Most New York Knicks fans would reflexively say, "Carmelo." He takes the most shots, and when it was time for All Star selection, Anthony was the lone Knick named.
While Carmelo Anthony may be the "superstar" by reputation, I would have to name recent Defensive Player of the Year Tyson Chandler as the team's most valuable member.
You see, I have a funny notion that defense actually matters. Whatever reason, we acknowledge its importance, while rarely letting the defensive end influence our assumptions on who superstars are. Carmelo Anthony, to his discredit, is an awful defender. Watch him closely and you find plays like the following in bunches:
Teams have been better with Carmelo Anthony off the court for five consecutive seasons, according to basketball value. Though of ideal small forward size, Anthony is slow laterally and prone to mistakes. He's also prone—quite frankly—to giving up on plays and not trying. It's possible that he gives better effort in bigger moments, but I have yet to glean any visual evidence of a shift.
In contrast, Tyson Chandler is quite good at defense. While I personally would have given my DPOY vote to Kevin Garnett, it should be acknowledged that the lanky Knicks center produced more than enough plays for a melodramatic highlight video
In all seriousness, Chandler was the fulcrum of a revamped Knicks defense that went from a ranking of 21st in the league in 2010-2011 to fifth in 2011-2012. The defensive improvement is largely responsible for dragging New York to the playoffs, despite Amar'e Stoudemire's injury and declining play.
If Tyson Chandler was the main defensive cog, then bragging rights for New York's offense naturally go to Carmelo Anthony. Except, the NYK offense wasn't much to brag about. According to John Hollinger's efficiency statistics, New York ranked 19th among all teams in 2011-2012 offensive production.
The Knicks were better on offense when Carmelo Anthony played, but with his drop in field-goal percentage (down to .430 from .455), Melo may not have helped the Knicks as well as he could have. In general, Anthony is a good offensive player, especially when featured at the 4-spot. Unfortunately, the Knicks are forced to start Stoudemire at that position, thus siphoning some of Anthony's offensive impact.
Tyson Chandler wins my "most valuable Knick" award because he actually provided some wonderful offense on his own accord. Tyson claimed a ridiculous .679 field-goal percentage last season, while chipping in 11.3 points.
While it is true that Tyson Chandler cannot create his own shot, he's incredibly efficient with the shots created for him. He doesn't do too much, and is quite good at what he does. This quality, combined with top quality defense, makes the underrated Chandler New York's most valuable player.