Following big victories by the International team in Australia and the United States in Virginia, Price said it was critical that these matches be closely contested.
'Everybody wants to see it come down to one game, one shot on Sunday,' he said earlier in the week. 'If that happens, then there will be a lot of interest in the event.'
Price nervously smoked a cigarette as he walked down a winding dirt path toward the second green Sunday evening. The pressure was stifling, and he didn't even have his clubs.
The one game?
Tiger Woods and Ernie Els, the best two players in golf for this occasion, in a sudden-death playoff to decide the Presidents Cup.
The one shot?
A dozen of them, all equally important, starting with the tee shots on the first of three extra holes and ending in darkness with two of the most pressure-packed putts ever hit.
Price was asked if he would like to be in that position.
'Not at this time,' Price said as he watched Els and Woods approach the green. 'When I was in my prime, it might have been different. But I'll tell you this: Everybody on our team, all 11 of us, want Ernie Els to be the one playing.'
The captains, Jack Nicklaus and Gary Player, ultimately felt it was too much pressure for any two players to shoulder, and they decided to call it a tie and share the cup.
Relief washed over everyone's faces on the green, International and U.S. players smiling and hugging each other at the end of four marvelous days of golf.
'The perfect decision,' Woods said.
Still, the tie left some with a feeling of unfinished business.
When the Ryder Cup or the Solheim Cup ends in a tie, the defending champion goes home with the trophy. The Presidents Cup rules stipulate that the matches are decided by a sudden-death playoff between two players whose names are placed in an envelope.
Nothing was decided.
Logistics have to be considered. Nicklaus and Players were hashing out a plan as they walked down the fairway of the second playoff hole, realizing descending darkness would allow for only two more holes.
Return on Monday?
'These people will be absolutely angry,' Player told Nicklaus, waving his head to thousands of fans who raced along dunes lining the fairways to see every shot.
Nicklaus and Player and most of their players spoke all week about sportsmanship and the betterment of golf, and a tie only seemed logical.
'We're playing for goodwill,' Nicklaus said later. 'We're not playing for blood. The Ryder Cup should be played for exactly the same reason. The game is bigger than this. The game is better than Gary, it's bigger than me.
'We're just pawns in the game of golf.'
Given the spirit of these matches and the quality of golf, a tie was acceptable.
Nicklaus and Player said they would urge the PGA Tour to do away with the playoff format.
That would be a mistake.
Els and Woods playing for more than just themselves is no different than what Hale Irwin and Bernhard Langer faced in the final match of the 1991 Ryder Cup, when Langer ultimately missed a 6-foot putt that gave the Americans victory.
Jay Haas was in a similar situation in the '95 Ryder Cup at Oak Hill, when he came to the 18th hole tied with Philip Walton, the trophy hanging in the balance.
Haas tried to guide his tee shot and popped it up into the right rough. He wound up making a double bogey, and Europe won the cup.
At the start of this week, Haas was asked if he would like to be in that position again.
'To have your match by the deciding match? Yes, I do,' he said. 'I probably didn't want that in '95. I wasn't prepared mentally, and it showed.'
Every player dreams of such moments. They aren't champions if
They feel otherwise.
Woods and Els, predictably, rose to the occasion.
Woods has faced his share of pressure putts. The biggest might have been a 6-footer for birdie on the 72nd hole of the 2000 PGA Championship, which he made to force a playoff with Bob May during his unprecedented sweep of the majors.
The 15-foot par putt Sunday on the third extra hole -- over a ridge, down a slope and breaking 10 inches to the right -- was far different.
'You let everyone down with one putt,' Woods said. 'That's a lot of pressure.'
Els felt it even more.
No one has finished second to Woods more often than the Big Easy. Els was playing before his home crowd, and already had been whipped by Woods in their marquee singles match earlier that day.
He made two huge putts in the Presidents Cup playoff -- from 12 feet on the second extra hole, and 6 feet in the gathering darkness, which turned out to be the final shot.
They were asked to compare the pressure with anything else they had faced.
'I'd like to hear what Tiger says first,' Els said, breaking into an easy smile. 'You were very calm, weren't you?'
'Man,' Woods said, shaking his head. 'That was one of the most nerve-racking moments I've ever had in golf.'
They shared laughs, just as they shared the cup.