From a Laker fan's perspective, I believe that Sheed needs to get more minutes than Perkins in this series if Boston wants to win. The Lakers struggle with outside shooting big men, and Boston's having a hard time spacing the floor. If you can't space the floor against the Lakers, it means that you have to come into the paint, where the long arms of Bynum/Gasol/Odom await. You're not gonna win that way. Sheed pulls one of those guys out of the paint, which opens things up for guys like Rondo, who had his shot blocked or altered several times yesterday for that exact reason.
You know the old saying "styles make fights"? That could very well be what we're seeing here. If I would have told you beforehand that the winner of last night's game would have been the tougher, more physical team, I believe that most Celtic fans would have assumed that they would have been the victors. Hot shooting can come and go, but physicality is something that you either have or you don't. The Laker team that showed up last night is the same one that I've been watching all year. This is a very physical squad, and the idea that we're similar to the '08 Lakers in terms of toughness is probably the biggest misconception about this team.
The teams that the Lakers have struggled with have been able to draw the Lakers away from this style...not beat them at it. OKC did it with athleticism, and Phoenix did it with outside shooting. The Celtics can't change their stripes at this point, but I think that they need to rely more heavily on the players that present matchup issues that the Lakers typically struggle with. I think Sheed is that guy.