As far as I know the only reason for using a pilot drill is to remove the material that would otherwise have to be squished away by the web of a large drill going in without a pilot. So your pilot drill diameter should be a bit larger than the distance across the web on the large drill.
But you also have to consider that for a deep hole it may be necessary to use a larger pilot drill simply because the depth to diameter ratio is too large for a small one.
However, if you use a drill with a split point grind a pilot hole is not really necessary.
Althoug I suppose if you are looking at a 3" drill maybe it is.