I have a different theory on the patriots sustained success that borders on an analytical anomaly in a sport that boasts parity.
Sure, Tom Brady has been a great QB, and Bellicheck is a talented coach -- but so what there have been plenty of those "Combos" over the years, they didn't necessarily lead to the sustained success over multiple decades that the patriots experienced.
No, their sustained winning is a combination of those things but also the "unseen hand" that is the NFL as entertainment value. The league has helped the patriots out quite a lot a long the way and over the years with the calls they have made (And not made) that have really impacted their seasons at crucial moments, and in big games. Slightly tilting the table more in their favor in those prime time moments.
When you tip the table in favor of already talented individuals, you get a Football dynasty that the NFL has banked billions off of. Everyone loves a hero (and a villain), and for every underdog you need the reigning champions. The NFL Knows this, and when Brady is gone the will choose their next Dynasty -- lets hope it's buffalo!:)