Paul, I realize there's enough bs games out there, but I don't think the NBA is disappearing anytime soon, so we move on.
As far as game theory goes, three- or more- cornered contests are nearly impossible to balance if all sides are to be in conflict at all times. Even the simplest complicit cooperation between any two sides would be enough to change the game from one of skill to one of numbers. This begins to even out if there are enough sides (say, nine or more), but it's still a sizeable advantage if two teams work together against others who are competing alone.
I still have confidence that this game of numbers can be restricted, if not eliminated, through unique game design. In the case of a defense that's twice the size of the offense, this could potentially be deflated by reducing the team members on defense (like in the tri-baseball example) or through the implementation of zones on the field where numbers are restricted (I'm thinking at this point of handball, where only the goalkeeper is allowed within six metres of goal).
On a side note, it pisses me off that I only get to see handball once every four years. I think I'd really love that sport if I could just, you know... watch it.
The thought of a multiteam game with a larger number of teams (like twenty or more) crossed my mind too. Not sure how something like that would play out, but it works in auto racing.