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.

Joe Saunders never made 100 Wins.  He never threw 1,000 Strikeouts.  He did not make a double digit bWAR.  He will not make the ballot.

While Jason Giambi is better known for being an inflated PED user, the fact remains that he was a very good hitter who was a former American League MVP.  Giambi would go to five consecutive All-Star Games, blasted 440 Home Runs with a .516 career Slugging Percentage over a twenty-year career.  He would also show solid plate discipline with three On Base Percentage Titles and retired with a very good 50.4 bWAR.