Mr. Ranadivé would be expected to pay the balance, plus 65 percent of the city’s investment through a 35-year lease agreement and property taxes. When all was said and done, Sacramento’s investment in an arena that it would own would be $86.7 million.

The proposal departed from almost every previous arena-financing deal. Arena-construction packages that relied on public investments typically featured taxpayers paying all, or nearly all of the development costs without ever being paid back.

Would Mr. Ranadivé bite?

He did. Visiting downtown Sacramento that day, he said, he envisioned crowds on the sidewalks, and in the space occupied by the near-empty 42-year-old mall, he saw a plaza surrounded by a state-of-the art arena, hotel, offices, restaurants and stores. And he sensed opportunity in a city desperate to keep its N.B.A. franchise.

In May 2013, as the principal investor, Mr. Ranadivé bought the Kings for $534 million, at the time the highest price paid for an N.B.A. franchise up to that date. (It’s since been eclipsed by the $2.2 billion paid last September for the Houston Rockets.) In buying the Kings, and agreeing to pay for more than half the new arena, he hoped to leverage his knowledge in technology, sports, information, and design to not only gain control of a sports franchise, but to revive what he considered an important American city.

Though Mr. Ranadivé has turned out be a somewhat polarizing figure among fans of the Kings, the project itself has since unleashed more than $1 billion more in new construction and redevelopment in surrounding blocks. And just north of the city center and Downtown Commons, on the site of the Sacramento’s former 244-acre Union Pacific rail yard, a local development group broke ground in the summer on a second sports-focused, mixed-use neighborhood anchored by a privately financed, $245 million, 20,000-seat outdoor major league soccer stadium.

“Four years ago, I said no other city is going to steal our team,” Mr. Ranadivé said. “The Kings are the heart and soul of the city.”