The trade that Twins fans have been craving, the move that could lock up another American League Central Division championship, finally became official on Monday.

Well, maybe not exactly the transaction that Twins fans wanted.

Still, the Guardians’ decision Monday to swap their most valuable starter on this year’s pitching staff, righthander Aaron Civale, to Tampa Bay for a minor league first baseman increases the chances that the Twins will be able to hold off Cleveland’s challenge for the playoff berth that comes with winning an admittedly putrid division race.

Now comes the question that means a lot more around Target Field: Can the Twins, before Tuesday’s 5 p.m. trade deadline, improve themselves?

Their need for more offense against lefthanded pitching is clear; The Twins rank dead last among major league teams in batting average, slugging percentage and on-base percentage vs. lefties. They average 4.67 runs in games started by righthanders but just 3.39 when facing a lefthanded starter.

Then there’s the bullpen, which has been operating without Caleb Thielbar for three months and Brock Stewart for one. The lack of depth showed in July, when Twins relievers allowed an average of two runs per game, posted a 5.19 cumulative ERA and blew six saves. The Twins acquired veteran Dylan Floro on Wednesday to buttress the pen but could use another upgrade.

President of Baseball Operations Derek Falvey has a surplus of lefthanded-hitting outfielders and multiposition infielders to offer in trade, and he indicated in mid-July that he is willing to consider dealing major league players to help facilitate a deal.

Twins manager Rocco Baldelli doesn’t have many expectations for trade deadline day, though. Partly, that’s because he insists he believes the Twins have enough talent on the roster to make a run in October. He also believes the importance of midseason trades is overblown by fans and the news media.

“I know this is a thing that a lot of people spend a lot of energy thinking about and talking about and writing about, and probably people at home love hearing about it,” Baldelli said. “I don’t spend a lot of time thinking about the trade deadline, to be very honest. But people must like it.”

Maybe that’s the disappointment talking. Baldelli presided over a team that added pitchers Tyler Mahle and Jorge López for a fistful of prospects at the deadline last year, believing it had cemented a division race similar to this year’s. Instead, the Twins melted down in September, and neither acquisition figures to ever pitch for the Twins again.

Either way, the manager fears his team, stuck in a five-game spiral and swept by the last-place Royals, might be too cognizant of the potential for roster changes.

“The trade deadline is an uneasy time for players. Always. No matter where your club’s at at that point, it’s a time where guys are probably more on edge than they should be,” he complained. “Most teams are not going to do a whole lot. Most players are not affected by the trade deadline. But many of them think they are going to be, every year. So you should do your best to not spend a lot of energy worrying about the trade deadline.”

Well, at least the Twins won’t have to worry about Civale quite as often. He’s started nine games against Minnesota and allowed more than three runs only twice. Coming off an oblique injury last month, the righthander shut out the Twins over five innings at Target Field. He owns a 2.34 ERA this year, and his 2.7 wins above replacement leads all Guardians pitchers.

The move makes sense for the Guardians for the future, however. Cleveland owns one of the lowest-scoring lineups in the majors, and the prospect it received from the Rays, Class AAA first baseman Kyle Manzardo, is regarded as one of the best hitting prospects in the minor leagues.

With an injury-wracked pitching staff, the Guardians appear to have calculated that even if they overtake the Twins — whom they trail by a game after losing 7-3 at Houston on Monday — their chances of advancing much further this year aren’t particularly strong.

Making a move, or declining to, on Tuesday might reveal how the Twins regard their own potential this year.