"I'll never forget it," said the Detroit Red Wings centre. "Joe Kocur handed me the Stanley Cup and I grabbed it. "Everything that I'd ever dreamed about as a hockey player from when I was a little kid came true that night when I grabbed it. It's the most special feeling I've ever had as a hockey player."
Any athlete in any sport will attest to it: That special feeling of going all the way creates an unquenchable thirst.
"Once you've experienced it, winning the Stanley Cup is something you can never get enough of," said Draper. "We've been fortunate to win three Cups in the last 10 years.
"Ask anyone in this dressing room and the guys who have won it want it more and the guys who haven't won it want to experience it for the first time. That's what makes this time of year so great, given the opportunity that sits there right in front of you.
"When you do win, it's the most rewarding feeling a hockey player can have. Two months of travelling and playing every other night, the sacrifices you make and your family makes and, when the moment arrives when you've got that Stanley Cup, everything is worthwhile."
Draper's pursuit of a fourth ring continues Saturday when the Red Wings take on the San Jose Sharks (2 p.m. ET) in a Western Conference semifinal that is all even at two wins each.
As far as Draper is concerned, the five years he's waited since the last Wings triumph has been far too long.
"You wonder," he replied when asked if he'd worried he'd never get another shot at the Cup. "There's so many great teams.
"You get close and then you lose and then you have to start all over again. That's probably the toughest part - getting back into training camp and realizing you've got camp and 82 games to go through again. It's so demanding to try and win the Cup that every sacrifice you put forward is worth it when you do win it."
So, every time the Torontonian jumps over the boards to take a shift, his blades flash as fast as he can move them. He checks as if his life depended on taking the puck away from an opponent. He wants another taste of iced champagne from the lip of the Stanley Cup.
"We're in a great series with San Jose," Draper said after practice Friday. "We've got a best-of-three at home here and we just want to keep this thing rolling."
Amen to that, says Dominik Hasek.
The skinny Czech quit after Detroit's 2002 title run but he came out of retirement looking for another championship fix.
"This is the reason why I came back," he said. "I didn't come back just to play.
"I came back to compete for the Stanley Cup. Now I have the chance. For me, it's the most exciting time of the hockey season.
"There's no better feeling in hockey than to win in the finals and to raise the Stanley Cup. I'm trying to do my best to have this chance again."
After their 3-2 overtime win Wednesday to even the series, it could be said that the Red Wings have the momentum, but coach Mike Babcock shoots down any such suggestion. Things can change quickly on the ice, he says.
So true. San Jose has twice led the series. It has had two-goal leads in three of the four games and lost twice. The Sharks realize that they have to stop going into a shell when they get ahead, that they must keep attacking. An intensified forecheck would help.
"We've been relaxing a little too much," said Jonathan Cheechoo. "After we get the first goal, we just have to keep going - act like the score is still 0-0.
"That's our biggest problem."
One just as big, perhaps, is the craving for another title that brings out the best in so many Red Wings. Many of them can't wait another five years.
Draper has his dream of a fourth ring, Hasek wants another, too, and nine of their teammates own championship rings, while the only San Jose player with NHL finger jewelry is Bill Guerin, who won't play Saturday due to a facial injury suffered in Game 4 when he was clobbered by a puck.