We upgraded by Amir Johnson and David Lee. Think about it, what really hurt us against Cleveland is Tristan Thompson. If we could have eliminated at least half of those excruciating offensive rebounds, then we could have taken a couple from Cleveland and maybe even won the series. We got killed from their offensive rebounds.
David Lee's teams have historically grabbed fewer boards when he's been on the floor.
By such a small amount that's it's within the margin of error. But that's the wrong way to look at it anyway-- the question is who's minutes is Lee likely to take, and try to figure out, from a rebounding perspective, if David Lee will rebound better than, say, Brandon Bass. Also, while we got killed in the boards in the playoffs, during the regular season we were just above league average in defeanive rebounding percentage. And, for what it's worth, Golden State, relevant both because of their title and being Lee's former team, was slightly below average.
I don't really think David Lee is the panacea to a rebounding problem that isn't necessarily a big problem (and, in fact, that is not what Celtics management highlighted when talking about bringing in Lee. They were most concerned about getting buckets in late-game situations when things get tighter.). But I do completely think David Lee is more likely to provide value to the team than was Crash, and in that respect, he's an improvement from last year.