KANSAS CITY, Mo. — The Kansas City Royals have slowly and methodically allowed their top prospects to climb through their farm system in recent years, piecing together a team they believe can compete in the wide-open American League Central.

All that’s been missing has been the pitching.

They dipped into the farm system to solve that problem, too.

The Royals sent top prospects Wil Myers and Jake Odorizzi along with two other minor leaguers to the Tampa Bay Rays on Sunday night for former All-Star James Shields and fellow right-hander Wade Davis, making an aggressive move to bolster a rotation that was one of the worst in the major leagues last season.

“We have to start winning games at the major league level, and the way you develop a winning culture is by winning major league games,” Royals general manager Dayton Moore said. “It’s time for us to start winning at the major league level.”

Kansas City, which hasn’t had a winning season since 2003, has long had one of the best farm systems in baseball, and slowly the cream has risen to the big league level — first baseman Eric Hosmer, shortstop Alcides Escobar, third baseman Mike Moustakas and catcher Salvador Perez form a fine nucleus. But there’s been a dearth of starting pitching for years, and that’s what Moore and the rest of the front office have been trying to fix this offseason.