Lansing Lugnuts
Graveman was selected in the 8th round, 235th overall, by the Blue Jays in the 2013 MLB draft. He received a signing bonus of $5,000, and was assigned to the Class-A Lansing Lugnuts. Graveman would pitch to a 1–3 record and a 4.31 earned run average over 39 innings in 2013.