As the losses mount and the home runs soar, the odds seem to increase that Brian Dozier might be hitting his way right out of the Twin Cities.

True, he is under contract for two more seasons at the bargain rate of a combined $15 million. But that only makes him more valuable should the incoming baseball-operations administration choose to make him available on the open market.

And yes, he had a starring role in the 3 1/2-minute marketing video the Twins sent out to their sagging season-ticket base in recent days. But that only increases his appeal to teams seeking a popular, outgoing presence around which to build a marketing campaign.

The Atlanta Braves, for instance, are just a short road trip from Dozier’s Mississippi roots in Hattiesburg and Fulton. They are moving into a team-funded stadium in the northern suburbs, and doing so with the second-worst record in the major leagues and a trove of unproven young pitching prospects.

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What’s that, you say? Those life-size cardboard cutouts of a smiling Dozier that were produced during his all-star season of 2014 have reappeared this month on the club level at Target Field?

Maybe that’s just the Twins’ way of extracting maximum value from their gritty little second baseman’s historic season before reality sets in and they decide to move him for a boatload of young pitching.

Stack up all of these theories and place them before Dozier as he sits at his locker before a recent game, and you’ll get a knowing smile and a wink.

“Oh, really?” Dozier said. “I don’t read too much into that. All I can know is I’m here for two more years.”

If only it were that simple.

VALUABLE EXEMPLAR

Twins manager Paul Molitor, who shared the stage with Dozier and team president Dave St. Peter in that unusual marketing video, has come to appreciate his second baseman even more this season.

It’s not only the power production, which has skyrocketed since a two-game benching in late May, it’s the nightly example he displays for a team buried in the standings.

Entering a weekend interleague series at the New York Mets, Dozier had made 102 consecutive starts, just one of them at designated hitter. Since that mental break against the Kansas City Royals on May 23-24, Dozier had been removed early for just 10 defensive innings.

“As his run has continued it’s been harder to take him out,” Molitor said. “I’ve talked to him a couple times here in the last two or three weeks about at what point does it make sense to DH or eliminate four at-bats in a given game and try to make sure he stays strong through the end.”

You can guess how those conversations have gone.

“He’s rather adamant that he feels really good,” Molitor said. “How it unfolds here and who we play and the meaningfulness of the game, whether he’s going to get a day or two (off) here, I’m not sure. But no, he wants to be in there.”

With a dozen rookies getting time in the field or on the mound this season, the example of one of the team’s few proven veterans has been invaluable.

“I think there are always things for young players to watch from your guys that have a little longer resume,” Molitor said. “How they handle the ups and downs and the adversities. We make that a point every year in spring training to the young guys. We tell them to look around the room and we point out the guys and what they’ve been able to accomplish and give them reason to make sure they’re paying attention.”

Seeing Dozier throw his body around in the field and run the bases with abandon and work opposing pitchers for walks rather than simply swing for the fences each time? Those are the type of lessons that could stick with an observant young teammate for an entire career.

“It’s my job to lead,” Dozier said. “It’s very tough. We have a lot of guys that haven’t had experience up here, not just experience winning up here, because I haven’t even really had that until last year, and even at that not even the playoffs. There’s a lot to be said for experience when you have a lot of people on the field that are inexperienced at trying to win baseball games at the highest level in the world.”

With injuries robbing the Twins of veterans such as Glen Perkins, Phil Hughes, Trevor Plouffe and more recently Joe Mauer, the emphasis on Dozier has only became greater.

“Brian has put together almost an indescribable season considering where he started and where he was after two months,” Molitor said. “You hope people are paying attention.”

WINNING COMES FIRST

No doubt the rest of baseball is watching, even with the Twins on track to draft first overall next June for the first time since taking Mauer in 2001 and just the third time ever.

The first time was 1983, when a little-known former minor-league infielder named Scott Boras advised college pitcher Tim Belcher to turn down the Twins’ $100,000 bonus offer, which he did. Belcher went to the New York Yankees in the secondary phase of the draft the following winter.

Will the Twins, in desperate need of pitching and with young infielder Jorge Polanco best suited for second base, make Dozier available this offseason? A steady flow of top scouts has made its way through the press room at Twins games this month in part to prepare for just that possibility.

At 29, they all agree, Dozier is smack in the middle of his prime. And while he probably won’t be a 40-homer man going forward, he has averaged 35 doubles, 27.5 homers, 96 runs and 667 plate appearances over the past four seasons.

There’s also that highly appealing contract, which gave the eighth-round draft pick lifelong financial security when he signed it in the spring of 2015, giving up three cracks at arbitration in exchange for a $20 million total guarantee. How much more would Dozier be worth now via arbitration if he’d gone year to year?

Then again, the Twins were unable to buy out any of Dozier’s free-agent years at the time of the deal. The cost for those, one might safely assume, now starts at $15 million a year and quickly heads north.

“First things first,” Dozier told the Pioneer Press. “You need to see after the season who is going to be our GM, which obviously plays a huge part in it.”

Regardless of who is running baseball operations, the Twins would likely discuss the parameters of a possible extension with Dozier and agent Damon Lapa before dealing away such a vital piece of their present and future.

“I know talking with (interim GM Rob Antony) he knows I’d love to be here for a very, very long time,” Dozier said. “We made that clear the past three or four years as we’ve been talking about extensions and that kind of thing. But there’s way too many (questions) and there’s a lot of other things involved that have to take place rather than just for me to say, ‘Hey, I’m open. Let’s do it.’ ”

After being part of four 90-loss teams in his first five big-league seasons, Dozier would need to hear what the new timeline for contention might be before signing on.

Will there be enough pitching in 2017? And with a dearth of free-agent mound options this winter, where do the Twins plan to find it?

“I want to win,” Dozier said. “I want to win more than ever. It’s a point in my career that I want to have everybody on the same page — to be dedicated to win and make sure to do that. That comes first.”