MLB Draft 2021: Yankees select Trey Sweeney 20th overall Share this story Photo by Mary DeCicco/MLB Photos via Getty Images The Yankees had the 20th overall pick in the 2021 MLB Draft, and the first round held more than its share of surprises as the selections began on Sunday night. Louisville catcher Henry Davis was a player who essentially no one had No. 1 overall, and yet that’s exactly where he went. Off went Jack Leiter to Texas, Marcelo Mayer to Boston (gulp), Kumar Rocker to the Mets, and a bevy of pitching options previously connected to New York (Gunnar Hoglund, Will Bednar, and Andrew Painter) to other teams.