Generally speaking, a ballplayer is a person who participates in a ball sport - most often Basketball, baseball, or football.
MLB player Curtis Granderson throws right.
MLB player Adam LaRoche bats left.
MLB player Aaron Loup throws left.
MLB player Jose Ramirez can bat right or left (i.e. he is a switch hitter).
MLB player Brian McCann throws right.
MLB player Abraham Almonte throws right.
MLB player Bryan Holaday bats right.
MLB player Anthony Rizzo throws left.
MLB player Arquimedes Caminero bats right.
MLB player Brock Holt bats left.
MLB player Chris Archer throws right.
MLB player Corey Kluber throws right.