Professional tennis player CoCo Vandeweghe (pronounced VAN-de-way) knew she needed to change her game. The epiphany came in February 2014 after a loss in the first round of qualifying at a Women’s Tennis Association tournament in Acapulco, Mexico. “I had no business losing that match,” Ms. Vandeweghe says. “I went home frustrated and immediately called my trainer and said tennis—skills, technique—has always been the priority. It was time to shift the focus to fitness.”

Ms. Vandeweghe, 23, turned pro in 2008 and quickly got...