Masters winner Reed - regarded as Captain America for previous Ryder Cup exploits.
It is arguably the strongest USA line-up since the famous 1981 team in which Bruce Lietzke was the only man who could not boast a major title. They romped to a nine-point victory in their first away match against the European continent.
Now though, the American team are enduring a barren run on the road which has stretched to a quarter of a century. They look well equipped to end that this week but Europe should not be underestimated.
It is the most enticing of sporting prospects, especially with an in-form Woods, a figure who genuinely transcends the sport, widening further the Ryder Cup's appeal after last Sunday's tumultuous victory.