Between plays on the field, Peyton Manning appears just a bit unhinged. The body language is manic, an eruption of gesticulating arms, twiddling fingers and fidgeting, stamping feet.

It is as if he hears voices in his head.

And for several seconds between each play, through tiny speakers in his helmet, Manning is listening to someone. It is a big responsibility to be the person talking in Manning’s ear. That person calls the plays that could decide Sunday’s Super Bowl for the Denver Broncos. It is a job that would seem to take on-field experience.

But Adam Gase, the 35-year-old offensive coordinator who instructs Manning between plays, never played professional or college football. On his high school team, he was an average player. And this season is the first time he has called plays at any level. Oh, yes, and in 2013 Gase designed and directed an offense that scored more points in a season than any other team in N.F.L. history.

In a macho, hyperorchestrated league that lives by a gladiator code and also aspires to leave nothing to chance, how did someone like Gase get the keys to the castle?