Team culture is a factor. And what is important is that the team is working as a team. I see nothing in that video to suggest there is an issue. Red flags for bad culture is a wide receiver pouting after a win he was not targeted enough.
Outstanding cap space management was a much greater factor in NEP's success than Belichick's sour demeanor.
Belichick's success didn't not come because of his personality, it came because he is brilliant at football. The reason why his coaching tree is so horrible is folks copy his personality rather than his football accrument. You don't need to be an asshole to be a successful coach. Belichick won in spite of being an asshole not because he was an asshole.





