Then, they wanted Xander Bogaerts, a prospect who has generated more anticipation in Red Sox Nation than perhaps any youngster since Nomar Garciaparra.
But here the Red Sox are clicking on all cylinders early in this postseason and the man who still plays shortstop every day is Drew. Game 3 of the American League Division Series against the Rays is Monday at 6 p.m. ET on TBS.
He was the choice of the organization -- at least for this season. And despite a concussion in Spring Training and then a right hamstring injury that sidelined him in July, Drew has been just what the team had hoped -- particularly down the stretch.
"It's a credit to [manager] John [Farrell] and the staff for ignoring the noise, I guess, and sticking with a guy who has been a proven player," said general manager Ben Cherington. "We felt he was an important part of this team for a number of reasons. I think having dependability at shortstop on the defensive side of the ball and a left-handed bat in that part of the lineup and balancing things out a bit were [important]. He's been a really important guy."
Over the final two months of the season, Drew turned into a vital hitter, giving the Red Sox a legitimate threat in the bottom portion of the order. In his final 198 at-bats of the regular season, he hit .292 with eight homers, 35 RBIs, a .367 OBP, .513 slugging percentage and .879 OPS.
"I feel good -- this second half I've felt great," Drew said. "I finally got in a rhythm, and am seeing the ball well. Hopefully you don't miss your pitch -- that's the main goal when you get up there at bat, because if you miss your pitch it is the big leagues, it's tough. You miss that one pitch you might not get it back."
In Saturday night's Game 2 of this best-of-five ALDS against the Rays, Drew got his one pitch and belted off the Green Monster for an RBI triple against David Price, one of the best left-handers in baseball.
So if anyone was wondering why Drew started Games 1 and 2 against Matt Moore and Price instead of the right-handed-hitting Bogaerts, Drew showed why.
"If there is an underappreciation [of Drew], it's probably outside of our clubhouse," said Farrell. "He's a very good player. He's a very sound defender, an above‑average defender. We know that there's been struggles against some left‑handed pitching in the past, but last night him starting against David Price was not even ‑‑ there was some consideration for Xander -- but as important as Stephen has been, and as well as he's played, that was a clear decision."
In a sign of the inner confidence Drew has, he didn't suspect he'd be opening the postseason as a spectator.
"Looking back over my career, my first three, four years I was hitting really good against lefties, better against lefties than righties," Drew said. "Then I had some injuries, then had some managers that never played me [against lefties], I don't know why. Then you kind of lose that confidence a little bit. I think over last month or so I've had some good at-bats together against lefties."
As pleased as the Red Sox are with Drew's late-season surge at the plate, his defense is what they value the most.
Drew starts and turns double plays with ease. And he always seems to wind up where the ball is hit.
Drew is on a one-year, $9.5 million contract, so Bogaerts might get his chance next year. But in the meantime, he's going to take lessons from the veteran.
"Man, the way he plays short, it's a different way, a really good way," Bogaerts said. "The way he attacks, he gets good reads on the ball. He plays shortstop exceptionally well. It's been good to watch him. I just watch him and learn. He makes every play. It doesn't matter where you hit it, he just gets to all of them. The way he attacks the ball is very unique, I would say. The way he reads those hops. He gets a good read on hops. He knows what to do with the ball."
Why does Drew never seem to get his due, even playing in a big market like Boston?
"I've had a lot of experience, I just go about my business. I play hard. People question my ability to play short and I've never questioned myself," said Drew. "I kind of thrive off it, you know? I think people realize now and come ask me, 'I didn't know you were kind of this good.' Not to toot my own horn but it's like, you know, playing in Arizona and kind of a smaller market, it's kind of unfortunate but it doesn't matter to me. It matters about my team, coming out and preparing, and I think I do a good job of that."
Drew was one of several unheralded players that Cherington targeted over the winter and proved to be right about.
"In the first few years in Arizona, he was a guy that was out there all the time and was an everyday player and one of the best shortstops in the league," said Cherington. "In 2011 and '12, he just got crushed with an injury. But we thought he was out of the tunnel on the injury and 2013 would be more like he had been for most of his career."
Another of the best traits Drew shares with his brother J.D. is the ability to tune out public perception.
"It's huge," Stephen Drew said. "Looking back over my career, when you can stay even-keeled and go about your business and trust yourself, it pays off because you look at John, and he trusts me. Over time, it works itself out."