The White Sox have been perhaps the most active team in baseball this winter, and after adding Yasmani Grandal, Dallas Keuchel, Edwin Encarnacion, Gio Gonzalez and Nomar Mazara to the roster, they’re now shifting their focus to bullpen upgrades, USA Today’s Bob Nightengale tweets. Chicago had previously been rumored to have interest in Nicholas Castellanos and, to a lesser extent, Yasiel Puig, but they’re not involved with either player at this time after filling up their corner outfield/DH mix.

The bullpen is another matter entirely, however. Holdovers Alex Colome and Aaron Bummer give the ChiSox a quality right-handed and left-handed option, respectively, but there’s limited certainty beyond that pairing. Righty Evan Marshall posted a terrific 2.49 ERA in 50 2/3 innings but had questionable secondary stats and a possesses a shaky track record. Flamethrowing sinker specialist Jimmy Cordero averaged 97.5 mph on his heater and posted a 2.75 ERA and 60.4 percent grounder rate in 36 innings, but he doesn’t miss many bats and has a limited track record himself. The first season of veteran Kelvin Herrera’s two-year, $18MM contract yielded disastrous results.

Collectively, White Sox relievers ranked 14th in the Majors in ERA (4.33), but that’s largely a function of the quality results posted by Colome, Bummer, Marshall and Cordero. And there’s also reason to take that number with a grain of salt; the Chicago bullpen’s matching 4.69 FIP and xFIP ranked 18th and 21st among MLB teams while posting the fifth-highest walk rate (10.8 percent) and fifth-worst strikeout rate (21.7 percent) in all of baseball. White Sox relievers were tied with Royals relievers for the worst K-BB% in the Majors.

Unfortunately for the Sox, a fair bit of the relief market has been picked over. Will Smith, Drew Pomeranz, Chris Martin, Dellin Betances, Joe Smith, Blake Treinen and Sergio Romo, among others, are all off the board on new contracts (MLBTR Free Agent Tracker link). The top unsigned names include Will Harris, Steve Cishek, Pedro Strop, Craig Stammen and old friend Daniel Hudson. There are still some quality names, and the trade market presents myriad opportunities to explore (Ken Giles? Josh Hader?), but many of the most appealing options found homes while the South Siders zeroed in on lineup and rotation enhancements.

The good news for Sox fans is that the team still hasn’t even topped its previous record payroll, however. There isn’t a name among the best remaining relievers that the ChiSox can’t fit into their budget — and that’s all the more true if owner Jerry Reinsdorf is willing to push spending levels to new heights as he strives to emerge from the long-running rebuild, as one would expect. The White Sox’ offseason moves to date have already made the AL Central race much more interesting, and it seems a few more additions could be on the horizon.