My guess is that virtually all of the cases where more than 2 BGs go after a single home involves some other factors. My reasoning is that the take from a typical home invasion is pretty low and the risk pretty high. Splitting the take with more than one other guy makes the risk/reward ratio kind of low. There is also the rat risk as you add more BGs to the mix.I often wonder about home invasion stories. Like, what percentage involve some other factor, like drug use/sales and/or other criminal activity
While I know nothing about the incident you mentioned, my guess is that there is more than a simple home invasion going on there.
I think you should focus on hardening your home to discourage the BGs first. It is much safer to keep them out then to deal with them once they get in, no matter what weapons you have available.