Week 15 Post-game AMA: The Backup Show

Of course there's a counter-argument to that--be stubborn with your best play/player, make the defense stop it (the best example being the Seahawks not running the ball with Marshawn Lynch on the goal line to win the Super Bowl)--but these things really come down to gut instinct.
According to Michael Lombardi, the Patriots installed a new goal line defensive package that year, but never used it until that famous play against the Seahawks' 11 personnel on the 1-yard line.

“When I first joined the Patriots in ‘14, they had just lost to Denver in a playoff game,” Lombardi said, “and one of the things that they were really bad [at] that season was in the red zone [and] goal line defense. So Belichick was obsessed with trying to find a goal line defense that could stop the run. And so that became the three corner defense. That defense was practiced all spring, was practiced all during the fall, never called until the Malcolm Butler interception play.”

“Get out of here,” Eisen interjected.

“This is true, Rich,” Lombardi continued. “This is true. So when you hear Pete Carroll, people say, well [you have] Marshawn Lynch, it [throwing the ball] was the dumbest play of all time. Why wouldn’t you run the ball? They couldn’t have run the ball. It was a goal line defense. Marshawn Lynch would have lost a yard on the play.

“So when Pete Carroll says they’re in goal line, he sees the goal line front, but they’re in goal line [with] three corners- first time they ran it all year- and Belichick didn’t want to give them time to adjust to what they saw on the field, so that’s why he let the clock play out.”
https://www.patspulpit.com/2017/2/1...didnt-call-time-out-at-end-of-super-bowl-xlix