And yet, for six straight years, fans at sold-out Major League ballparks have seen the six-foot-six Wright standing tall among the chosen 25 for Opening Day introductions each time.
"I never put the cart before the horse," Wright said. "I have to go compete for a job and win a spot, and I want to make sure I'm on the team before I worry about anything else. So unfortunately, that means I'll spend the first month of the season living out of a hotel while I look for a place to stay."
Pitching for 18 Major League seasons with 10 organizations, Wright has had to get used to starting fresh. Each year brings a new city, clubhouse, rental home and teammates. Almost everything is new -- except his job as a reliable reliever with a knack for getting big outs.
"The longer I've been around, the easier it's gotten to step into a new clubhouse with a new group of guys," Wright said. "The anxiety isn't as bad when you already know two or three guys from playing with them on other teams. I feel like I'm pretty easy to get to know."
Wright, in fact, is known as a solid, low-key teammate who prefers to stay under the radar, and that's partly why he has succeeded where so few have -- extending his career to nearly two decades by making the switch from the starting rotation to the bullpen. It's not common for a middle reliever to have teams come calling year after year with offers, but Wright manages to keep the phone ringing each offseason.
"I've got to be careful about where I sign," Wright explained. "I'm here to win a job and get out on the mound as much as possible. I need to go to a team that needs me."
And in 2013, that meant the Rays. Wright had interest from plenty of teams this past offseason, but he also had plenty of reasons to choose Tampa Bay.
"I want to pitch in the playoffs, and this team is expected to get there," Wright said. "Looking at what they had built over the last five years, this was the most excited I've ever been to join a team.
"I kept hearing about how great Joe Maddon was, and I was really excited about the opportunity to play for him. All spring, everyone kept calling and asking what it was like to be around Joe. That just speaks volumes. Nobody asked me how Don Mattingly was last year."
Though he was excited to join his new team, signing with the Rays did present challenges. Wright had spent every one of his previous 20 Spring Trainings in Arizona, so spending his 21st in Florida caused some hesitation. And as is the case every year now, he would once again have to pack up and say goodbye to his wife Marnie, 9-year-old daughter Presley Kile and sons Jett Alan (6) and Kingston Cash (4).
In a sport that requires players to be away from home for more than half the year, having a normal family life is not only difficult, it's almost unachievable. But Wright's commitment to his wife and kids is apparent when he speaks about them.
"It's hard leaving in Spring Training and being away from them," Wright said.
Wright spends Spring Training and the first few months of the season alone, then his family joins him after the kids get out of school in June. He takes pride in finding a suitable house for them to stay in during the summer and counts down the days until they can finally join him.
When Presley Kile -- named after Wright's former St. Louis Cardinals teammate Darryl Kile, who died tragically of a heart attack in 2002 -- was born in 2003, she gave Wright a new motivation to succeed. He always wanted to do well and make his managers and himself proud. But with the birth of his daughter, he had a new driving force: "It became all about my family, my children."
Because he can't spend every day with them during the spring and summer, Wright makes the most of his time with his family at home during the offseason.
"When I'm there, I make sure I'm really all there," he said
Wright focuses all his energy on his wife and kids and making sure that he's contributing to the family.
"When I'm home, I want them to know it, and I want there to be a sense of joy and relief in the house that daddy's home," Wright described. "And that's why I get up at six o'clock in the morning, get coffee for my wife or let her sleep if she wants, get the kids up, get them dressed, get them fed, get them to school -- do all the things that I can't do when I'm not there."
But as the saying goes, behind every good man is a good woman. And Wright is quick to praise his better half.
"Without my wife and how awesome she is, I would never be able to do this," said Wright with a big smile. "It takes a special, special woman to be a baseball wife. I'm very blessed."
So with the support of super mom Marnie and the admiration of his three kids, the 38-year-old keeps putting a jersey back on each year in hopes of finally achieving the dream that has eluded him during his entire Major League career: the chance to pitch in the postseason.
More than anything, Wright wants to pitch in a World Series game, and as Maddon has stated, win the last game of the season.
"I want to win the World Series and taste the champagne," Wright said. "I see guys wearing goggles and stuff -- not me. I want it in my eyes, I want to feel the burn."
And the ground-ball specialist thinks he has a good chance to do that with the Rays. At the very least, Wright's having the most fun he's had in his career.
"I'm having the time of my life right now," Wright said. "I've thought to myself, 'Why did it take me this long to sign here?' I've seen things like penguins and merengue bands in the clubhouse that I've never seen before in 20 years of baseball."
Wright's hope is that he'll get to go out on a high note, winning a World Series with the Rays while having the most enjoyable season of his career. But if a championship ring doesn't come this year, he'll pack his bags, leave his family for Spring Training and once again try to defy the odds for another chance at a ring in 2014 -- if he gets a nod of approval from the boss, that is.
"Once my wife tells me it's time to come home, then I'll probably come home," Wright said. "I'll probably try to talk her out of it, but then I'll probably come home."