And there is just one thing about that sweltering afternoon that Cone might change -- his reaction after the final out. With Orlando Cabrera's popup safely nestled in Scott Brosius' glove, Cone planted both hands on his heads and dropped to his knees before being tackled by catcher Joe Girardi.
"I look at that last part and I say, 'What am I thinking about, dropping to my knees?'" Cone said. "It was completely unrehearsed. That's not something you think about doing. I just remember collapsing from exhaustion, and now I look at it and think, 'Maybe I should have done something different there.'"
For the rest of the world, the story of Cone's 88-pitch performance on July 18, 1999 needs no revision. Cone relived his day of perfection on Saturday, throwing a ceremonial first pitch before the Yankees' matinee against the Tigers.
"I can't believe it's been that long already," said Girardi, who caught Cone's toss. "It seems like just yesterday that we were out there together."
A decade ago, it was a sweltering afternoon in the Bronx -- Yogi Berra Day -- as the Hall of Famer snagged a ceremonial first pitch from Don Larsen, reuniting the battery that combined for a perfect game in the 1956 World Series. Cone's attention was elsewhere because of the events.
"I just remember warming up before the game and not really even thinking about the game, because Yogi was riding around in this convertible," Cone said. "We were just laughing. Yogi is like a cartoon character. I was happy-go-lucky."
By the end of the afternoon, in front of a crowd of 41,930 that spent the final few innings on their feet, Cone had found even more reasons to smile.
Blessed with a slider that seemed to stop in mid-air before making a hard left turn, Cone knew that the free-swinging Expos lineup had never faced him and his variety of arm angles. They didn't have a chance.
"It was probably the best slider I've ever had, against the right lineup," said Cone, who struck out 10. "I could throw it for a strike that day, I could just miss with it, and I could sweep it off the plate. It was probably the best command and break I ever had."
It was an outing that was almost lost to the elements. The clubs waited out a 33-minute rain delay in the bottom of the third inning, and there was some question if Cone would resume the game. But the showers stopped, and Cone came back out relaxed and sharper.
"The thing that was amazing to me was how much better his stuff got after the rain delay," Girardi said. "A lot of times, it can be the opposite. He came back and he was lights-out."
By the fifth inning, Cone had started to consider how the storylines might go. Not only was it Berra's day, but David Wells had thrown a perfect game against the Twins on that same mound the year before. Three seasons after Cone had to leave a no-hitter at Oakland because of a pitch count, his first game back from an aneurysm, this one might be meant to be.
"This is unbelievable," Cone said. "A lot ran through my mind. I'm 36 years old and this is probably the last chance I'll ever have to be in that position. I was well aware of it. In some ways, I'm thankful that I was older so I could appreciate what was going on."
As the zeros piled up, the Yankees began keeping their distance between innings. The only one to sniff at superstition was Chili Davis, the hulking designated hitter, who had warmed up Cone while Girardi strapped his gear back on between innings. Cone took it easy, lobbing hit-me fastballs.
"In between innings, Chili came up to me and said, 'You know, I used to catch in the Minor Leagues. I can catch your [stuff],'" Cone said. "He said it just like that. Something like that. It really made me laugh and helped to break the ice. Chili was my guy."
With the fans standing for the ninth inning, Cone struck out Chris Widger on three sliders, then got Ryan McGuire to fly out to left field on a ball Ricky Ledee battled to see. In the field, shortstop Derek Jeter said he still wanted the ball hit to him, but he felt extra pressure.
"Don't screw up," Jeter said. "It was tough. It was a day game, and day games change everything because the infield is hard, the sun is in your eyes. There's a lot of things that come into play. But it's pretty much, 'Don't screw up.'"
Cabrera popped a 1-1 slider into the sun and Cone squinted at it, pointing to the ball and hoping that Brosius would see it too. He did, and Cone was soon being hit with a bear hug from Girardi, piled on by Jeter and second baseman Chuck Knoblauch, and then the whole roster.
"It was just one of those things that was meant to be," Jeter said. "What can you say? He was perfect."
The jersey Cone wore wound up in the National Baseball Hall of Fame, and Yankees manager Joe Torre provided Cone with one of the few keepsakes he has from that game, a bag of muddied American League baseballs that were thrown out of play by home-plate umpire Ted Barrett that afternoon.
"I wasn't much of a collector," Cone said. "I'm kicking myself."
Cone's career certainly had more highlights than just those 27 outs. After winning 194 games over 17 Major League seasons with the Royals, Mets, Blue Jays, Yankees and Red Sox, Cone likes to point out that he was a member of all four Yankees World Series teams from 1996-2000.
But when he encounters fans as he did Saturday on the Suite Level, it seems all they want to talk about is that sweltering afternoon in 1999. Cone hears stories from people who claim to have been in the upper deck, the teenagers listening at the Jersey Shore or the firefighters watching on a small TV set.
"I get them every day, almost," Cone said. "The further removed I get from this game, the more I appreciate that this was my signature moment."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.