K.J. Choi has plenty to celebrate after his biggest PGA Tour victory. (Streeter Lecka/GETTY IMAGES)

There’s no explaining how a man can stand over an 18-foot birdie putt on the 72nd hole of a tournament — in one of golf’s best amphitheaters, the banks around the 18th green at TPC Sawgrass — and execute the purest of pure strokes to make birdie and force a playoff, and then not 20 minutes later face an uphill putt of three-and-a-half feet to extend that playoff, and flat-out miss. Yet that was David Toms’s fate Sunday evening at The Players Championship, exhilaration to devastation — win to loss — in less than half an hour.

“I just wasn’t there on the putt,” Toms said.

So there stood K.J. Choi — so often a solid supporting player, rarely golf’s leading man — holding the Players trophy on TPC Sawgrass’s signature island green, the 17th, perhaps the biggest victory of his career secured. It was at the 17th that Choi took the lead in regulation with a sliding 10-foot birdie putt, and it was there that Toms handed him the tournament by three-putting from 18 feet — including that last, little miss — on the lone playoff hole.

“Right now, it’s my dream to have my hands on this trophy,” Choi said.

To be sure, Choi is a worthy winner of any event. Scarcely a player on tour would be surprised if the South Korean — even now, just shy of his 41st birthday Thursday — eventually won a major championship. He won the 2007 AT&T National at Bethesda’s Congressional Country Club, site of next month’s U.S. Open. He has been in the mix at the Masters, and his nerves rarely show.

But the defining shots on this long day — rain pushed part of the third round into Sunday morning, so Toms endured 32 holes on the day, Choi 27 — belonged to Toms, the 44-year-old Louisianan who won the 2001 PGA Championship but hasn’t won on the PGA Tour in five years.

“With the lead or around the lead the whole time,” Toms said, “it’s tough when you haven’t been there in a while.”

With third-round leader Graeme McDowell completely unraveling en route to a closing 79, Toms was in control much of the day. But he made a decision at the par-5 16th that kept Choi in the game, hitting his 244-yard approach into the water rather than laying up. That bogey — and Choi’s own miss of a five-foot birdie putt — left the pair tied headed to the 17th. There, Choi took the outright lead with the birdie that got him to 13 under.

“For some reason, today, I felt very comfortable out there,” Choi said through an interpreter.

At that point, there could have been others in the mix as well. Paul Goydos, who lost a playoff to Sergio Garcia here in 2008, had makeable birdie putts at both 17 and 18. He missed both and finished at 11-under 277, alone in third.

Nick Watney, who won over a field that included all of the top 50 players in the world at Doral, might have accomplished a similar feat here if not for the 481-yard, par-4 14th. Twice he made double bogey there, and his bogey in the final round stopped any momentum. He also played the par-5 16th — statistically the easiest hole on the course — in 1 over. The result: Watney played Nos. 14 and 16 in 6 over, the other 16 holes in 16 under, and finished tied for fourth.

“I feel like it’s never easy,” Watney said. “But I thought I would know how to handle myself. . . . I’m pleased with the way I hung in when I didn’t have my best stuff.”

McDowell’s struggles, though, were more stunning. He ended the third round with an unlucky double bogey — his approach from the right rough hit the right side of the green, and somehow shot across the entire putting surface into the water — but he still carried a one-shot lead into the afternoon 18.

But McDowell pushed one drive deep into pine trees at 6, then yanked one into a hazard at 7. “At that point, I just felt the life kind of drain right out of me,” he said. He eventually put balls in the water on both 17 and 18, and tied for 33rd.

“Everything I tried just went wrong,” McDowell said.

That’s what Toms could have thought when he approached his ball in the 18th fairway, having hit one of his best drives of the tournament at Sawgrass’s toughest hole. Down one, Toms needed birdie. But his ball found a divot. He had 178 yards in, and he choked down on a 5-iron, a brilliant shot to 18 feet. The putt he stroked next — “the best putt I’ve had in an awful long time,” he said — left him pumping his fists repeatedly, a birdie that put him in the playoff.

The putt in the playoff, though, elicited a decidedly different response.

“I was probably thinking ahead and thinking about the next hole,” Toms said, “and I just got up there and missed it.”

One unlikely make, another unlikely miss, and K.J. Choi — not David Toms — had his biggest win in years.