I was taking in the deliciousness of the threads (sorry, it was an awesome win by the Pats) when I read this post. It's not about the talent difference, the talent difference between teams is miniscule. If you are in the NFL, you are the top of the top of athletes. Now there are the occasional freaks of nature, that look like men among boys out there (see Gronkowski or Antonio Brown or Jerry Rice, etc). The advantage is the mismatches Patriots create through their scheme. For instance, during the game, if you watched whenever the Pats were on offense, they would have pre-snap movement. Brady and other QB's do this to understand if the Defense is running pure man, zone, or a mix of zone/man. Since no one followed anyone ever, the Pats always knew it was pure zone. Here's the cool part. Because it was pure zone, Brady could change the offensive alignment to create huge mismatches, where you had linebackers on wide receivers...etc. Also, part of Brady's genius is his ability to look at film, see a defensive alignment, then look at the field, and understand from the film, which defensive alignment the opposing team is in within seconds. Then, within a few more seconds, he creates the play alignment in his head that will almost always create mismatches. Brady knew on every play, along with his team mates where the soft spots would be in all of your zone defense alignments from film study.
Additionally, because of Brady's ability to process pre-snap reads so quickly, the Patriots run an offensive system called the Erhardt-Perkins System. This bascially means that every coverage and wide reciever route changes based on what the defense presents at the snap. So Brady and his other offensive players all have to understand the coverage, make a route adjustment based on that coverage, and then run the same route Brady thinks they are going to run based on what the defense is presenting, without any communication at all. It's a system based on having extremely intelligent players, that process defensive alignments instantaneously. The Patriots only bring in players that have the film study dedication and mental acumen to process this offense. This is a big part of the reason they are so hard to stop. Each play could have 10 different route trees the players run, just based on what the defense is showing. With so many combinations, it's almost impossible to know which exact route the players will run.
Finally, most defensive and offensive coordinators will run the scheme they like no matter what. Because that's what they know and it's the scheme they feel most comfortable with. While BB will change his scheme's and plays based on the skillsets of his players. It's why so many good players go to new scheme's and fail. Because their coaches aren't accounting for their strengths and weaknesses. The Patriots try to only put players in positions that play to their strengths and never put them in a position that showcases their weaknesses. Only when they have high injury seasons and a player has no choice but to move into an area that's a weakness. It's also why all of BB's assistant coaches are homegrown. He never brings in an outside Offesnsive or Defensive coordinator, he needs people that have grown up in his system or they are useless to him.
The Defense does the same thing as the offense based on film study and will know, based on your offensive alignement what play you are in.
So the normal questin to ask is, why doesn't every team run that system? Because it's so difficult to run. You need to have the right players, with the right acumen, and processing speed. Because you only have seconds to understand everytihng during game time. It's hard to implement this system and requires complete control over drafting, player acquisition, coaching staff, and team management. No other coach in the league that I know of, has what BB has. Which is complete control over everything. Often times the coach has his domain and the GM has his domain. If you don't have that level of control, then you can't effectively run this system. So that's whyt he Pat's are consistently on top, because of the genious of BB and the ability of Brady to effectively run that offensive system.