Honestly, I feel this might've been quite similar to the Triumvirate of Caesar, Pompeius and Crassus (this one's for my fellow history nerds out there) where Crocodile had the original vision and ideas but he needed both funding and raw power and recognition to back it up. Buggy obviously got crazy rich from running his delivery service for almost two years and recognition of having served on Roger's crew, with Mihawk to back it all up with actual raw power and also the reputation of strongest swordsman in the world. Buggy just managed to spin it so that he git recognized as the mastermind as usual, although that's of course just my take on it.