"There was one time in the Bahamas, playing blackjack, that we sat down for a little while with Matt Damon, and we sat there and played for a little while," Walker recalled of a gambling evening where athletes and thespians mixed.
A baseball odd couple, they sat on the dais in a penthouse hotel ballroom, baseball's newly minted Hall of Famers.
Jeter, a first-round draft pick, came within one vote of being the second unanimous pick.
Walker, a youth hockey player who took up baseball at age 16, was elected in his 10th and final try on the baseball writers' ballot, making it with just six votes more than the 75% required.
"I don't care where they put me — put me in the restroom," he said. "But to be next to Mo is quite a thrill."
Mr. Cool as always, Jeter was unassuming, humble, collected and quick with a quip to deflect. Walker was more raw as they told stories of their passage from amateurs to elite: Of the 19,960 players to appear in a major league game, they will be Nos. 234 and 235 inducted to the Hall, according to its tally, including 134 chosen by the Baseball Writers' Association of America.
"It doesn't get any better than this," Jeter said. "There's no more awards. There's no other place you can go. This is it."
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Walker, like Jeter, put on the cream-colored Hall of Fame jersey. When he took the phone call Tuesday informing him of election, he was wearing a garish yellow-and-black SpongeBob SquarePants shirt. His 20-year-old daughter Canaan sent a text "Way to go, dad. ... You're trending," he recalled.
"I knew we're going to go sit outside and hang out up front, so I just wanted something a little warmer," he said.
Jeter was an $800,000 bonus baby, won five World Series titles and became captain of the Yankees. Among baseball's best-known stars, he was a GQ icon, no hair ever out of place — back when he had hair.
"How's it look?" he said after putting on the Hall jersey.
Walker was somewhat dazed.
"Pinch me," he exclaimed.
Born in British Columbia, Canada, Walker signed with the Montreal Expos for $1,500.
"Bought my girlfriend a necklace and she dumped me and had only about $1,000 left from that $2,000 Canadian," he said.
He was so unfamiliar with baseball when he started his pro career that during a 1985 New York-Penn League game he ran across the infield from third to first after a drive that was caught on a hit-and-run, not realizing he had to retouch second on the way back. In 1994 while with Montreal, he handed the ball to a fan after Mike Piazza's foulout, thinking it was the third out and allowing the Dodgers' Jose Offerman to tag up from first and sprint to third.
Walker spent his best decade in the mile-high air of Colorado's Coors Field, then finished with St. Louis. His only Series appearance was when the Cardinals were swept by the Red Sox in 2004. He points out he was 0 for 18 in his career against Wally Whitehurst, a pitcher with a career record of 20-37.
Asked whether he would be in the Hall if he hadn't raked in the thin air, he quickly replied: "Absolutely not."
"I get it. Coors Field's a great place to hit. There's no backing away from that," he said. "But I believe with that, I did it better than anybody else at that ballpark. So that had to be some consideration, I guess."
Jeter, of course, played for the Yankees' famously demanding owner George Steinbrenner.
"He had a real tough time comprehending that over a course of a 162-game season you may lose a game," Jeter recalled. "I can say I had the same mindset on the field."
He was the perfect pinstriped player, a Yankees lifer.
"My parents used to always tell me, look, you have to sit back and enjoy the moment," he said. "I was just never able to do it. I don't know if that's a character flaw or if it's part of the reason why I'm here. It was always just, what's next?"
Walker is every bit as much a competitor, which helped him overcome his late start.
"I just took up 10-pin bowling after I retired and I threw a perfect game two years later," he said. "So I love the challenge of trying to learn something new. Baseball was new for me."
While preparing for his induction to the Hall on July 26 in Cooperstown, Jeter will be in the midst of his third season as CEO of the Miami Marlins. He has endured two last-place finishes and the lowest attendance in the major leagues, unfamiliar results and environs.
"I preach patience, even though I have none," he said. "I didn't get into this to lose. I could have stayed home and retired. Just ask my wife. She probably would have been a little bit happier if I was at home every day and retired."