Mobs spawn naturally within a square group of chunks centered on the player, 15×15 chunks (240×240 blocks). When there are multiple players, mobs can spawn within the given distance of any of them. However, hostile mobs (and some others) that move farther than 128 blocks from the nearest player will instantly despawn, so the mob spawning area is more-or-less limited to spheres with a radius of 128 blocks, centered at each player. In multiplayer, mob caps are shared by all players, no matter where they are.
-- Minecraft Wiki
So, if I core out a 240-block radius around my farm, will that prevent the game from doing spawn attempts at all outside the farm, thus causing 100% of all spawn attempts to be applied to the farm's platform? Also, does it try to spawn in lit caves, or are lit solid blocks equivalent to air?