If that belief holds up through the rigors of the 162-game season, the Red Sox might wind up with one of the best bargains of 2013.
Drew and the Red Sox officially announced a one-year deal on Wednesday that will be worth $9.5 million.
For a 29-year-old shortstop with solid defensive skills and pop in his bat, that could be money well spent.
"I'm really excited to be there [in Boston] and I know it's going to be a good fit for me," Drew said in a conference call on Thursday.
In signing Drew, the Red Sox have kept with their winter-long strategy of signing veteran players to short-term deals.
Red Sox fans hope this signing is reminiscent of another deal Boston made with a Scott Boras client three winters ago in third baseman Adrian Beltre.
Beltre had a major revival during his one year in Boston, and perhaps the same can happen for Drew.
Drew will wear No. 7 -- just like his brother, J.D. Drew, who played for Boston from 2007 until his retirement after the 2011 season. The Drews are the 11th set of brothers to play for the Red Sox, the last being Pedro and Ramon Martinez.
Drew, who turns 30 in March, split last season between the D-backs and the A's as he came back from a nasty break of his right ankle, an injury sustained in 2011.
"He was one of the better everyday shortstops in baseball for quite a stretch there," Red Sox assistant general manager Brian O'Halloran said on Wednesday. "And then he had the really bad ankle fracture that he suffered in 2011, and it took him the full year to get back out playing, which is understandable. It's a really, really difficult injury. But he played well down the stretch, and he also helped out Oakland in their stretch drive into the playoffs after the trade.
"We brought him in for a physical exam, and our folks were very pleased with his progress. It's obvious to them how hard he had worked given the nature of that injury, how hard he had worked to strengthen it. We feel that he's going to be fully healthy for us and is going to make us a better team. We're excited to have him."
While a big market can rattle some players, the reverse effect is that it can greatly increase the status of someone who thrives in a more scrutinized environment.
J.D. Drew played for the Red Sox from 2007-11, helping the team win a World Series his first year and coming up with some more big hits in October the following year. However, injuries and underperformance were a story line throughout his $70 million tenure in Boston.
But that isn't causing J.D.'s younger sibling any trepidation.
"I'm laid back, but probably put a little more emotion on my shoulder," Stephen Drew said. "You know, at the end of the day, me and J.D., I'm a different person than J.D. and J.D. is a different person than me. I always told people coming into it, playing shortstop, I had a little more pressure, playing in the middle infield, and I've kind of dealt like that.
"I've always kind of been under my two older brothers. It's kind of nothing new to me. At the same time, I kind of look at J.D. as a role model for me. I always have. We carry ourselves, looking at people that look at us, as a role model for little kids. I really don't throw my helmet. I don't throw my bat. You'll see that. You guys have probably seen that when I played there.
"There's times it will get frustrating. But at the end of the day, me and J.D. are a little different. I've always been geared to play the game. I love to play the game. I respect J.D. I look up to him a lot, learned things from him that have always been with me and stayed with me, but at the same time, we're totally different players. I like to have fun, cut up and have a good time as well."
J.D. Drew gets aggravated when his brother is unfairly labeled.
"What aggravates me is that he's been kind of lumped into an 'injury-prone' kind of deal. Stephen's never been injury-prone. This guy has played 150 games a year for most of his career until he breaks his leg in half," J.D. Drew told MLB.com last week. "And then, of course, you can't do anything in the middle of the season. You play 70 or 80 games, you have a broken leg, of course you're going to miss most of the next year trying to come back from it.
"'Oh, he's as brittle as J.D.' No, that's crazy. I think he's going to come back with a really nice season, and you've got to understand, what made me more frustrated was Arizona throwing him under the bus like he hadn't given them anything over a four- or five-year career."
Stephen Drew looks forward to proving to everyone just how healthy his ankle is now.
"The ankle is doing tremendous," Drew said.
Drew hit just .193 with two home runs in 40 games and 155 plate appearances for the D-backs but did better once he was dealt to the upstart A's, with five home runs and a .250/.326/.382 line. He had a mutual option for $10 million that both he and the A's declined in favor of a $1.35 million buyout.
With Drew in the fold, youngster Jose Iglesias is pushed to another year at Triple-A Pawtucket. The 22-year-old has an incredible glove, but he hit just .118 in 77 Major League plate appearances last season.
Iglesias will have pressure from within the system, too, with slugging 20-year-old shortstop Xander Bogaerts right on his heels. Bogaerts finished the 2012 season at Double-A Portland, and he did just as well there as he did at Class A Salem. Bogaerts, Boston's No. 1 prospect as ranked by MLB.com, had a .307/.373/.523 line between both levels and figures to start again at Portland in 2013.
According to FanGraphs.com, Drew was a plus defensive shortstop by Ultimate Zone Rating from 2009-11.
Entering his eighth Major League season, Drew hasn't spent any time in the American League outside the stint with Oakland. Arizona took him as the 15th overall pick in the 2004 First-Year Player Draft, and he's a lifetime .265/.328/.433 hitter. He reached double-digit homers from 2007-10 but hasn't been able to get enough plate appearances the last two seasons.
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. MLB.com reporter Evan Drellich contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.