The "game manager/system" label was more valid during Brady's early years when New England was known for their elite defenses. For the last 7-8 years their defense has been okay and if it weren't for the prolific offense they'd be near the bottom. Opposing offenses have to go into "shootout mode" vs New England and become predictable.
The craziest Brady stats are his numbers in cold-weather games. Since 2001 Brady has played in 29 games at a freezing or below temp. The Patriots are 24-5 in those games and Brady has a 91.4 passer-rating.