Quoted from sethbenjamin:
I agree that the most sure fire method to ensure the post stays put long term is to now swap it out for one that attaches with a nut from below. Even with a hardwood dowel, the hole is going to be weaker than it would otherwise have been. Granted it isn’t getting slammed in the line of fire (any post that is should *definitely* not be wood threaded, I change them over all the time from factory), but a through-bolted connection will put the worry to rest for good.
I’m a recovering cabinet maker; whenever you pre-drill (and you should always pre-drill), make sure that the bit is the diameter of the core of the screw. The threads should be cutting a path but the body of the screw should not be getting any resistance. When in doubt, test it on a piece of plywood or hardwood scrap. It should drive comfortably without excessive force and when it’s seated it should be very firmly in place.
Not trying to make anyone feel dumb, not at all, just passing along something I learned in the cabinetry realm, it’s never steered me wrong.
Here is a pilot hole chart:
I use somewhere between the hardwood and softwood sizes, sometimes, as I have numeric sizes bits, but its a good reference: