The 2015 Twins improved by 13 victories over 2014, remained relevant until the season’s final weekend and ushered in a wave of top prospects who have their fans excited about the near future.

Those are enough reasons to head into the offseason pleased with what they accomplished. But that’s not quite how the Twins are looking at things.

“This season didn’t go as well as we hoped, and that’s the big thing,” second baseman Brian Dozier said. “You play to get in the postseason and have a chance to go to the World Series, and that did not happen.”

That reveals the attitude adjustment the Twins made in 2015. Over the course of the six-month season, the Twins went from a team that hoped it could win to a team that expected to win.

As the Twins head for their offseason homes following a 83-79 season, how it ended will serve as a launching point for 2016 as they try to catch the Royals, who won the AL Central by 12 games over the Twins and are trying to return to the World Series.

“Eighty-three wins, it’s a step up, but if it wasn’t for the second [wild-card] spot, our story line might be a little different,” Twins manager Paul Molitor said. “It changes the dynamic of how people look at your season, because of the format, and I try to be realistic — you see the upper-echelon clubs, the amount they’re winning, we have a ways to go. We’ve moved in that direction, but you have to set your sights high.”

The Twins began to scatter after Sunday’s season-ending loss to Kansas City at Target Field. Ricky Nolasco left for a European vacation right after the game. Byron Buxton hopped in a car with his father and drove home to Baxley, Ga. By Monday morning, only a handful of players still had gear left in their clubhouse stalls to clean out. All of those offseason travel plans were a few days away from being canceled, because the Twins woke up Friday one game out of the second wild-card spot, only to get swept in three games by the Royals.

So what happened between 2014, when the Twins suffered their fourth consecutive season of at least 90 losses, to 2015, when they positioned themselves for an unexpected playoff push?

• The team ERA of 4.07, 19th in the major leagues, was down exactly half a run from 4.57 (29th overall) in 2014. The starting rotation’s 4.14 ERA was nearly a run better than the 5.06 of a year ago. The future looks encouraging, as the Twins can choose among Kyle Gibson, Phil Hughes, Ervin Santana, Tyler Duffey, Tommy Milone, Nolasco and prospect Jose Berrios for their rotation next year. And reliever Trevor May could return to starting after bailing out the bullpen the second half of the season.

• Offensively, the Twins actually scored fewer runs, 696, than the 715 they scored in 2014. This happened as offense, league-wide, rose during the second half of the year. The Twins were third in baseball with a .279 batting average with runners in scoring position, but overall, it was not the offense Molitor envisioned.

“I think we have a chance to be a team that combines power with putting pressure on you,” Molitor said.

• Their defense improved as well. They were tied for 12th in the AL in defensive runs saved, a stat that measure how many runs a player saves or allows compared with the average player. That’s a low ranking, but their rating of minus-21 was a vast improvement from their 2014 league-worst minus-90.

Their outfield defense, in particular, improved this season, and it could be well above average if the Twins break camp with Eddie Rosario, Byron Buxton and Aaron Hicks — all fleet and strong-armed — as the grouping.

Notice that doesn’t include outfielder Torii Hunter. Unquestionably the heart and soul of the team, he has to decide if he wants to play another year and how much he wants to play. Players want the 40-year-old free agent back, but will the Twins have a role for him that he’s comfortable playing?

One example of how important Hunter is viewed is how reliever Casey Fien responded when asked about expectations for 2016.

“I’m anxious to see what Torii is going to do,” Fien said. “That’s pretty much my first thought. He was our leader. He kept things cool. He made us more like a team, a unit.”

Hunter was brought back for a second tour with the Twins because he could help mentor developing players such as Buxton, Hicks, Rosario and Miguel Sano. And it’s those players who could have the Twins positioned to be a factor in the years to come. Berrios could join that group next season. Max Kepler debuted last week and also could contribute next season.

“The thing I’m glad about is that some of those guys got playoff experience the last couple of weeks,” first baseman Joe Mauer said. “We have been playing in that type of atmosphere, and it is good to get that feeling back. We haven’t had that for a while. It’s a different feeling, and I think these guys got to experience that and learn from that.”

Now the Twins want to take everything they learned about themselves this season and use it to take another step in 2016.

“As the year went on, we got more and more confident,” reliever Glen Perkins said. “We felt we had a chance to win every game. That’s a good feeling to have going into next year.

“We won 83 games this year and we’re going to be better next year. There is no doubt that our goal is to make the playoffs next year, and it is a realistic goal.”