The Atlanta Braves selected Graham out of the University of Oregon in the 4th round in the 2015 draft. Graham was a catcher at Oregon until he couldn’t break through for a starting job and moved to the mound with some notable success for the Ducks.
With the Braves, he was assigned to advanced rookie Danville, where he made 6 appearances, 5 of them starts. He totaled 17 1/3 innings with a 2.60 ERA and 1.15 WHIP and a 3/21 BB/K ratio. That caught the eye of a number of prospect folks. John Sickels had Graham as the #20 prospect in the entire Braves system coming into the year based on good scouting reports that he received.