The phrase "whole premise" refers to the main idea or concept that something is based on. It is the fundamental belief or assumption behind a certain argument, story, or situation. Full definition
Whole premise fell on it's face at that point. (firstshowing.net)
And knowing you like your stats / facts, and coming back to whole premise of what you originally said ie: «Mertesacker is poor in the air and rarely wins even 1 on 1 air duels». (justarsenal.com)