MINNEAPOLIS -- The Twins non-tendered left fielder Eddie Rosario and reliever Matt Wisler at Wednesday night's deadline, making both players free agents. The move with Rosario came as no surprise; the decision on Wisler, on the other hand, came as a significant surprise after he had been one of the club's most effective relievers in 2020.

The Twins agreed to terms with four of their other arbitration-eligible players -- José Berríos, Mitch Garver, Byron Buxton and Tyler Duffey -- and tendered a contract to Taylor Rogers, who is expected to reach an agreement with the team.

The Twins placed Rosario on outright waivers prior to the deadline in an effort to give all 29 other teams the ability to assume his projected salary for 2021, his final season of arbitration eligibility. Rosario would have been due a raise from his $7.75 million salary in '20. President of baseball operations Derek Falvey said that the Twins would remain engaged with both Rosario and Wisler about alternate contracts moving forward.

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Rosario has played his entire six-year career with the Twins after he was selected by the organization in the fourth round of the 2010 MLB Draft.

"You¡¯re focused on your own team¡¯s news, but as I was looking around the league, I saw a few more names of players who¡¯d been with teams for a number of years," Falvey said. "I know those are difficult decisions for any organization, but for us, and with Eddie in particular, certainly, again, I want to stress it doesn¡¯t preclude us from having any other dialogue going forward."

Since Rosario's debut for the Twins with a homer in his first career plate appearance in 2015, he ranks third on the Twins with 119 long balls and leads the club with 388 RBIs. Though Rosario has been one of the Twins' most consistent sources of power for six seasons, his free-swinging tendencies and low on-base rates have limited his value, leading to a career .310 on-base percentage and .788 OPS from the heart of the order.

Rosario did improve his walk rate to a career-best 8.2% in 2020, alongside 13 homers in 57 games, after vowing during Spring Training to work on his patience at the plate. But his spot on the club is in jeopardy due to his rapidly increasing salary and the Twins' abundance of young corner outfielders, following the debuts of both No. 2 prospect Alex Kirilloff and No. 12 prospect Brent Rooker in 2020.

"We felt like with where our team is, with where we may have opportunities for depth and ways to add to our Major League club and where there are other holes where we want to try and fill, we felt this was the best decision for the team," Falvey said. "They¡¯re always agonizing. They¡¯re always difficult. And we very much appreciate everything Eddie has done up to this point. He¡¯s been a big part of this team over the last number of years. So those are always difficult decisions. But he was a pro about it."

Kirilloff is considered one of the best hitting prospects in the Minors, while Rooker's power bat could also make up for the loss of Rosario's home run ability. No. 3 prospect Trevor Larnach is also a corner outfielder and could debut with the Twins at some point next season.

Though Rosario has an advanced arm in left field, leading to 53 outfield assists in his career, Statcast has evaluated him as a negative defender for each of the last four seasons, bottoming out at minus-18 outs above average in 2019 and minus-1 in '20, further limiting his value.

Falvey said that the unexpected decision to non-tender Wisler came after the Twins couldn't come to an agreement with his agent on a deal for 2021 because the club is looking to avoid the uncertainty of the arbitration process with eligible players in light of the shortened 2020 season and the difficulty for both sides in evaluating historical comparisons for salaries.

Wisler could have done well in the arbitration process after making $725,000 last season due to his breakout campaign with the Twins, during which he pitched to a 1.07 ERA and 35 strikeouts in 25 1/3 innings after he was claimed off waivers from the Mariners during the offseason. Throwing sliders on an MLB-high 83.4% of his pitches, Wisler posted the second-most strikeouts of any Twins reliever and served the Twins in a variety of roles, from opener to closer (for one game).

"We obviously targeted Matt, got him last year, pitched well for us, so we¡¯ll stay engaged with his agent and work through him among a number of other relievers that are out there in this class," Falvey said. "I would say at this point, no reason to think we wouldn¡¯t continue having some dialogue with him."

Wisler's exit is particularly glaring in light of the Twins' depleted bullpen due to the departure of Trevor May to the Mets and the additional losses of Sergio Romo and Tyler Clippard to free agency, which means that the Twins have lost four of their most impactful relievers from 2020. Though Minnesota agreed to deals with Duffey and Caleb Thielbar on Wednesday, building out the bullpen depth will clearly be an offseason area of emphasis for the club.