Graveman attended Benjamin Russell High School, where he posted a 6–3 record with a 1.19 earned run average and 90 strikeouts over 63 innings in his senior year. In 2010, his first year at Mississippi State University, Graveman was used primarily as a reliever and finished the season with a 2–4 record and a 7.02 ERA. In 2011, he made 14 appearances (9 starts), compiling a 5–0 record and a 3.65 ERA. Graveman was drafted by the Miami Marlins in the 36th round of the 2012 Major League Baseball draft, but did not sign with the team. In his senior year at MSU, he made 16 starts, including all of the team\'s 10 starts against teams in the SEC, and posted a 4–4 record with a 2.81 ERA and 59 strikeouts.\n', '

Graveman was selected in the 8th round, 235th overall, by the Blue Jays in the 2013 Major League Baseball 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​2⁄3 innings in 2013.\n', '

He began the 2014 season with Lansing, but was promoted to the High-A Dunedin Blue Jays after making 4 starts for the Lugnuts and posting a 2–0 record with a 0.34 ERA, including a near no-hitter over the Beloit Snappers. In Dunedin, he compiled an 8–4 record in 16 starts, with a 2.23 ERA and 64 strikeouts. Graveman was promoted to the Double-A New Hampshire Fisher Cats and made just 1 start, a 6-inning win over the Binghamton Mets, before being promoted to the Triple-A Buffalo Bisons. In his Triple-A debut, he took the loss, pitching 6 innings in a 2–1 loss to the Norfolk Tides. Graveman would allow only 1 earned run in his following 3 starts, bringing his ERA to 1.04 through 26 innings with Buffalo. He finished the 2014 minor league season with a 14–6 record over 167​1⁄3 innings, with an ERA of 1.83, 115 strikeouts, and a WHIP of 1.03. He also gave up only 2 home runs and issued 31 walks, for a BB/9 of 1.7. On September 3, Graveman was named to Baseball America\'s First Team All-Stars for 2014.\n', '

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