When I look for information on mob spawning and mob grinders I find a lot of links to these two items:
The problem is, they seem to have contradictory information in them.
The first one espouses the much-credited idea that to improve your mob spawning area you must light up all the caves around it. This is built on the assumption that when the game goes to spawn a monster, it looks for an appropriate place to put one, so eliminating anywhere but your mob machine would increase the rate of mobs spawning within it.
The "Mob Spawning Science" post claims an algorithm that goes chunk by chunk, and within each chunk it picks a random block and sees if that block is a legit spawning location (standing on something, correct light level, etc.). If so, it puts a mob there. (I'm simplifying, but this is the idea.) This would imply that for any given block in a chunk, there is a 1/32768 chance of it being selected. So given a block X that is a nice, dark, mob-spawnable place, it has a 1/32768 chance each time the chunk is processed of spawning a monster regardless of any lit or unlit caves anywhere around it.
So which one is correct?
Best Answer
Technically, placing torches will decrease your overall mob spawns; the game does pick a single random point within the eligible chunks to spawn a monster, and if that point is not suitable, the monster doesn't spawn. Therefore filling other caves with torches will reduce the number of spawn-friendly points, reducing your overall monster count. This does technically help your mob grinder because you don't have mobs lurking in neighboring caves counting against the mob cap (and ultimately taking it all up, preventing anything from spawning in your grinder).
The best solution would probably be to use a vast water network to drag all the mobs from all nearby caves into your grinder, so you maximize spawn area, but bring any mobs from all the viable spawn points into a single area.