Lyly Overbay would have a solid Major League career where over fourteen seasons he would amass 1,355 Hits.  He would lead the National League in doubles in 2004.  With a sub 20 bWAR he might struggle though to make the Hall of Fame ballot.

Predominantly used as a middle reliever, Kyle Farnsworth, would parlay his skills into a sixteen year career in Baseball.

Josh Beckett would have a very good career in the Majors where he would win the World Series twice, and was a three time All Star.  Those two World Series wins have to be mentioned in high regard as the pitcher woud be named the World Series MVP in 2003 and the ALCS MVP in 2007.  Beckett had a vast arsenal of pitches and the starter was the American League Cy Young runner up in 2007.

Three times Jose Valverde would lead the league in Saves and did so for three different teams.  Valverde proved to be an effective closer for many years and he did come close to 300 Saves, however his overall stats do not put him in the Hall of Fame range and his very poor playoff performances could keep him off of the ballot.