From OTM, non-tendered players that the Sox may have interest in. I've highlighted the guys I'd think about targeting (though any of the relief options could fit here).
Infield
Hanser Alberto (BAL) would fill the hole at second base. The 28-year-old (he’ll be 28 for the entire 2021 season) wouldn’t be a dynamic signing and his ceiling is limited due to his lack of power and patience, but the high-contact hitter has been a roughly two-win player for each of the last two seasons. (That’s extrapolating 2020 over a full season.)
Travis Shaw (TOR) would provide depth at first base. A former fan favorite in Boston, this would make a ton of sense. Shaw is coming off a pair of below-average seasons at the plate so he likely won’t be commanding an every day role on the open market. The Red Sox could use some left-handed insurance behind Bobby Dalbec, though, and Shaw fits that mold.
Daniel Robertson (TB) would fill the hole at second base. There’s the obvious Bloom connection here with Robertson being a former Ray, and it was only a couple years ago that he had a 128 wRC+. That mark was down to 71 in 2019, though, before rebounding to 119 in only 24 plate appearances this past summer. Robertson will turn 27 shortly before Opening Day.
Outfield
David Dahl (COL) may have been the most surprising non-tender. The former top prospect is coming off a brutal season and has had trouble staying healthy his entire career, but he’s also been an All-Star and will be 27 next year. The Red Sox may be hesitant to sign another lefty, but the upside could be worth it here, particularly for a team building up like Boston.
Kyle Schwarber (CHC) was once one of the most intriguing hitting prospects in the game. Defense is an issue, but the power is very real and this is a chance to buy relatively low on that. That said, the idea of a defense with Schwarber in left and Andrew Benintendi in center shakes me to my core.
Eddie Rosario (MIN) was available to all teams on waivers and went unclaimed. He’s arguably the best player regardless of position on this entire list and has received MVP votes in each of the last two seasons. The biggest issue for Boston here may be that he is another lefty.
Adam Duvall (ATL) fills the right-handed potential need here. Duvall has legitimate power and has been on a 46-homer-per-600-plate-appearances pace the last couple years. That has come in a platoon role, though. Still, depending on how much they’re willing to spend this year having him in a platoon with Benintendi isn’t the craziest idea in the world if there is roster space to make that arrangement work.
Albert Almora (CHC) would probably fit into that platoon situation in some way, shape or form. He’s not a starting player but he’s a high-contact right-handed bat who can play center field.
Nomar Mazara (CHW) is a former top prospect who some people (read: me) have been betting on in fantasy for what seems like decades at this point. He’ll still only be 26 next season so it’s not hard to continue buying in, but he’s had five seasons in the majors and he’s never even been average at the plate by wRC+ and had a mark of 68 last season. He’s also another lefty.
Delino DeShields (CLE) brings a ton of speed and can cover a ton of ground in center field, but his offense has never really been that of an everyday player. This would be an underwhelming way to fill the hole in the outfield, to say the least.
Tyler Naquin (CLE) is similar to DeShields in that he is a solid defensive player but is much better utilized as a bench player than someone to play close to every day.
Starting Pitchers
Carlos Rodón (CHW) was the third overall pick back in 2014 and still had a ton of promise as recently as 2017. However, he’s never been able to take that next step and has been backtracking in terms of performance the last couple of years. He would be a decent enough reclamation project, but certainly not a top-tier target.
José Ureña (MIA) was, like Rosario above, recently available on waivers. He was the ace of the Marlins staff a couple years ago when they were at the deepest valley of their most recent rebuild, but like Rodón is a nice depth add rather than a top-tier target.
Tyler Anderson (SF) doesn’t have a ton of name recognition nor does he have big-time recent performance. That said, he’s been roughly league-average by park-adjusted ERA in four of his five major-league seasons and could be a solid plug-and-play back-end starter.
Relief Pitchers
Archie Bradley (CIN) should command a good amount of interest on the open market. He emerged as a true late-inning reliever almost as soon as he converted to relief with the Diamondbacks and while he’s not on the level of the top-tier relievers this year he’s not all that far off.
Matt Wisler (MIN) is probably the name that will get the most surprising amount of buzz for the next day or two. He came out of nowhere this past year to post a dominant 1.07 ERA with a bunch of strikeouts. I’m not sure how much I buy in, but it’s at least worth a closer look.
John Brebbia (STL) is the kind of good-not-great reliever that can be underated in the free agent market. He did miss all of 2020 after undergoing Tommy John surgery, so that throws a bit of a wrench in things, but before that he was roughly 20 percent better than league-average by both results and peripherals for two straight years.
Keynan Middleton (LAA) made his debut in 2017 and became the Angels closer by the end of that year. He started 2018 in that role as well, but then suffered an injury that eventually required Tommy John. He’s only pitched 35 1⁄3 innings over the last three seasons combined, but the upside is still there and he’s entering his age-27 season.
Hansel Robles (LAA) is another former Angels closer, serving in that role in 2019. He’d been mostly solid for his career before this past summer, but his command tanked in 2020 and he ended the year with an ERA over 10.00.
Chasen Shreve (NYM) may be a familiar name from his days with the Yankees, but he emerged as a solid multi-inning option for the other New York team last year. This wouldn’t be the new closer, but he could be a nice low-key addition.
Also gives him an inflated fWAR.