Pappas was 23 years old at the time and coming off three seasons in which he'd established himself as one of the American League's better pitchers by winning 43 games for the Orioles.
To say Pappas did not lack confidence would be an understatement. In fact, in those early days, a few of his teammates thought he might have been blessed with a bit too much.
• Former All-Star Pappas passes away at 76
Anyway, back to Steadman's question about beating the Yankees, which not too many teams did in those days, especially the Orioles.
"If I pitch a shutout and hit a home run, we'll probably win," Pappas said confidently.
You can look up what happened next. On April 18, 1962, Pappas threw six shutout innings and hit a home run as the O's beat the Yanks, 1-0.
That story speaks volumes about the man who died Tuesday at 76. Pappas will be most famously -- and in many ways, unfairly -- remembered for being part of something he had absolutely no control over: one of the most lopsided trades in baseball history.
After the 1965 season, the Orioles made Pappas the centerpiece of a deal that brought Frank Robinson to Baltimore. While Robinson led the O's to four American League pennants in six seasons and won the Triple Crown that first season, Pappas found himself stuck on a string of Reds teams that didn't come close to the World Series.
And that trade should not be Pappas' legacy, because the truth was he had a very, very good career. He pitched 17 seasons in the big leagues and won 209 games for four teams. Pappas made two All-Star teams and pitched a no-hitter.
That too many people remember Pappas for being traded for Robinson is one of those strange, unfair things about sports.
"That doesn't bother me," Pappas told the Baltimore Sun in a 2009 interview. "There's nothing I could have done to prevent it."
The Orioles signed Pappas out of Detroit's Cooley High School in 1957 for the lofty sum of $4,000, sent him to the Minor Leagues for three games and brought him to the Major Leagues at 18 that season.
If Pappas wasn't exactly the Doc Gooden of his day, he arrived with about as much hype as a kid in Baltimore could have. His debut came in the eighth inning of an August game against the Yankees, and his first three hitters were future Hall of Famers: Enos Slaughter, Mickey Mantle and Yogi Berra. Pappas gave up a single to Mantle but retired the side, then gave up a single in the ninth inning before retiring the side again.
"My first warmup pitch went 50 feet over [catcher] Gus Triandos' head," Pappas said. "Mickey got a hit -- I heard it go by my ear, but I never saw the ball. It probably would have killed me."
Pappas won 25 games before his 21st birthday, and in nine seasons with the O's, he never had a losing season. In 1965, at 26, he was well regarded to the point that he helped prompt the Reds to trade Robinson, a future Hall of Famer and one of the five or six greatest players in baseball history.
Pappas was bitterly disappointed about leaving the Orioles, but he came to accept it as being part of the business. His teammates knew him as being honest and blunt for having a fiery competitive streak.
One thing, though, appeared to eat at Pappas until the end of his life. On Sept. 2, 1972, he flirted with history. Pappas was 33 years old and retired 26 straight Padres while pitching for the Cubs at Wrigley Field. But one out from a perfect game and a full count on Padres pinch-hitter Larry Stahl, umpire Bruce Froemming called a ball.
Pappas got the next hitter to finish the no-hitter, but he never forgave Froemming for the walk.
"To this day, I just don't understand it," Pappas said in 2009.
Pappas' life had moments of tragedy. His wife, Carole, disappeared in 1992 and was found five years later, her car having plunged into a pond near their home in a Chicago suburb.
He remarried and is survived by his wife, Judi. He was a frequent visitor to games in Chicago until late in life. Among the hundreds of friends he made: President George H.W. Bush.
Bush singled off Pappas in an old-timers game in 1984, and as Pappas said, "We've been friends ever since."
But the Orioles remained front and center in Pappas' heart. He won 110 games during the franchise's growing years.
Two summers ago, when the O's were celebrating their 60th anniversary in Baltimore, Pappas was brought back as a member of the team's Hall of Fame. He wasn't sure he'd be remembered as anything more than "the guy they traded for Frank Robinson" and was clearly touched by the warm ovation he received.
"They gave me my big shot," Pappas said later. "I will always appreciate that."