Not long ago, David Cone -- who is about to make Sunday Night Baseball on ESPN a whole lot better this season -- was looking for a movie to watch with his 10-year-old son. As they were searching Netflix and Amazon, a trailer for Kevin Costner’s wonderful baseball movie, “For Love of the Game,” happened to come on the screen.

“What’s that?” David’s son asked.

“My life,” Cone said.

The movie tells the story of an aging Tigers pitcher named Billy Chapel, at the end of his career, trying to pitch a perfect game against the Yankees at Yankee Stadium. As he does, across those nine innings, it is as if his whole life is passing before his eyes -- and not just his baseball life.

The movie came out on Sept. 17, 1999, following the other iconic baseball movies Costner had already done: “Bull Durham” and “Field of Dreams.” But the one that resonated the most with Cone, then and now, was the one about a 40-year-old Chapel trying to find the magic, and immortality, of a perfect game, and doing it at Yankee Stadium.

It is exactly what Cone had already done on July 18, 1999, on Yogi Berra Day, with Don Larsen (who of course had pitched the only perfect game in World Series history for the Yankees in 1956) in the house, having thrown out the first pitch that day to Berra, who happened to be using Joe Girardi’s catcher’s mitt.

• An oral history of David Cone's perfect game

Cone was 36 on that Sunday afternoon, not all the way at the end of his fine career but close enough, pitching against the Expos almost two months before Costner’s movie came out. In this case, it was a moment of life, Cone’s baseball life, imitating art.

“It really was my life, that movie,” Cone said recently. “I guess the timing was just part of the magic of the whole thing.”

When “For Love of the Game” did open, Cone received a note from Kevin Costner that read, in part: “You captured what I was trying to do with the movie.”

I asked Cone if, when he thinks back on his own perfect game, he was having the same kind of flashbacks, about almost everything, that Costner’s Billy Chapel did in the movie.

“For me,” he said, “the flashbacks about some close calls I’d had, those were the thoughts I was fighting.”

Cone talked then about taking a no-hitter into the seventh inning with the Mets one time before it was broken up, and about a game between the Blue Jays and the Rangers in 1995, when Benji Gil broke up his no-hit bid with one out in the ninth.

“My mentality was pretty basic. The longer the game went,” Cone said, laughing, “I just kept telling myself not to blow it.”

There was a pause at his end of the phone, then he said, “In so many ways, I think of it as my last hurrah.”

Cone said he pitched “pretty well” for the Yankees in the 1999 postseason. He pitched a little better than that, with a 2-0 record, seven innings of two-hit ball against the Red Sox in the American League Championship Series and seven innings of one-hit ball against the Braves in the World Series. But he went 4-14 the next season for the Yankees, even if he did get one big out -- against Mike Piazza -- in the Subway Series between the Yankees and Mets. There would be a brief, failed comeback with the Mets in his later years.

In Cone's mind, though, the last hurrah was that July day at the Stadium, a movie moment of his own, with both Larsen and Berra in attendance.

“I threw 88 pitches that day,” Cone said. “There was a huge ‘8’ in Yogi’s honor behind home plate. Go figure.”

Another pause, then he said, “Maybe it was meant to be.”

There was never a better or more intelligent baseball interview, before games or after games, than Cone when he was still pitching. He transferred his ability to talk about baseball to the YES booth and will do the same now for ESPN. He doesn’t have an act. He is just himself, smart and knowledgeable about the art of pitching, and with a low-key sense of humor.

A lot happened to Cone, a Kansas City kid, after he broke in with the Royals in 1986. He became, truly, one of the most gifted and creative starting pitchers of his time, retiring with a record of 194-126, eventually being a part of five World Series-winning teams: one with the Blue Jays and four with the Yankees.

Finally, near the end, Cone had his own Billy Chapel game at Yankee Stadium, as a Yankee. I asked him the other day if he had ever watched the whole game, and he said he had, when he was working with Jack Curry on his book, “Full Count: The Education of a Pitcher.”

“Were you nervous?” I asked.

“It surprised me how much, actually,” Cone said. “And when I got to the ninth the way Costner did? I was still telling myself not to blow it.”