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...Still, history of this league shows that only a few coach reinvented themselves and won after each a long period of losing. Most coaches that have a 7-9, 7-9, 7-9 record are shown the door, not given an extension in the middle of that...
The argument is circular. How many coaches get a chance to reinvent themselves after a long period of losing if they get fired after losing? For every Fisher, there is a Bill Cowher.
Just for perspective, Belichick started out 6-10, 7-9, 7-9, 11-5, 5-11 and 5-11 and had 12 years of NFL coaching experience before his 1st head coaching gig and 22 years of experience before his first year as the Patriots head coach.
By comparison, Payton had 10 years NFL experience before his first head coaching gig and did much better in his first 5 seasons with the Saints than Belichick did with the Browns (that's the Ravens Browns not today's Browns) and Payton just finished his 20th year in the NFL.
I'm not saying Payton will have the same success as Belichick, just that it seems premature to write him off when you look at his career in comparative context.