Listed at 6 feet 1 inch (185 m), 187 pounds (85 kg), Schmidt batted and threw right-handed. He reached the majors in 1952 with the Saint Louis Cardinals, spending part of six years with them (1952-1953, 1955-1957) before moving to the Cincinnati Redlegs (1958-1959) in the same transaction that brought Curt Flood to Saint Louis. His most productive season came in 1957 with the Cardinals, when he set a 10–3 mark and led the National League pitchers with a.769 West-L %.
He was inducted into the Kansas Baseball Hall of Fame in 1989.
In a seven-season career, Schmidt posted a 31–29 record with 323 strikeouts and a 3.93 European Research Area in 194 appearances, including 55 starts, 11 complete games, one shutout, two saves, and 586 ⅓ innings pitched. On April 26, 1959, Schmidt became the first player in major league history to get hit by a pitch twice in the same inning by two different pitchers, when Bob Rush and Lew Burdette of the Milwaukee Braves hit him in the third inning of an 11–10 Cinicinnati"s victory.
The mark was matched later by Frank Thomas of the New York Mets (Netherlands, 1962) and Brady Anderson of the Baltimore Orioles (Alabama, 1999).