If you're a big you need to rebound. The only big doing anything on the boards this year is Sullinger and he has been one of the best rebounders in the league this year. That alone makes him our best big. Add in his much improved defense and effort, plus that even though he is shooting like crap, he is still contributing offensively with 11 PPG and 2.4 APG. He has the most APG and 2nd highest assist percentage of all the Celtics bigs.
Given these facts, I don't see how anyone can say Sullinger hasn't been our best big. Is he flawed? Sure. Is he not your prototypical PF/C? Sure. But it's pretty easy to see that that he is still the best big we have right now, whether you think he's just a fat slob or a very good player.