As Kayla Harrison, the only American to win a gold medal in judo, prepared for the Rio Olympics at her coach’s dojo in Wakefield, Mass., in March, she spent most of the morning wrestling on the mat. She practiced pins, chokes, armlocks and other submission moves. In judo, this is called “newaza,” or grappling techniques. Unlike the match-ending throws that lift competitors off their feet and slam them down, newaza isn’t flashy or explosive. In American judo, it’s a religion.

“All over the world, I’ve been to so many training...