Hoping to be a big part of that run is 29-year-old rookie Chris Copeland, who has been impressive since making his way over from the Belgian League.
On the last day of the regular season in a game against the Atlanta Hawks, the forward scored a career-high 33 points, capping off a great first year in the NBA.
With Pablo Prigioni doubtful, Iman Shumpert is likely to move back to shooting guard, opening up a space at small forward. Having started 13 regular season games, Copeland is the logical candidate if the Knicks want to continue going with a small lineup.
Even if Prigoni is healthy, Copeland has earned the right to feature heavily in what will likely be a condensed rotation, with his offensive ability making him an X-factor for the Knicks.
Copeland's per 36 minute scoring average of 20.3 points is the highest on the team besides NBA scoring champion Carmelo Anthony, and this can make a big difference against a strong defensive team like the C's.
The Celtics are a team that tightens things up defensively in the playoffs, and players like Avery Bradley, Paul Pierce and Kevin Garnett will be difficult to score on, even for an offensive juggernaut like the Knicks.
Shooting 42 percent from downtown, Cope is capable of spreading the floor, but also has the skill to drive to the basket and score in the post.
After Melo and J.R. Smith, Copeland can be a genuine third scoring option for the Knicks, which will be so important with defenses keying in on their two stars.
The major criticism of Copeland this season has been his defense. Mike Woodson has struggled to keep him in the rotation simply because he's so weak on that end of the floor.
Still, Copeland has been improving steadily in that area over the course of the season, and has actually looked pretty good over the last month or so.
With the injuries piling up, Copeland has also had to spend time at small forward, power forward and center, which is just the kind of versatility New York will need down the stretch.
There are other options—like Steve Novak and new signing Quentin Richardson—but the small forward spot should be Copeland's. He's proven himself to be a better shooter than both, and once you factor in his versatility it's a no-brainer.
It's been a long time coming for Copeland to get his big chance in the NBA, and he has to be pinching himself with the opportunity to start for one of basketball's great franchises in their most important season in years.
As Flinder Boyd—a former teammate of Copeland's in Europe—wrote on SB Nation, a chance like this was nothing more than a pipe dream a year ago. The forward had been cut twice in the Spanish Second Division, and wasn't expecting a call from the NBA after falling so far under the radar.
The fact that he's here now is a credit to the Knicks' European scouting, and more importantly, Copeland's determination.
Clearly, Copeland has a lot of mental strength, but the playoffs is going to be a huge jump from anything he's ever seen before in his professional career.
If he can keep improving as he has done all season, Copeland has a chance to really make a name for himself here, which is more than you can say for most players with such a shaky career path.