If North Korea’s propaganda machine is to be believed, “Supreme Leader” Kim Jong Un comes from a long line of mythical heroes.

His grandfather was the greatest genius ever to have walked the Earth. His father was a prodigy in all areas, proving himself a crack pistol shot—on horseback—by age 5.

So International Olympic Committee President Thomas Bach was pleasantly surprised during a March meeting in Pyongyang when the North Korean dictator broke the ice with a self-effacing remark about his own diminutive size and portly physique.

“Even if it may not look like it, I love to play sport, and especially basketball,” Mr. Bach, a former Olympic fencer, says Mr. Kim told him.

Mr. Kim has a way of overturning expectations. When he inherited power in North Korea in December 2011, expert opinion was he’d be toppled or killed within a year. Filmed red-faced and sobbing at his father’s wake, the pudgy would-be dictator in his late 20s didn’t seem up to the Darwinian task of extending the bloody Kim dynasty to a third generation.