RIO DE JANEIRO — For most athletes at the Olympics, a gold, silver or bronze medal is the ultimate payoff for years of training and sacrifice.

But when the American wrestlers take to the mats at the Rio Games, they stand to head home with a lot of green, too. One wrestler could earn half a million dollars for winning a second consecutive gold medal, and his teammates could also take home substantial earnings for finishing first, second or third, making their potential paydays the envy of athletes not named Phelps or Bolt.

The bonuses would come courtesy of a fraternity of well-heeled former wrestlers, several of whom happen to have made it big on Wall Street. Together, they have endowed wrestling to a degree that other Olympic sports can only dream about.

In other words, they are rich and obsessed. Chief among them are Michael E. Novogratz, a private equity tycoon who wrestled at Princeton, and David Barry, who wrestled at Columbia and is the president of Ironstate Development Company. They aim to give a lift to a sport that was nearly booted from the Olympic program several years ago.