Here is something that has been on my mind lately.
If you were GM of a major league team, and you could hire three of the best sabermetric minds in the country, and put them to work on a problem to solve, what problem would you give them? Don't worry about who the sabermetrics minds are...assume that they are extremely bright, knowledgable about both numbers and baseball in general, and motivated to succeed.
Call this the Manhattan Project of Baseball. You take these guys, give them all the money they want for research and access to any information they need, and give them problem to work on. What project would you give them?