The tournament so desperate to be hailed golf’s fifth major begins its 35th edition at the TPC Sawgrass in Florida today with the no. 1 player in the world absent. That Tiger Woods chose April 15 for surgery on his left knee rather than three weeks before the Masters, or any of the other majors, suggests the Players Championship still ranks considerably lower on his to-do list than PGA Tour commissioner Tim Finchem would like. The arthroscopic procedure to repair cartilage damage was carefully timed so that Woods could compete at Augusta and hopefully be back to something close to his best in time for the U.S. Open in June. Ideally, he could fit in a tournament prior to Torrey Pines — the Memorial Tournament, say — but missing the Players, while certainly a shame, would be no great sacrifice, especially if it meant being healthy for the rest of the year and perhaps the remainder of his career. And if, by scratching from the Players Tournament, he could somehow needle Finchem just a little by reminding him that he is the boss and wouldn’t miss playing “gimmicky” holes like the 17th, then so much the better.

The hundreds of millions of dollars Finchem has spent on marketing his tour’s flagship event, updating the venue, and ensuring that the purse on offer is the biggest on Tour — $9.5 million this year, with $1.71 million going to the winner and $1.026 million to the runner-up — have obviously done much to secure the Players a great deal of coverage and hype, but one suspects the only way it will ever be granted its dearest wish of becoming a fifth major is if the golfing public grow so bored with the debate regarding its status that they ultimately relent and agree to adding it to the list, just to avoid the PGA Tour’s hard sell.

But while the hoopla might be considered excessive at times, there’s no doubting the quality of the competition. All but Woods from the top 50 in the FedEx Cup standings are present, as are 45 of the world’s top 50 ranked players. Teeing it up will be 101 PGA Tour winners and 24 major champions. Some will say, with some justification, that Woods’s nonattendance loses the eventual winner some measure of credibility, but it should be noted Woods has not enjoyed anything like the same success at Sawgrass as he has had at Torrey Pines, Firestone, Bay Hill, or Augusta National. As Geoff Ogilvy said on Tuesday, it’s not as if he’s dominated the place.

The course, once derided for its peculiarities, is now regarded as an appropriate venue for an event of this stature, following the numerous upgrades it received two years ago. The fairways are now firm and fast instead of soft and spongy — thanks to the 53 million pounds of sand that were dumped on the fairways and 22 miles of piping laid beneath them — and a good deal more strategy is required to navigate the 7,215 yards. Sawgrass’s targets are still well-defined, but no longer can a player aim for just anywhere in the fairway or take dead aim at the flag without fear of leaving himself a very nasty chip or putt should he miss.

The rough will be more demanding this year, too. Though not as long as it was when the tournament was held in March, when the early-season timing encouraged overseeding and heavy watering, the rough is still an inch or two longer than it was last year. The head superintendent, Fred Klauk, preparing the course for his 23rd and final Players Championship, was careful to ease the field into the new-look course with a relatively painless setup 12 months ago, but he says the layout will “show more teeth” this year and present a much stiffer challenge.

Those who look most likely to meet that challenge include Stewart Cink, whose form this year has been good enough to add to his rather meager four career PGA Tour victories, but whose final round scoring average of 71.71 in the seven strokeplay events he has completed in 2008 (90th on Tour) is cause for concern; Anthony Kim, whose outrageous talents were on display in Charlotte last weekend; 2004 champion Adam Scott, who arrives with a win and a tie for eighth from his last two starts, and, of course, the defending champion, Phil Mickelson. A year after switching from Rick Smith to Butch Harmon in an effort to simplify his swing and become less wayward off the tee, the world no. 2 is still finding too few fairways (57.06% for 155th on Tour) but is hitting 60% of greens in regulation from the rough (fifth on Tour), which suggests he’s not missing them by much. And now that he is comfortable with his long game, he has been able to devote more time to chipping and putting, which, he says, were neglected a little while he focused on swing changes.

The man, or rather, the golfer, remains an enigma, however. While you have to put money on Mickelson winning a tournament or three every year, you can never be sure what those tournaments will be. For all this talk of greater consistency, he still seems just as likely to win a major following three missed cuts as he is to miss the cut after three successive wins. That’s part of what makes Mickelson such a fascinating player and part of the reason an estimated 500 million viewers from 200 countries will tune in to the Players at some point this weekend. If Lefty puts on a show like he did last year, some might even forget Tiger Woods isn’t there.

tonydear71@comcast.net