Born in Cleveland, Mississippi, Hancock graduated from Vestavia Hills High School in Vestavia Hills, Alabama. After high school, he was selected in the fourth round of the 1996 Major League Baseball draft by the Milwaukee Brewers, but did not sign. An Alabama fan, Hancock instead attended college at Auburn University in Auburn, Alabama, because the Tigers offered him a better scholarship. Hancock was selected by the Boston Red Sox in the fifth round (155th overall) of the 1998 amateur draft and signed with the Red Sox, making his major-league debut on September 10, 2002. In December 2002 Hancock was traded to the Philadelphia Phillies for Jeremy Giambi. On July 30, 2004, he was traded along with Andy Machado to the Cincinnati Reds for Todd Jones and Brad Correll. The next day, Hancock was the winning pitcher for the Reds in a game against the Houston Astros (a suspended game that began the day before while he was still with the Phillies).
