PEORIA, Ariz. — The field, according to Fernando Tatis Jr., consisted only of the Chicago White Sox, the Cleveland Indians and the Tampa Bay Rays. In 2015, the shortstop had limited options.



“When I was trying to get signed,” Tatis said, “I was not that big of a prospect.”



Tatis, then 16, found himself in the shadow of more heralded teenage baseball players from his native Dominican Republic and other Latin American countries. Vladimir Guerrero Jr., Juan Soto and others entertained seven-figure offers. Tatis wielded some name recognition, but didn’t draw as much attention. He was, as Padres general manager A.J. Preller recalls, a “skinny, young tryout kid, basically.” His market was depressed in part because major-league organizations coveted Yoán Moncada, a Cuban star who would draw athletic comparisons to Bo Jackson.



In baseball, of course, few things go exactly to plan. While Soto and Guerrero have...