ELMSFORD, N.Y. — There have been many years of waiting, of watching, of wanting. There have been many years in which the Knicks haven’t been a threat at all, other years in which they have been thrust to the side by teams such as the Celtics and Heat.

There have been no winning years. At least not in the playoffs.

It has been 13 years since the Knicks made it past the first round of the postseason, reaching the Eastern Conference finals in 2000. Since then? Not even close, with just three wins in four first-round series.

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But this, it seems, could be their year. This could be Carmelo Anthony’s year. In fact, given their talent and their seeding, many expect it to be their year, or at least for the Knicks to make their return to the Eastern Conference finals.

“Is there pressure to do it? Maybe,” coach Mike Woodson said. “But again, we put ourselves in this position, so we’ve got to like the position we’re in.

“It starts tomorrow. We’re like 15 other teams that’s trying to sniff this championship. I think we’ve got as good a chance as anybody in this league to get it done.”

The Knicks are the second seed in the Eastern Conference, buying them a first-round matchup with the seventh-seeded Celtics, a team with more experience and more success. Still, this should be the Knicks’ series to lose, something the Celtics are emphasizing.

“As far as them taking an underdog role, I’ll leave that up to them,” Anthony said. “But we’re not going to underestimate these guys. We can’t. We know what they did before.”

That puts the onus on the Knicks and on Anthony, who was acquired from the Nuggets to make this happen. And there is an understanding of that.

“At the end of the day, our clocks are ticking,” Woodson said. “I’m 55. Some of these guys are old-head guys. They don’t have a lot of time left, man. So the urgency of winning it right now is now.”

That’s for the Knicks. That’s also for Anthony.

In recent seasons, a few stars around the NBA have found their moments and their titles. There was Dirk Nowitzki in 2011. There was LeBron James in 2012. Both stars cemented legacies that had been wanting, that had been judged incomplete without a championship.

Anthony is still waiting. This might be the year he’s waiting for.

“That’s the fun part,” he said. “That’s the challenging part, but that’s the fun part — to know that we have an opportunity to do something special here. That’s the fun part. And I think that’s going to be in the back of our mind every thought.”

For now, though, Anthony said he was trying to simplify the process, trying to make it easier on himself and his teammates, in a most obvious way. As he said, “This year I’m focused on winning Game 1 first. That’s the most important thing.”

Jason Kidd, for one, understands. It took him until his 17th year in the league to win his first title, which came with Nowitzki in 2011 with the Mavericks. Anthony hasn’t waited that long, with this being his 10th season. But chances like this don’t come around every year.

Though he hasn’t spoken to Anthony about it, Kidd said, “Winning a championship, that’s what you’re measured on, when you look at the great players in this league.”

But does that put pressure on Anthony? Did that put pressure on him?

“There is no pressure because there’s great players who haven’t won championships,” Kidd said. “You just hope you’re at the right place at the right time. And you have to be lucky. Hopefully this is the year that the luck is on the Knicks’ side.”

Making that quest more difficult is the absence of guard Pablo Prigioni, the 35-year-old rookie who sprained his right ankle in the Knicks’ last game of the season Wednesday. Woodson said it was “doubtful” he would play Saturday. “I just don’t see it,” said the coach.

That means a change in the starting lineup, with either Chris Copeland or James White likely to take Prigioni’s spot.

“I’ll sleep on it tonight and come up with a decision tomorrow,” Woodson said.

But whoever else is on the court, Anthony will be there. And he is thinking about only one thing: winning this series and moving on toward a title. He’s not alone.

“That’s all I coach for,” Woodson said. “If it could happen here, for the city of New York and these wonderful fans that we’ve had all these years, it would be the most beautiful thing for me.”

And as Anthony said, “The time is now.”