Unfortunately for the Red Sox, there is a relative dearth of talent among free agent infielders this offseason, particularly when it comes to first basemen. The best first baseman available this offseason via free agency is Carlos Lee, who hit .264 in 2012 as a member of the Astros and Marlins. Yikes. Go down the rest of the list and you'll find the rest of the players are even older than Lee (Jason Giambi and Jim Thome), offensively inept (Eric Hinske and Xavier Nady, for instance), or were injured a great deal last season (Lance Berkman). The next-best hitter to Lee is Lyle Overbay, who hit .259 last season but went just 2 for 20 (.100 batting average) after he was traded from Arizona to Atlanta.
So the best statistical option for the Red Sox at first base is to attempt to sign Lee and let James Loney, who hit just .230 in his 30 games as a Sock last year, walk.
The options at shortstop for the Sox include starting Pedro Ciriaco or Jose Iglesias, or finding a player via free agency. Jose Iglesias is purported to be an excellent defensive player, but his offensive numbers are absolutely dreadful. And the Sox should probably get a free agent third baseman through free agency, which leaves Ciriaco as the starter at short for Boston next season. He did hit well in his time with the Sox this past season, and is comparable to Iglesias in career fielding percentage as a shortstop(.976 for Ciriaco versus .981 for Iglesias).
Why do the Sox need a free agent third baseman? Will Middlebrooks has a career fielding percentage of .949 as a third baseman, and Ciriaco is even worse at the hot corner (.932 fielding percentage).
Jeff Keppinger is named on Cot's Baseball Contracts' (the site where all the names of free agents on this blog post came from) list of potential free agents as a second baseman. He's able to play third too, however, which is definitely a reason for the Sox to go after him. He has a .964 fielding percentage at that spot, which, though nothing to get overly excited about, is certainly an improvement from the defensive stats of Middlebrooks and Ciriaco. His batting average and on-base percentage were also very good last season with the Rays, which would add more AVG and OBP depth to a lineup which should be very good in such statistics if they follow the advice of this blog.
The last position of the infield is second baseman, which the Sox luckily have covered with Dustin Pedroia. Beyond second-base, though, the GM of Boston should be very busy in the coming months putting together a decent team, and a reliable infield.