The elder Martinez has been bringing his son to the ballpark since his Cleveland days, a practice that continued in Boston last year and Detroit this season.
"He loves to come out to the ballpark and hang out with the guys. He just loves it," Martinez said. "He can go through the whole lineup and do everything -- imitate every guy here."
The elder Martinez lost his own father when he was just 6 years old, and that has shaped his relationship with his wife, son and 4-year-old daughter, Maria.
"That's why I just want to spend as much time as I can with him, because you never know," Martinez said. "I never had that chance, the opportunity to have my father around me."
Victor Jose has a jersey sporting his name and his dad's number, a bat and gloves, and hangs out at his father's locker after games.
He plays catch during batting practice and steps to the plate to take pitches from Martinez. He can hit the ball to the outer edge of the infield, much to the amazement of players on other clubs.
When the Tigers take their pregame swings, the young Martinez can be seen near the dugout having a catch with players, fielding fungoes from Miguel Cabrera or following his dad around the cage.
He's pretty much a member of the team.
"When he misses a day, you want to know where your little buddy is at," Brennan Boesch said. "He's just great."
Boesch and Victor Jose have a close bond. Boesch can speak Spanish, and though the younger Martinez knows that, he sticks to English with Boesch and speaks some Spanish with the Latin American Tigers.
Boesch has nothing but praise for how Martinez is raising his son and hopes to do as well when he has kids.
"He's just one of those kids that brightens you up, no matter what," Boesch said. "This game has got its ups and downs, but he's always smiling. So for me, I'm happy to have him here every day, and since Spring Training, I've had fun hanging around him. He reminds you of yourself when you were a kid and how much you loved baseball."
On Sunday, the Tigers hosted Family Day at the ballpark, with wives, girlfriends, parents and kids hanging out on the field.
Martinez loved seeing all his teammates' kids, and "He's great with them," said Don Kelly, whose 2-year-old son spent time with the elder Martinez. "You can tell he loves to be around his son. He goes out in the field and just plays catch with him, [throws] BP all the time. He definitely enjoys having kids around and playing with them."
As he played with the children, Martinez had a smile that was just as big as theirs.
"I always have fun with the kids," he said. "I'm just going to have fun. There's nothing better in the world than looking in a kid's face and [seeing] that big smile. For me, there's nothing better than that."
Martinez's career began when we was signed as a non-drafted free agent by the Indians in the summer of 1996 out of Venezuela. After putting up Minor League MVP seasons in 2001 and 2002, he spent most of 2003 in the Majors and became a regular.
In August 2004 -- Martinez's first full season in the Majors -- Victor Jose was born. He began bringing his son to the Indians clubhouse when he was 2 years old, and the kid fell in love with his father's job.
The business of baseball undoubtedly takes a toll on players, but sometimes the families deal with more of the burden, moving away from family, friends and established lives. Martinez has changed homes three times in the last three years, going from Cleveland to Boston in the summer of 2009 and to Detroit this past November, when he signed with the Tigers as a free agent.
"It was tough for him," he said during Spring Training of his son's upheavals. "We had to talk to him a lot. He's a kid, so we kept trying to make him understand. This is the hard part of the game."
But when his father plays his former teams, Victor Jose has an even better time.
When the Tigers had a three-game series in Cleveland at the end of April, the younger Martinez played catch before a game with Indians president Mark Shapiro and his son. When the Red Sox visited Comerica Park a few weeks ago, he played catch with Kevin Youkilis and received hugs and high-fives from several Red Sox players.
"I think he's officially the cutest kid in the American League," Red Sox manager Terry Francona said during Spring Training.
Martinez thinks his kid would want to be a pro ballplayer, but he hasn't put any pressure on him to do so. If he does, Victor Jose has a great head start. So good, in fact, that Francona jokingly tried to trade for him in Spring Training.
"We're trying to make a move today," Francona said. "We're trying to acquire Victor Jose [Martinez]. They've asked for [Carl] Crawford, but we're holding out for a little less."
Though very young, Victor Jose is very respectful when it comes to giving players their space, and he is very well behaved.
That's something that Martinez has made sure of: that his son is neither a distraction nor a nuisance.
"That's one of the things that makes me happy and proud to bring him to the ballpark -- I know he's going to behave himself and enjoy the game," he said. "For a kid that's his age, I know that he's going to be good when he's in the cage or doing whatever he wants to do."
Because of the constant possibility of moving or being away from his father, Victor Jose is homeschooled. Martinez wants to make sure he spends as much time with his family as he can, and homeschooling allows his son to go the ballpark often and move around with his family.
"We don't have a lot of time with the family," Martinez said. "Maybe a lot of people think we have the best life, but personally, I'm a guy that I love to be with my family. I'll do anything it takes to have them around with me.
"I think they've been great, the teams, for me and my life. They've helped me in my whole career. Anything I'm going to do, I'm going to do around family."