The Twins’ scheduled Sunday game against the Tigers was postponed by rain at around 10:30 a.m., but the line for the Target Field batting cage — and a session with hitting coach Tom Brunansky — was not exhausted for at least another hour.

Aaron Hicks, Josmil Pinto and Brian Dozier were among the players who took their turns in the cage with Brunansky, the former Twins star right fielder in his second season as hitting coach. In 2013, the Twins had the second-most strikeouts in baseball, were the second-worst team in the majors at hitting with runners in scoring position and ranked 25th in runs scored.

Through the first four weeks of this season, though, the Twins offense looks much more capable.

And that has come from demanding more out of Twins hitters. More preparation, more attention to detail. The Twins entered Sunday fourth in the majors in runs scored, first in walks and 11th in batting average with runners in scoring position.

“The thing about last year was that it was a strikeout-fest,” said Brunansky, repeating a reporter’s description. “We were overmatched, and they weren’t competing. We’re striking out some now, but you see guys go up with an idea and a game plan and they go up and they are competing pitch to pitch, at-bat to at-bat. And that was part of something that we stressed in spring training.”

Fewer at-bats have been given away, and the Twins have amassed a good number of clutch hits up and down the lineup. And players no longer looked overmatched.

Third baseman Trevor Plouffe hit .254 last season with 14 homers and 52 RBI. He is batting .310 this season with 17 RBI and is holding down the No. 3 spot in the batting order. Adjusting his stance to drive the ball to the opposite field more has helped.

Chris Colabello was not ready for prime time last season, batting .194 in his first 55 major league games. This year, he is standing closer to the plate and hitting the ball to all fields after being mostly an opposite-field hitter last season. His 27 RBI already are a club record for April.

Josmil Pinto is batting just .230 but has walked 17 times and has hit five home runs — not bad for the rookie.

Brian Dozier is batting just .217 but has seven homers, six stolen bases and a team-high 19 walks. The Twins have four players in the top 11 in walks in the American League.

“The biggest thing right now is, every single person, whatever they are supposed to be doing, whatever their primary role is, they are doing,” Dozier said.

In spring training, Brunansky had all the hitters sit down in the batting cage at Hammond Stadium while he addressed them. In what was straightforward and, at times, fiery, Brunansky told the group that the bar was being raised. They were expected to put in the effort to be prepared, from working on their swing to knowing what the scouting report on the opposing pitcher was. And he often hears players repeating things that were said in that meeting.

“That meeting was big for us,” Plouffe said. “Not giving away at-bats and sticking with our approach and routine. In this game you’ve got to have a short memory. It’s hard to do that when you are young. It’s hard to forget about a bad day and you want to change something and have a quick solution. But the more at-bats we get under our belts, it’s clearer that you have to maintain what you are doing.”

The Twins offense is not fixed. Aaron Hicks is batting .188, and Brunansky is working with him to cut down on the furious hacks he takes. Dozier has pop but needs to raise his average. Joe Mauer is batting an un-Mauer-like .266 with 26 strikeouts and is working with Brunansky on some minor adjustments.

The offense was supposed to be a work in progress this season, but so far it has been much more than that. What’s scary is that it could be much better if a few more hitters turn the corner.

“Rather than Bruno standing on deck and telling them, ‘He’s going to start you with a slider,’ we want our hitters to know that,” Twins manager Ron Gardenhire said. “They are studying themselves. He gives them the information and they are taking it and reading it and they know what [the pitcher] is going to do.

“I think Bruno has made them become accountable for their own actions, rather than baby-sit them, and it is working out.”