After being taken by Houston in the Rule 5 Draft from the Los Angeles Dodgers in the winter of 2007, the left-hander either needs to make the Astros' roster or face leaving the only organization that has given him a chance in the Major Leagues.
Wright has only one full season under his belt, and parts of three others with the Astros. The southpaw is hoping he was impressive enough at the end of last year and so far in Spring Training to make the big league club. In 12 innings through 21 games at the end of last season, Wright posted a 1.50 ERA with 11 strikeouts. So far this spring, he's hurled four innings and allowed two earned runs.
"I know this is a pretty big year for me, being out of options and everything," Wright said. "So I'm just trying to come in and get off to a good start and ride the momentum into the season."
The 27-year-old has set his focus this spring on maintaining control of his pitches and allowing fewer runners to reach base.
"I think early in my career that was the thing that hurt me the most, the free bases that I would give up, and then I would give up a hit and that would be a run or two," Wright said. "So I'm mostly just trying to work on my control and limit the number of baserunners that I have per appearance."
The biggest influence on Wright's game has been teammate and 10-year Major League veteran Brandon Lyon. The two pitchers have lockers side-by-side in the clubhouse, allowing Wright easy access to his right-handed counterpart's wisdom and advice.
"I've learned a lot from Brandon over the last couple years, just about being a professional and how to go about being a relief pitcher for a year-in and year-out basis," Wright said. "It's one thing to have some success, but to do it for a long period of time is a different thing.
"That's the main thing I'm trying to learn from a veteran guy like that who's done it for so long, is how do you do it for that amount of years?"
So how do you do it?
"The biggest thing I've noticed about Brandon is his ability to kind of let things just roll off his back," Wright said. "You don't take one bad outing to the next. And that's the one thing I struggled with a little bit earlier in my career, where if I had a bad outing, it would follow me to the next outing.
"Just watching him and how he goes about his business, he prepares each day the same way and he just has trust and confidence in his ability. He doesn't overanalyze things or overthink it at all when he's out there pitching."
As Wright takes as much as he can from watching and listening to his teammate, he hopes that he can provide a positive influence on other pitchers around him as well. Being the longest-tenured man in the Astros bullpen is a strange experience for Wright, but it also gives him a chance to take on a new role amongst his peers.
"It's weird, to be honest," Wright said of having been in Houston's bullpen the longest. "I remember when I was a Rule 5 pick over here and I was surrounded by veterans. Even my pitching coach now was in the bullpen with me, so it's a little weird.
"But I'm actually looking forward to being able to maybe take on a little bit more of a leadership role. I've been around a little bit more than some of the guys we have in the bullpen. It's kind of fun. I haven't experienced everything, but I've experienced enough to where I can help somebody."
Wright is also looking to help himself this spring, right on to the Astros' roster for Opening Day. Having been with the Major league Club, Wright believes he knows what it takes and he just needs to prove to the organization that he is ready to be back.
"The main thing I try to control is how I go about my business and how I pitch," he said. "I feel I am a big league quality left-handed reliever, and it's up to me to go out and show it. That's my main focus day in and day out."
Though he only has four outings and four total innings so far in March, Houston manager Brad Mills was impressed with what Wright was able to do late in the season last year.
"The way he threw the ball after he came up from the Minor Leagues last year was pretty good," Mills said. "And so we're looking, hopefully, that he can fit right into our bullpen in that role, obviously as being one of our left-handers out of the 'pen this year."
Wright isn't taking anything for granted.
"I've been competing my whole life," he said. "I'm not the biggest guy in the world, but I enjoy competition and it's something that brings out the best in me. So I would say that's my biggest strength, is how big of a competitor I am."
Alexis Brudnicki is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.