I know there is a minimum and maximum mounting distance, but is there a calculator for finding an optimum mounting distance?

For example, I was looking at a Sony VPL-VW60 Projector with a 120" 16:9 screen. What would be the optimum mounting distance for it?

It would mainly for watching sports and movies in HD.

Here's some specs:
Std. Lens: Focus:
Power
Zoom: Power, 1.71:1
Throw Dist (feet) : 6.9 - 30.9
Image Size (inches) : 40.0 - 300.0

Thanks for the help!

There is no optimum without specifying whether you want more brightness or more contrast. Given your screen size, you would probably need the extra brightness with mounting the projector closer. Do stay away (say inches) from the closest distance because no lens peforms best geometrically at its extremes,