A theoretical baseball question

[SossMan]

What would the range of batting averages be if every batter in MLB knew what pitch the pitcher was trying to throw?

Assumptions:
- The pitcher doesn't know that the batter knows
- The batter knows that the pitcher is going for an inside fastball...this doesn't mean that the pitch will actually be inside...the pitcher may miss out over the plate, high, etc...
- Manager's don't know that the batter's know (for either team)

What would the 'average' BA be for the entire MLB?

What average would lead the league?

How many homeruns would lead the league for a given season?


*question originally derived from this thread **warning NSFOOT