It doesn't pick up random IP addresses. If you post from your phone, your IP address is constantly changing. If you post from a friends house, different IP, if you post on your laptop at the airport, different IP address. If you unplug your modem and replug it in, different IP. Keep in mind too, that everyone in your house behind your router has the same IP, most people in your office have the same IP, a bunch of people in a school library behind the internet connection have the same IP.
Blocking a user by IP is pretty useless because it's extremely easy to get a new IP address, either by resetting your router or going through a proxy (basically someone else sends all their internet traffic through my computer so it looks like it's coming from my IP and not theirs).
It's very unlikely that you would have the same IP for more than a few months at a time. It's entirely possible that I could have the same IP address you had two years ago, but it's VERY unlikely considering how many IP addresses there are. Though SheCheers is right too that there are more internet connections than there are IP addresses.