So for sports viewing with some ambient light, I need 2530 lumens, correct? (23FL *110" screen)

So I need a projector that does roughly 850 lumens with a screen with a gain of 3?

The 850 would need to be the real lumens after factoring any loss for the throw. Can I easily measure how many lumens I'm actually getting?

I was going to ask about estimated costs for just these items, but I'm a little ways out on this, so I expect prices will continue to come down as the technology gets better.