Steve Stricker, right, receives congratulations from Jack Nicklaus after winning the Memorial. Stricker is the top-ranked American heading into the U.S. Open. (JAY LAPRETE/REUTERS)

When Padraig Harrington closed out his victory in the 2008 PGA Championship, the golf world was in something of a working order. Tiger Woods’s enthralling victory on one healthy leg in that summer’s U.S. Open still enveloped the sport. Even with Woods on the sidelines healing up, Harrington seemed a worthy player to fill the void.

Golf, back then, had a nice, settled, star-filled order: Woods was the No. 1 player in the world. Phil Mickelson and Harrington, with three major championships apiece at that point, ranked second and third. Sergio Garcia and Vijay Singh, two of the most recognizable faces in the international game, ranked fourth and fifth. The group of favorites for any major championship was easily identified.

Handicapping this week’s U.S. Open, which begins Thursday at Congressional Country Club in Bethesda, will not be nearly so simple.

Woods? He won’t be there, because he is again injured. Harrington? He hasn’t won on either the PGA or European Tours since that 2008 PGA and has missed the cut in four of his last five majors. Singh? He’ll be missing a major championship for the first time since 1994, after deciding against playing in a qualifying tournament. Garcia? His last victory came in November 2008.

The message: Dump the entirety of the 156-man field into a popcorn popper, and guess which kernel bursts first. The last 10 majors have been won by 10 different players. The last four have been taken by players who had never won one before. Four players — Woods, Lee Westwood, Martin Kaymer and Luke Donald — have been ranked first in the world since the last U.S. Open.

So who, then, might be the favorite this week?

“It’s like pinning the tail on the donkey,” two-time Open champ Curtis Strange said last week. “You got no chance.”

Even when Woods isn’t involved in a tournament — nagging injuries to his left knee and Achilles’ tendon will force him to miss his first Open since 1994 — he has a way of dominating the conversation. That used to be because any victory over a Tiger-less field could be marked with an asterisk.

Now, Woods’s absence is a further reminder of how the landscape of the sport has shifted in the past two years. Even had he played at Congressional, Woods hardly could have been considered a favorite, having fallen to 15th in the world rankings after going winless since September 2009.

“We went for a long time where Tiger was the only [player with] multiple victories on the tour” in a given year, said Jack Nicklaus, who holds the record with 18 major championships. Now, “the young kids say, ‘Hey, I can do that.’ So all of a sudden it brings it on. For a while, it didn’t look like anybody could bring it on.”

Among those who have brought it on: Kaymer, a German who won last year’s PGA Championship in a playoff, then won his next two starts. England’s Westwood is almost certainly the most accomplished player in the world without a major championship, and at 38, there is some urgency to his pursuit. Donald, the Englishman who’s currently No. 1, is a diligent worker with an exceptional short game who, in Nicklaus’s estimation, “is quite capable of winning major championships.”

Throw in defending champion Graeme McDowell, who not only survived a brutal Sunday last year at Pebble Beach to thrust himself into the international spotlight, but then further proved himself by winning the clinching point in the Ryder Cup.

Include South African Charl Schwartzel, whose birdie-birdie-birdie-birdie finish at Augusta was an unprecedented run to the title, yet hasn’t exactly made him a recognizable man on the street.

“Somewhere along the lines people called me ‘Schwarzenegger,’ ” he said. Still, he knows he has it much easier than compatriot Louis Oosthuizen (pronounced: west-HI-zen), who last summer won the British Open at St. Andrews out of nowhere.

Check out all those names — McDowell, Kaymer, Westwood, Donald, Schwartzel, Oosthuizen — and throw in Rory McIlroy and Paul Casey. All have either won major championships within the last year or are ranked in the top 10 in the world — or both. None are American.

“Golf is very global,” McDowell said.

That, too, has helped establish this open Open feel. Should a non-U.S. player win at Congressional, it will be the first time — since the inception of the Masters in 1934 — that international players have reeled off five straight major wins. Since Woods’s last major victory, at the 2008 U.S. Open, players from Africa (Schwartzel and Oosthuizen), Europe (McDowell, Harrington and Kaymer), South America (Argentina’s Angel Cabrera) and Asia (South Korea’s Y.E. Yang, the first for the continent) have combined to win eight majors. The United States, in that span: Lucas Glover at the 2009 U.S. Open, Stewart Cink at the 2009 British Open, and Mickelson at the 2010 Masters. Three.

Think it’s not a sea change? From 1971-93, a span of 23 years, precisely one non-American player won the U.S. Open (Australia’s David Graham in 1983). Entering this week’s event, Americans have won just two of the past seven.

“This is sort of a world game, and I don’t really look at too much where a player is from anymore,” Nicklaus said. “Just look at his ability to play golf.”

The top-ranked American entering the Open is Steve Stricker, a straight-as-a-9-iron Wisconsinite so practical that once, when he won a flashy sedan for making a hole-in-one, he traded it for a minivan. The biggest of Stricker’s 10 PGA Tour victories came two weeks ago at the Memorial tournament, which Nicklaus hosts. It helped him overtake Mickelson in the rankings, moving him to fourth. But is he a star?

“No,” Stricker said decisively. He doesn’t even feel like the best American.

“We know who the top guys are,” Stricker said. “They’re just not on their games right now.”

Indeed. Woods is unable to play. Mickelson has been mediocre, with one top-five finish since January. The best American bets at Congressional might be Bubba Watson, who has won three times in the past year and has the kind of flair and creativity that could make him a true star; Dustin Johnson, who led the Open through 54 holes a year ago; Nick Watney, who did the same at the PGA; or Matt Kuchar, the perma-smiled Floridian who spits out top-10 finishes but only truly contended as a pro in a major at last year’s PGA, where he faded over the weekend.

“The transition in golf, it’s as big as there’s ever been,” said Strange, who will work the Open as a commentator for ESPN. “With the backing off of Phil and Tiger Woods and the incredible amount of young players, 30 and below, playing well from all over the world — we’ve been saying this, but especially since Tiger has no longer been No. 1, you can flip a coin.”