BATON ROUGE, La. — When the quarterback Joe Burrow visited Louisiana State in the spring of 2018 as he considered where to transfer from Ohio State, he came well prepared. His mother, Robin, met with an academic adviser to map out a graduate studies program, while Burrow visited with the Tigers coach, Ed Orgeron, and two offensive assistants. Burrow brought along his father, Jimmy, a 30-year college coach, and an older brother, Dan, who like their father played at Nebraska.

Before long, Joe Burrow was in front of a board, mapping out protection schemes.

The meeting, scheduled for 30 minutes, lasted two hours.

The main concern on Burrow’s mind: Though L.S.U. had the pedigree to command the spotlight and the talent to breed expectations, it had for years been an offensive backwater, a place where championship ambitions often died.

What assured Burrow that Orgeron, who cut his chops as a defensive line coach, could evolve from the run and play defense formula that Nick Saban and Les Miles used to win national championships more than a decade ago?