A 26th Round selection by the St. Louis Cardinals in the 2011 Major League Baseball Draft, Graves made 17 appearances, with 10 starts, posting a 4-5 record, 5.91 ERA and 28 strikeouts of 45.2 innings of work as a freshman at Missouri in 2012.
In high school, Graves helped to lead Francis Howell to a 2011 MSHSAA State Championship during his senior season in which he was named a First Team Louisville Slugger All-American and All-Metro Player of the Year in St. Louis after going 9-1 with a 1.95 ERA and 70 strikeouts. Graves was named the 2011 Missouri Gatorade Player of the Year after splitting time between the mound and shortstop and was also a three-time All-State selection. An All-Conference standout quarterback, Graves fielded many opportunities to pursue a collegiate football career.