Then one day Whitey was thumbing through a baseball book on John McGraw's New York Giants, and it hit him like lightning.
"I saw they had a third baseman by the name of Buck Herzog," Herzog related. "I know darn well that Casey thought I was his grandson -- which, of course, I wasn't. And that's why he spent so much time with me."
Then, chuckling, Herzog said, "Had he ever asked me how my grandfather's doing, I would have said, 'Fine.' " -- without hesitation, he added.
Herzog, a captivating baseball raconteur much like Stengel was, will be inducted into the Hall of Fame on July 25.
Like Casey, Herzog was elected to the Hall of Fame for his achievements as a manager, as he had an unimpressive playing career in the Major Leagues. He'll be inducted along with outfielder Andre Dawson and National League umpire Doug Harvey.
Whitey, with his wife, Mary Lou, was in Cooperstown on Monday, touring the shrine during a day of orientation -- a primer for what he calls "icing on the cake."
Walking past a life-size statue of Ted Williams, Herzog remarked, "He's the best hitter I ever saw. Had he not spent all those years in the military, he would have hit 800 home runs."
Earlier, over lunch, Herzog rattled off anecdote after anecdote about many of the players he had during his managerial stops in Kansas City and St. Louis.
Halfway through the main course, he took a call from Hall of Famer George Brett, who played for Herzog when he managed the Royals and guided them to three consecutive division titles (1976 to 1978).
"Nice of him to call," said Herzog, quickly returning to tales about Joaquin Andujar, Jack Clark, Tommy Herr, Ozzie Smith, et al.
During Herzog's 11 seasons with the Cardinals, beginning in 1980, he won one World Series (1982, over the Brewers) and two other NL pennants (1985 and 1987). He said nothing was more hurtful than losing the 1985 World Series to the Royals when a blown call at first base by umpire Don Denkinger in Game 6 probably kept the Cardinals from winning that game and the Series.
Had it not been for Stengel, the legendary manager who won seven World Series and three other American League pennants with the Yankees, Herzog wonders what turn his career would have taken.
"I remember once Casey telling me that someday I would manage," he said. "He mentioned he saw leadership qualities in me."
Herzog, fresh out of New Athens (Ill.) High School, signed with the Yankees as a free agent in 1949 "for a $1,500 bonus and $150 a month. They signed [Mickey] Mantle the same year for $1,100 and $150 a month. Should have been the other way around."
After a productive season in the Minors in 1955, Herzog made the Yankees' 40-man roster and went to Spring Training in '56 with the Major Leaguers.
"When they gave me No. 74, I didn't think my chances of making the club were very good," he said. "But Casey was the man I looked up to the most. He spent an awful lot of time with me and taught me an awful lot about fundamentals I had never heard before. He had a great influence."
In a Spring Training game in 1956, "Mantle got sick, and instead of changing the lineup, Casey put me in the third slot. There was no way I should hit third, but he didn't want to rewrite the lineup.
"[Dodgers pitcher] Carl Erskine in the first inning broke off a 3-2 curveball, and I took it for a strike three. The next time I went up, Casey called me over and said, 'Tra-la-la.' What? 'Tra-la-la.' I didn't know what he was talking about, but I went back in the batter's box looking for a curveball, because Erskine had one of the best. I hit a line drive that Charlie Neal jumped up and caught, doubling the guy on second base.
"Casey came running up to me, screaming, 'See what I mean, tra-la-la!' I went back to the hotel and said to myself, 'What the hell was he talking about?' I finally figured out he was telling me to relax. He had his own language, and most of the time, it took you a day and a half to figure it out."
On Easter Sunday in 1956, Herzog, then considered a prospect, was traded to the Washington Senators, but during every game against the Yankees, he spent time with Stengel.
Stengel managed the New York Mets for four seasons beginning in 1962 and was still with the organization in 1966 when Herzog was hired as third-base coach. Herzog then moved to the Mets' front office for six seasons as their director of player personnel.
"When I was in player development, [Stengel] would come over to Payson Field in St. Petersburg during Spring Training before the Mets exhibition games and spend an hour with me. In a lot of ways, he's responsible for my being here today. Even before I ever played in the big leagues, I have pictures Casey autographed with me and him -- 'To a great leader' and stuff like that.
"For some reason, Casey knew I was going to manage in the big leagues. He knew that 20 years ago, before anyone else."
"He would say, 'You're going to manage someday and be interviewed a lot, and you'll have to handle the media. The first thing you say is, 'How much time you got?' Say [the answer is] 'Ten minutes.' 'How many questions are you going to ask me?' They say, 'Three.' He said, 'Let them ask you the first question, talk for 10 minutes, and you'll only get in one-third of the trouble.' That's good advice.
"Then he said, 'Don't ever hire your buddies as coaches. Just get the most capable people, because if you don't die on the job, you're going to get fired anyway.' And that's true, too. In the old days, managers hired their buddies because there wasn't much teaching done at the big league level."
Herzog, in all seriousness, said that above everything else, Stengel said he'd teach his teams how to win those five or six extra games by "running the bases better than anybody, scoring from first to home better than anybody" and winning more pennants than any other team.
That's exactly the way Herzog managed and why he's about to be inducted into the Hall of Fame.
Hal Bodley is the senior correspondent for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.