I assume "batter board" is another term for "Batters Eye" in
center field. If not then this answer will not apply to your
question.
The Batters Eye is for the batter to have a "backdrop" that will
allow him to see the baseball come from the pitchers hand.
Generally these are green or black because they allow the white
ball to be seen easily. If you are in the outfield on a line drive
hit to you, then you might appreciate having this as when you are
at bat. A white ball being thrown at you 80-90mph that you cant see
because someone in the center field bleachers is wearing a white
shirt right where the release point is for the pitcher would not be
a good thing.