Ok, no physics here, nor do I race. I recently went from triple to a compact cassette. I live in the flat world of Flordia--so hills are not my fortey--or they used to not be. We do have some hilly areas that I train in.
Nor do I race.
I was very afraid to lose my "granny gear" for when I did ride the hills.
I LOVE my compact cassette. I think it allows me more range while in my "small ring". SO I can hill climb and then handle the flats. With a triple I was always having to then get out of my small ring to my middle chain ring and also dropping back down again. AND dropping my chain. So for me it was a good deal! And I climb much better!