The Twins are holding their Winter Caravan. They fly players in from warmer climes, stick them in a van and drive them to Your Town to sign autographs with whichever fingers are not yet frostbitten.

Front office members make the trips, too, purportedly to promote the team but more likely to search every high school gym in Minnesota for lefthanded relievers.

The Twins are right to not pretend they can buy sustained success in free agency. This winter, though, they are making a mistake by sitting on their wallet.

They are right to trust their farm system to fill most of their needs. They are wrong to stand pat on relief pitching.

Here’s how their winter pursuits have gone: They didn’t re-sign Brian Duensing because they wanted to improve their bullpen. Soon, they will probably be forced to re-sign Brian Duensing to improve their bullpen.

In fact, the Twins have waited so long to pursue bullpen help that a lot of the most recognizable names among remaining free agent relievers are all too familiar.

The Twins could re-sign Joe Nathan, who at his best was on par with Mariano Rivera. Nathan’s most ignominious moment as a Twin came when he was asked to pitch three innings in one game. Now it might not be sensible to ask him to pitch three innings in a season.

The Twins could re-sign Joe Beimel, who pitched for them in 2004. You could say he was with them for a cup of coffee, but given his tattoo-ology, it was more like a dab of ink.

They could re-sign estimable veteran Neal Cotts, who had a good season. In 2013.

They could sign estimable former Twin Craig Breslow, who had a good year. In 2013.

Glen Perkins is an All-Star closer who needs to prove he can condition himself to pitch well for a full season and under the pressure of a playoff chase. Kevin Jepsen was impressive last season and has put two strong seasons together. He’s ideal as a setup man and backup closer.

Casey Fien, at 32, is facing an important year in his career and in the Twins bullpen. Trevor May seems destined to be a reliever, and the Twins need him to be good in that role once again. The Twins also have more hard-throwing relievers in their farm system than ever before.

They are one veteran, hard-throwing lefty reliever away from entering the season with a well-rounded and intimidating bullpen. The problem is, they missed out on their two most obvious targets.

Tony Sipp re-signed with Houston. So the Twins probably never had a shot at him.

The one that got away in a way that hurts is Antonio Bastardo, who has reportedly agreed to a two-year deal worth $12 million with the New York Mets.

That’s a lot of money for a pretty good reliever.

This is one of those times when the Twins would have been wise to overspend.

Bastardo would have fit the Twins bullpen perfectly. Perkins, Jepsen, Bastardo, May and Fien, plus a long reliever who doesn’t refer to Minnesota as a “city” — that was today’s gratuitous cheap shot at Ricky Nolasco — would give the Twins a strong bullpen in an era when strong bullpens win championships.

Free agency isn’t over. Maybe the Twins will find a lefty who will perform well. Maybe Fernando Abad, signed to a minor league deal last month, will reprise his strong 2014 season with Oakland and perform better than Bastardo at a much lower price.

But the Twins’ plan this offseason was to find relievers who were better or more reliable than Duensing and Blaine Boyer, and their lack of aggressiveness to date suggests they might not be able to do better than either one.

The problem with free agency is that a rational general manager can reject every proposed deal as outrageous, but proceeding rationally in free agency means signing no one, or signing only those undervalued by the rest of baseball.

Sometimes proceeding rationally means failing to improve your team. Like the Twins, this winter.