As Sid Edwards tells it, he was driving through a gusty storm, with lightning streaking the sky, when he reached a fateful crossroads.

He could turn right — proceed as usual, opening up the weight room at Istrouma High School in Baton Rouge, La., where he was the head football coach. But on this July day, he said, divine intervention steered him in the other direction.

Shoving his doubts aside, he headed toward City Hall, where he handed in paperwork to enter the race to lead Baton Rouge, the state’s capital and second-largest city. He had no money, no staff, no real shot at success — or so it seemed to nearly everyone, including him.

Despite his dim prospects, Mr. Edwards blazed to the front of a crowded field and into a runoff election in December against the two-term incumbent mayor-president, as the position is called.

And then he won. He took office this month.

“I don’t use the word ‘miracle’ loosely,” Mr. Edwards, 61, said in an interview. “I think God wanted me in this position. I think I’m ordained.”

Another, more temporal, explanation: These are tough times for incumbents or politicians perceived as defenders of the status quo, not only in Baton Rouge but worldwide. And in this city, a simmering dissatisfaction with violent crime, fraying infrastructure and a general sense of unchecked decline led voters to oust Sharon Weston Broome, who had 36 years of political experience, and replace her with “just an old ball coach,” as Mr. Edwards described himself.