It might seem crazy for any team, and in particular one that lost 103 games last season, to trade away its best player. But the Twins, who continue to weigh offers for second baseman Brian Dozier, have a surprising amount of experience at this.

Trading Dozier for unproven prospects, no matter how elite, probably won't be popular among Twins fans. The 29-year-old slugger just completed a historic season at the plate — his 42 home runs are the most ever hit by an AL second baseman — and he is under contract for the next two seasons at a below-his-value total of just $15 million. Baseball bosses Derek Falvey and Thad Levine clearly understand the sentiment: At a mid-December "town hall" with season ticket holders, they deflected questions about whether they intend to swap Dozier, and acknowledged his esteem among fans.

"It's always a difficult decision when you're talking about players who mean so much to the Twins community, and who have meant so much to the franchise for a long time. In Brian's case, among a number of other players on the team, we know they're embedded in the fabric of who the Twins are," Falvey told one questioner. "But you always need to balance those decisions with the longterm health of the franchise."

Added Levine, "[Dozier] had a spectacular season. What he did in the second half was really an epic performance. We don't take that lightly." But, he said, "we're going to continue those dialogues" about what direction to take.

It's a direction that the Twins have taken several times before. In fact, should Dozier be dealt, he would only rank among the top half-dozen players ever traded in his prime (as opposed to, say, moving Justin Morneau in 2013) by the Twins. One big difference, however: Dozier, unlike past stars swapped by the Twins, wants to stay in Minnesota.

Here's a look at the five best players, as measured by baseball-reference.com's Wins Above Replacement (WAR) calculations, traded by the Twins:

Chuck Knoblauch, 1998: Frustrated by five consecutive losing seasons, the All-Star second baseman instructed his agent to demand a trade, a move that embittered fans against him. Knoblauch was coming off the three best seasons of his career; his 6.7 WAR in 1997 ranks as the best ever by a Twins hitter who was immediately traded away, and his 8.6 WAR in 1996 still stands as the second-best season in Twins history.

Shortly before training camp opened in February, Terry Ryan granted the former Rookie of the Year's request, shipping him to the Yankees in exchange for pitchers Eric Milton and Danny Mota, shortstop Cristian Guzman and outfielder Brian Buchanan. While Knoblauch went on to win three consecutive World Series in New York, the Twins fared pretty well, too; Milton turned into a reliable 200-inning starter within a couple of seasons and became an All-Star in 2000, while Guzman became the Twins' starting shortstop for six seasons, led the AL in triples three times, and earned an All-Star spot in 2001.

Rod Carew, 1978: Relations between the seven-time batting champion and the Twins were irreparably broken when Carew learned that Minnesota owner Calvin Griffith had called him "a damn fool," in an appearance at the Waseca Lions Club, for signing a contract that paid him an average of only $170,000 despite his MVP season in 1977. Carew declared publicly that he had no interest in playing anymore for the Twins, who shopped him throughout the 1978 season. Carew's WAR declined from 9.7, the best by a hitter in Twins' history, in 1977 to 4.9 in 1978, but he still won the AL batting title and posted a .411 on-base percentage.

Griffith was unimpressed with the offers he received until the following February, when he accepted four players from the Angels: catcher Dave Engle, pitchers Brad Havens and Paul Hartzell, and the Angels' top young prospect, outfielder Ken Landreaux. Carew quadrupled his salary in Anaheim and remained an All-Star for six more seasons, while the Twins kept Landreaux for only two seasons before trading him to the Dodgers. Engle played five seasons for the Twins, and Havens eventually lasted two seasons in Minnesota's rotation.

Carew and Griffith eventually reconciled, too. When Carew was elected to the Hall of Fame in 1991, the first person he called to thank was the former Twins owner.

Bert Blyleven, 1976: After debuting as a 19-year-old in 1970, the righthander quickly became a cornerstone of the Twins' rotation, pitching at least 275 innings in each of the next five seasons. But Blyleven chafed at Griffith's unwillingness to match the salaries being paid by his competition, and finally demanded to be traded. In June, Griffith accepted a package of three young players — infielders Mike Cubbage and Roy Smalley and pitcher Jim Gideon — plus veteran righthander Bill Singer from Texas, along with another important factor: A check for $250,000.

Given a chance to play every day, Smalley and Cubbage blossomed into solid regulars for the next five seasons, with Smalley posting a career-best WAR of 5.9 in 1978. Blyleven, though, managed to pitch 202 innings for the Rangers in just four months, posting a 2.76 ERA, and went on to enjoy a Hall of Fame career that included 287 wins and 3,701 strikeouts.

Frank Viola, 1989: Like Carew and Blyleven, the 1987 Cy Young winner grew unhappy with the Twins' unwillingness to match the contracts being handed out by teams in bigger markets. Viola's agent wrote a letter demanding better pay for the popular lefthander, but when it became public, some teammates criticized his method.

By mid-1989, with the Twins out of the AL West race, Minnesota began accepting offers for Viola, and at the trade deadline, they accepted a package of four young pitchers from the Mets. Tim Drummond had only one season in Minnesota, but the other three — Rick Aguilera, David West and Kevin Tapani — made the trade a success for the Twins. Aguliera saved 254 games and made three All-Star games, Tapani replaced Viola as the ace of the staff and won 75 games in seven seasons, and West contributed in the bullpen and rotation.

Johan Santana, 2008: The two-time Cy Young winner asserted all along that he didn't want to leave Minnesota, but with free agency only a year off, he understood that the Twins were unlikely to ever agree to pay him the market rate. He was right. After two months of considering various offers from the Red Sox and Yankees, newly promoted general manager Bill Smith finally accepted rookie outfielder Carlos Gomez and three pitching prospects — Philip Humber, Kevin Mulvey and Deolis Guerra — from the Mets.
Santana quickly signed a $137 million contract in New York, and had three solid seasons for the Mets, with a cumulative ERA of 2.85 in 88 starts and the first no-hitter in Mets history. But a shoulder injury all but ended his career; Santana has pitched only 21 big-league games since 2010, and none in the last four seasons. Gomez, meanwhile, showed flashes of potential in two seasons before being traded to Milwaukee. But the three pitchers the Twins received for Santana pitched a total of 15 career games and 22 innings with the Twins.