And here's why......
The two constants in the backfield during the Super Bowl championship seasons was Brady and a big, down hill runner who they could pound between the tackles effectively and eat up some clock.
I was curious what the run/pass splits looked like for their championship seasons and it showed a pretty even balance between run/pass, see below.
2001 (11-5): 473 Run/482 Pass- 49% Run
2003 (14-2): 473 Run/537 Pass- 46% Run
2004 (14-2): 524 Run/485 Pass- 51% Run
This made me curious to see what the run pass splits looked like during the years they didn't win the title. Maybe it's coincidence, but they weren't as successful during the years where there was a larger delta between run/pass (with the exception of 2006, that year was pretty balanced).
2002 (9-7): 395 Run/605 Pass- 39% Run
2005 (10-6): 439 Run/564 Pass- 43% Run
2006 (12-4): 499 Run/527 Pass- 48% Run
2007 (16-0): 451 Run/586 Pass- 43% Run
I'll leave out the 2008 year as Brady wasn't playing so that drastically changed the offense.
This year they are currently at a 30/70 run/pass split through two games and have looked aweful the majority of the time..
These stats don't mean everything as defense and special teams are involved as well, but in this large sample size, they show the relative success of a balanced offense......