The 5-year-old Derek's attempts to guess the actual retail values of vehicles, vacation cruises and household goods were inevitably fruitless, and Dad would win, time and time again. Looking back through the haze of time, there was a lesson to be learned -- one of many that Jeter would carry with him all the way to Yankee Stadium.
"Always work hard and don't let anyone outwork you," Jeter said. "Stay positive. I think that's the biggest thing. I'm not a negative person and I always try to stay positive regardless of what happens. Those are lessons that I learned from my Dad."
Jeter's childhood proclamation that he would one day play shortstop for the Yankees is well-known, but part of the source of his inspiration was from his father, who was a college shortstop before eventually beginning a career as a substance abuse counselor.
"He played when he was in college, so I wanted to be like him when I was younger," Jeter said. "But he never pushed me into it at all. My parents supported anything I wanted to do, but they never once pushed me into playing baseball."
He may have discovered the game on his own, but once he showed a passion for it, Jeter's parents helped fuel that. Many an early evening was spent on the grassy fields of Kalamazoo, where Jeter and his younger sister, Sharlee, could be found fielding grounders and taking swings with his mother, Dorothy, and his dad.
"It was a family thing," Jeter said. "My sister played softball, and my high school was in my backyard, so we had a baseball and softball field there. We'd go as a family, and I'd hit, and we'd go over and my sister would hit. We did that together."
That helped tighten the bond between Jeter and his father, though -- like in any household -- there were occasional clashes. Jeter found his childhood to be tough at times, but fair.
Each August, Jeter was presented with a contract drawn up by his Dad on a legal pad, permitting him to play sports only if he complied with a series of expectations that included posting high grades, participating in extracurricular activities and avoiding drugs or alcohol.
"That was every year, it wasn't just one," Jeter said. "That was every year I had to do that, and that was more than baseball. That had a lot of things in it. As a kid, you don't understand it, but I think as you get older, you appreciate it."
The idea worked. Jeter said he never violated one of the clauses, for fear of disappointing his parents. Years later, he would indeed look back and believe that the code of conduct he was expected to uphold -- on and off the fields of play -- would help shape him as he prepared for a Major League career.
"I think who you are as a person -- your personality, your characteristics -- those are things that you learned at home," Jeter said. "So I was always taught to respect other people, respect opponents and treat people how you want to be treated.
"There were a lot of times when you clash with your parents, but they were pretty good at explaining things. When you're a kid, you don't always agree with what they're saying. But my parents were always good at explaining, 'Why,' whether I agreed with them or not. They always gave me pretty good explanations."
Today, Jeter's attitude in the clubhouse -- even after the most crushing of Yankees losses -- can be described as relentlessly optimistic. There is always another game to play, another opportunity to prove yourself, another chance to make things right.
When Jeter was in one of the worst slumps of his career, enduring an 0-for-32 drought in April 2004, he put his uniform on each night expecting to get a hit his first time up. That positive outlook, Jeter believes, took its cues straight from Dad.
"No question," Jeter said. "Especially when you play in this sport, you play a game every day, you're going to have a lot of negatives -- a lot of failures. If you can try to take a positive out of every day you play and not dwell on negatives, that's something that I learned."
Given Jeter's background, it is not surprising that he continues to speak daily with his parents. Both are instrumental in helping Jeter operate his successful Turn 2 Foundation, along with Sharlee, while Jeter chases his 162-game schedule into October.
"It means a lot," Jeter said. "My parents have always been supportive throughout the years, and not just since I made it to the Major League level. They were supportive of me and my sister throughout the years. We have a pretty close family and that means a lot."
Jeter said that, on this Father's Day, he expects that he will tell his Dad, 'Thanks,' but that is not anything unusual in and of itself -- Jeter thinks that is an appreciative sentiment that should be relayed more than once every 365 days anyway.
Their relationship has evolved and matured over the years, but Jeter says that he knows with any pressing issue, his Dad is still one of the two people he would probably first turn to.
"We're more friends than anything," Jeter said. "I think as I've gotten older, you still have the father-son relationship, but we've become closer friends. We're pretty close. He's still my Dad, but moreso, a friend. Along with my mom, they've known me the longest, so I would definitely go to them first with anything."