A day after Rangers team president John Davidson said making the playoffs was “a goal,” but “improvement” was the main focus for the team, in came second-year head coach David Quinn to answer just how he plans to marry those two ideas.

Quinn went back to one of his philosophical tenets, something he evoked all throughout his first year with the Rangers.

“I’m big on intentions,” Quinn said Friday at the team’s practice facility in Tarrytown as a handful of players completed their on-ice testing before the first full-team practice Saturday. “Mistakes are going to happen, but what are your intentions?

“To me, if you’re playing with the right intentions, a lot less mistakes are going to happen. And if we get everybody to play with the right intentions, that transition is going to be a lot easier for these young players. So that’s a message we’re going to send from Day 1.”

There are both similarities and differences between this year and Quinn’s first behind the Rangers bench, when very little was expected of them and the organization continued dismantling the veteran roster to rebuild with youth. A year ago, he was also strapped with the idea of developing the young talent while still trying to stay competitive. But when players started being traded and the losses starting piling up en masse, it naturally got a little ugly.

The biggest difference now is the influx of talent, from Artemi Panarin to Jacob Trouba to Kaapo Kakko to Adam Fox. It’s unlikely the Blueshirts are ready to compete for a Stanley Cup right now, but they are hoping to set the building blocks in place to make that jump sooner rather than later.

Though general manager Jeff Gorton has orchestrated the whole franchise turnaround — with support from Davidson since his hiring four months ago — it’s still on Quinn to do the daily, hands-on work that is going to morph this hopeful image of a team into one that is going to be able to win consistently at some point soon.

So it goes back to the players understanding what Quinn is asking of them.

“The hope is that the veterans — which I know they will — I think they understand what’s expected,” Quinn said. “One of the things I really liked last year was the connection between the coaches and the players, and the buy-in. I think our veterans certainly understand the way we want to play and what’s expected on a daily basis.”

For all the dark malaise that colored the second half of Quinn’s first season, it is notable that the team never quit. He was the first one to point out the need to improve defensive-zone coverage and the penalty kill, but it wasn’t from a lack of effort — just execution.

Which is why there is such optimism with all the fresh faces.

“The moves we made over the summer are just a continuation of what we’ve been doing over the last 16-17 months,” Quinn said. “Within the walls of our locker room and the walls of this building, we feel good about the direction we’re going in. We’re just going to continue to work at getting better daily.”

Quinn also made it very clear that he has already been projecting what his opening-night lineup might look like, with line combinations and defensive pairings. He has also considered how to lessen the workload of 37-year-old goalie Henrik Lundqvist, in the hope of avoiding another second-half swoon like those that defined Lundqvist’s past two years.

There will be question marks as the season goes on, but the biggest obstacle Quinn will face is how to deal with the present and future at the same time. He dealt with it in the past, but things sure do feel quite a bit different now.

“I think excitement is the right word,” Quinn said.