Actually, you block the FQDN (fully qualified domain name), which is a combination of your modem's MAC address and the NIC or router's MAC address. This way it does not matter if the IP changes. It is not hard to block a specific modem this way. Do a reverse lookup on your IP to get you FQDN. (nslookup xxx.xxx.xxx.xxx)If you block the account, the guy just goes and opens a new account and he's back in business.
The thought is to block the guy from using the board period and assuming he's doing so from home, you block the IP address, you pretty much block the guy unless he wants to change IP, or go to the library.
There's really no fool proof way.
Many times admins will use use wildcards in the blocked address and innocent users can then get blocked just by having a similar IP to the banned one.