CHICAGO – Thad Levine's gut feeling is the Twins are about to turn a corner.

That evaluation stems from something Oakland A's executive Billy Beane once told the Twins general manager: In a six-month season, the first two are to assess, the next two are to address and the last two are to enjoy.

About two months into the season, the Twins are 12-22 after Wednesday's 13-8 loss to the White Sox — ahead of only the Detroit Tigers in the American League Central. And the team Levine and Co. built to win a championship isn't even looking like a playoff team, with bullpen breakdowns and hitting halts.

"Knowing how hard we're working toward a specific end, and when you see it manifest in a different direction, you feel for the players, you feel for the fans, and ultimately, for management," Levine said. "… This is not how we envisioned it going, and I think we're all cognizant of the realities of the game, which is that sometimes things happen that are unexpected."

While Levine is disappointed, he's not yet to the point of considering an overhaul or even ruminating on which players might be attractive to playoff teams in the trade market.

"I just don't think we're there yet," Levine said, adding if there are a handful of players he could see being prized trade pickings in the summer, that should mean they can turn the Twins into a championship team as well. "… If the answer is more than I can count on one hand, then I'm going to try to apply myself to figure out how can we help them win together."

Pitcher swap

The Twins made a late roster move ahead of Wednesday's game, placing lefthanded pitcher Devin Smeltzer on the 10-day injured list because of left elbow inflammation and recalling righty Shaun Anderson from Class AAA St. Paul in his place.

Smeltzer appeared once in relief this season against Pittsburgh on April 24, pitching 4⅔ innings and allowing one unearned run on one hit. Anderson, 26, came to the Twins ahead of this season in a trade with the San Francisco Giants and has yet to appear for the Twins.

Anderson landed shortly before first pitch and was on the mound relieving starter J.A. Happ by the fourth inning. He pitched two innings and gave up four runs, one earned, with three strikeouts.

Injury updates

Center fielder Byron Buxton and outfielder/first baseman Alex Kirilloff are improving daily, according to the club.

Kirilloff has been on the injured list because of a right wrist injury and is working on hand-strengthening exercises. He recently gained clearance to start working in the weight room, and the plan is for him to wait until the team returns to Target Field on Friday before he starts swinging again.

Buxton plans to address the media Thursday about his right hip injury. His symptoms have continued to improve during his light rehab, which will ramp up as much as Buxton's pain tolerance allows. He earned clearance to throw and do strength and conditioning. He is also starting on his dynamic movement preparation.

College reunion

Ahead of Tuesday's series opener in Chicago, Trevor Larnach and Nick Madrigal met near second base at Guaranteed Rate Field. This unusual pregame tete-a-tete between opposing teams wasn't contentious, though.

Madrigal, the White Sox second baseman, and Larnach, the Twins outfield call-up in the wake of Buxton's injury, were college teammates at Oregon State when the Beavers won the 2018 College World Series. This was the first time they have crossed paths at the MLB level.

Larnach, who joined the Twins in Detroit on Friday, finally got his first big-league hit in his final at-bat Wednesday, lining a two-strike double to right field off Chicago closer Liam Hendriks.