KANSAS CITY, Mo. — In 10 seasons in the major leagues, Billy Butler made an All-Star team, appeared in a World Series and spent his summers roping doubles in ballparks across America. Yet as he returned home to Idaho last summer, his first without baseball in decades, he searched for avenues to sharpen his competitive spirit.



He had spent the 2016 season batting .284 with five homers while playing in 97 games for the A’s and Yankees. But with little interest for his services, and his career on the precipice, he found an outlet in an unlikely place:



A local softball team named Pharmgrade in the Idaho Falls Parks & Rec men’s league.



“Obviously,” Butler said, “we do well.”



Playing games at a local park, and against opponents who have not played competitive sports for years, Butler put his sweet right-handed swing to good use. He crushed dingers at a staggering rate. He led his team in homers, slugging and...