But that's just not the way he was raised.
Griffey Jr. recalls one lesson in particular his dad taught him, a lesson he'll pass on to his own kids (athletes themselves; son Trey is a redshirt sophomore wide receiver at the University of Arizona, while daughter Taryn will join her brother at Arizona playing basketball this fall. Youngest son Tevin, 12, plays football, too).
"[I'll tell my kids] to be themselves," said Griffey Jr. "[My dad] said, 'Hey, just be yourself. You're not Joe Morgan or Pete Rose or Lee May. You're my son, just be my son, be yourself.' That's one thing I learned. It's tough to be yourself, so why try to be somebody else?"
So Junior stayed true to his roots -- those of a keep-your-head-down, hard-working family from Donora, Pa.
"I was very proud of my hard work and his hard work," said Griffey Sr. "We worked together, and I tried to work on the mental side [of Junior's game], which is probably the toughest side for him -- and he did an outstanding job both ways. Physically, he had the talent -- he was a five-tool player. But the mental side I worked on with him, because I wanted to make sure he did the right things."
There is no doubt these days that Junior did all the right things.
Just ask Bench, who has known the younger Griffey since Junior was a kid in that legendary 1975-76 clubhouse.
"I remember when he got to high school, he could do anything," said Bench. "There wasn't anything he couldn't do. He's just one of those gifted athletes. His parents [Ken Sr. and wife 'Birdie'] were great role models, they meant a lot, and they raised a good kid.
"When you watched him play, it was a thing of beauty -- of power, of precision, of speed. It was very special. I'm glad to see his success. He's so humble and quiet in so many ways. He's not going to stand up and beat his chest. He's going to just say, 'I played and had a good time.' You don't have to give him anything more than that."
Echoing Bench's praise is Junior's longtime agent, Brian Goldberg, who has known the Griffey family since 1978 -- when Goldberg and Ken Sr. were in the same University of Cincinnati "Introduction to Communications" class.
The story goes that Ken Sr. had been trying to learn some public-speaking skills during that 1978 offseason, and Goldberg, then a freshman law student, was the first to recognize his famous classmate.
"I was the first person in the class to recognize [Ken Sr.]," Goldberg said, "but I kept it low-key and introduced myself after class. He was very friendly and asked me to keep it low-key so that he could actually learn what he was supposed to be learning.
"The first time I met Junior, he was 8 or 9 years old. But when he was the first player picked in the Draft in 1987, they let me represent him. By that time, I had went on to law school and became an attorney.
"It was great watching him grow up. He was just a typical teenager. But when he got drafted, all of the attention was on him for baseball, [and so] he had to grow up quickly. I am so proud of him. For all of the years I've worked with him -- and still do -- never once has he gotten into any trouble. I'm proud of him, not just as a ballplayer, but as a person."
That last point is especially important. Despite playing during the "Steroid Era," Junior's name was never tarnished.
Junior, like his dad, is known as a loyal guy and a team player.
"My dad played for the Reds, so I wanted to play for the Reds," said Junior. "And when he played for New York, I wanted to play for the Yankees -- and when he went to the Braves, I probably wanted to play for the Braves. It's just like any other kid: Whatever your dad did, that's what you wanted to do. It just so happened that my dad played for the Reds."
So when the opportunity arose in February 2000 for The Kid to come home, the Griffeys and their fans rejoiced.
"When [Junior] came back to Cincinnati, there were a lot of old friends that wanted to reconnect with him, which he did," Goldberg recalled. "But what a lot of people don't realize, [they] would drive up to Detroit or Cleveland -- which was a reasonable drive -- and they would watch him play. Junior would always reserve a block of rooms at the hotel and throw a big party for all of his old friends. He would love it when his old friends would come up and see him play."
Junior's Cincinnati career never quite flourished the way some thought it would.
"The thing about Junior is that he never wanted to be, 'it,'" said Bench. "He just wanted to play baseball. So when he came back here, I think it was overwhelming in many ways for him, because he never wanted to be 'it.' But they treated him like he was going to take them to the Promised Land. Junior just wanted to be part of the cast, a member of a team. You want him to produce, you know he'll produce. But it's not his job to win a World Series -- it's a whole team."
Yet, The Kid doesn't harbor too many regrets.
"The one thing [I do regret] is not being able to win a championship," said Griffey Jr. "I think everyone dreams of winning it, but it just wasn't meant to be."
And why should he have any regrets? He's earned his reputation as one of baseball's sweetest swingers, with 630 home runs to his name, and a place in history as half of the best father-son duo ever to take the field. Not to mention, he's also a role model for several current Reds -- including outfielder Jay Bruce, who played part of the 2008 season with Junior.
"I played with him, and we stay in touch," said Bruce. "I consider Ken a friend and someone I really looked up to and idolized growing up. I think he was the guy who everyone looked up to. But I don't think you could really model your game after Ken Griffey, Jr., because he did everything so well.
"When I was young, I hit just like him. I still kind of stand straight up, with the hands where they are and the elbow and everything. But Ken was the guy. Had he been able to stay healthy throughout the whole thing, we could have been looking at someone who completely changed the game of baseball."
Bruce will always remember a few of his friend's feats.
"When I played with him, the 600th home run was something that was pretty amazing," said Bruce. "And one time, he was sick and he was in the clubhouse, and they asked him to pinch-hit in the bottom of the ninth against the Pirates. He hadn't taken a swing all day -- he was sick and wasn't feeling well at all. He walked up to the on-deck circle, went to the plate and hit a walk-off home run. It was something that I'll never forget as a player. It's something that I still marvel at."
Reds third baseman Todd Frazier is also in awe of both Griffeys.
"That sweet swing [Junior] had, and to meet his dad every year, talking to him about the stories he had," said Frazier. "It's really true about baseball: You get to meet some really great guys and you get some good friendships along the way. I've never met Junior. But the way Senior is, I'm sure Junior's a real class act, as well."
Bench said he recognized how special the father-son dynamic is between the Griffeys.
"I don't think Ken Sr. could be any happier," said Bench. "He was proud of his son from the very beginning. It's a rare thing that they got to play together, hit home runs in the same game together [author's note: back-to-back dingers to boot!], do all of this stuff together. I think it was a foregone conclusion that [Junior would be] in this Hall of Fame. It was just a matter of time. And when the time comes, he'll be in the Baseball Hall of Fame."
Senior was happy to soak it all in.
"For me, it was just watching him grow," said Griffey Sr., "getting better, doing all of the things he was supposed to do."
So when the moment comes for Junior's induction into the Hall, will the tears flow, too?
"I'll tear up maybe, but I won't cry," Senior laughed. "Oh, [Junior will] probably cry.
"Then, we'll laugh when it's all over."