"When all the complications started that's when it really hit me what was to come," Drew said. "You always hear the cliche, that until you have a child you don't know what it's like. People think they know, but you really don't know until you have a son or daughter, how much it changes your life. It changes it for the good."
Hank Drew is now more than seven months old and in a year full of firsts for the family, this will be Drew's initial Father's Day as a dad.
He'll spend the day on the baseball field in Detroit, thousands of miles from home. Just part of being a Major League Baseball player.
"You just miss the little things sometimes when you're on the road," Drew said.
It is quite a lifestyle adjustment for Drew, who grew up in Hahira, Ga., population 1,600. The 27-year-old still spends his offseasons in that area where his father David used to work for Bayliner Boats.
"He spent as much time as he could with us," Drew said of his father David. "He was there for things."
While he wouldn't trade his job, Drew does wish it didn't require him to be away from Hank and Laura so much.
Hank crawled for the first time a couple of weeks ago while Drew was on a nine-game road trip through Denver, San Francisco and Los Angeles.
"I love this game," Drew says. "I play it because I love it, but you're away from your family a lot during the season. I'm a small-town boy, who travels on the road to big cities, and has a wife and a son now and that's tough. It changes things."
Technology helps shrink some of the distance.
Drew uses Skype to keep in touch with them while he is on the road so that Drew could see Hank crawl.
"When you can see him on video rather than just talk on the phone it's pretty cool," Drew said. "It was neat to see him crawl, but the best part was how he smiled when he was crawling."
Other times, Laura and Hank will join Stephen on the road for longer trips.
"Life is too short and they grow up too fast to miss stuff," Drew said.
It's been a frustrating season for the last-place D-backs on the field and while Drew has always been able to put the game in proper perspective thanks to his faith, having Hank around has added to that.
"You come home with the stresses of baseball and you see your son, it totally changes you," Drew said "Just the way he smiles. He can't talk yet, but the funny thing is when I walk in the room he gets a big grin and that is something special. It's awesome. When you get home and see your son and he smiles at you, whether you had a bad day or whatever, it takes your mind off it. It shows you there's more to life than baseball."
Baseball in a lot of ways is the family business. Drew's older brothers Tim and J.D. were first-round picks, like him, who went on to play in the big leagues. Tim has since retired, but J.D. still plays for the Red Sox.
Might Hank carry on the family tradition? If he does even play baseball it will because he wants to, not because his father wants him to. Drew remembers fondly how David was supportive of he and his brothers, but never pushed his sons.
"I think too many parents today try to force their kids to do something," Drew said. "If he wants to play, I'll be glad to support him, but he's got to want to do it and he's got to enjoy it. I want him to do what he wants to do. I just want to share in the experiences of his life, not tell him what he should be."
Drew is not the only D-backs player to be experiencing his first Father's Day as a dad. Mark Reynolds' son Jacob was born two days after Hank and Kelly Johnson's son Cole was born a month later.
The shared experience has given them plenty to discuss during the down times on the road.
"We go out to eat and talk," Drew said. "We'll be like, what's he doing? How are you handling this? In baseball you meet a lot of guys that have the same identity as you. It's been neat to watch those guy's kids grow too."