Here are the last 8 seasons. They're 38-10 against the AFC East. They won the division all 8 years. Got a bye every year and played nothing but home playoff games except for 2 AFC Title games (which they lost both).
If you can't say that the mediocrity of this division hasn't helped their cause, you're either a) not smart or b) making an outright choice to refuse facts, data and logic.
2017 = 5-1 (1st rd bye + 2 home games – SB appearance)
2016 = 5-1 (1st rd bye + 2 home games – SB appearance)
2015 = 4-2 (1st rd bye + 1 home game – Loss in AFCC @Denver)
2014 = 4-2 (1st rd bye + 2 home games – SB appearance)
2013 = 4-2 (1st rd bye + 1 home game – Loss in AFCC @Denver)
2012 = 6-0 (1st rd bye + 1 home game – Loss in AFCC at home against Baltimore)
2011 = 5-1 (1st rd bye + 2 home games – SB appearance)
2010 = 5-1 (1st rd bye + 1 home game – Loss at home against NY Jets)
So let me blow this entire their division gets them everything.... And I'm not a Pats fan, although I do like them. I'm a Cardinals and NFC fan first and foremost.
2017 NE 5-1 (13-3), Pitt 6-0 (13-3), KC 5-1 (10-6)
2016 NE 5-1 (14-2), KC 6-0 (12-4), Pitt 5-1 (11-5), Texans 5-1 (9-7)
2015 NE 4-2 (12-4), Cin 5-1 (12-4), Hou 5-1 (9-7), Den 4-2 (12-4)
2014 NE 4-2 (12-4), Den 6-0 (12-4), Ind 6-0 (11-5), Pitt 4-2 (11-5)
2013 NE 4-2 (12-4), Ind 6-0 (11-5), Den 5-1 (13-3)
2012 NE 6-0 (12-4), Den 6-0 (13-3)
2011 NE 5-1 (14-2), Balt 6-0 (12-4)
2010 NE 5-1 (14-2), Pitt 5-1 (12-4)
Let me make this more lucid - over the last 8 years, they have the same or worse record in division than 16 other division leaders. Of those 16, they have a better regular season record 10 times and are tied 4 times and behind 2 times.
Bottom line their division does not help them more than any other team in the AFC. Maybe the AFC east sucks year in and year out (partially due to the Patriots beating them) but other teams in the AFC teams benefit from equally sucky or more sucky teams. They have earned most of the byes by beatings teams outside their division more than other AFC teams have beaten teams outside their division.