I don't think so...we may be defining 'minions' differently.. for me it's more of a 'kiss @##'... they don't really coach, they mimic, or in a better 'light', as sometimes happen, they are able to effectively translate the coaches philosophy into good results.. that may be Bellichick, granted.. I don't think so. I don't think Bellichick plays a 'system', per se. I think he plays his players... then brings in asst's who best, (better even than he), can create and tweak 'system's' to match their inherent talents.
IOW- I don't think Bellichick has a 'magic formula'... welll, unless simply getting quality people AND on the same page is 'magic'... now that I think about it, it may be.