This has been discussed before, but with the recent news regarding Belicheck being possibly fired (which blows my mind) and Josh McDaniels getting fired (again), it bears repeating.
Bill Belicheck - he's 87-97 after Tom Brady left.
Charlie Weis - he went 35-27 as the head coach of Notre Dame and 6-22 at Kansas in college after leaving NE. His one year as Florida's offensive coordinator in 2010 his offense was 102nd.
Josh McDaniels - He went 11-17 as head coach of the Broncos, and 20-33 as head coach of the Raiders after he left NE.
Bill O'Brien - He went 15-9 as Penn State's head coach, then 52-48 as Houston Texans' head coach after leaving NE. He did make it the college national championship game with Alabama in 2021 but lost to Georgia.
Romeo Crennel - yes, he's on the defensive side. However, he went 24-40 as Cleveland's head coach after leaving New England, then went 4-15 as Kansas City's head coach and 4-8 as Houston Texans' head coach.
Eric Mangini - yes, another defensive guy. However, he went 23-25 as the Jets' head coach after leaving New England and then 10-22 as the Brown's head coach.
The main points I have read with quoted contributions from Welker, Gronkowski, and Edelman was that Brady was a player coach on the field and held everyone on offense accountable. He put together off season sessions as well as in season extra practices to keep the offense running. This left Belichick to focus more on the defense and special teams. They could adapt on both sides of the ball quickly because each side had a taskmaster to keep them headed in the right direction.