It varies from ISP to ISP and point in time. Back when dial-up was the norm
everybody got a new IP every time they connected and disconnected. With
faster cable and ADSL connections it's less likely you'll be disconnected at
all. You IP address can stay with you for months at a time in many cases.
Even when a connection is temporarily disconnected it may re-issue the same
IP address. I believe with my ISP in order to get a new IP address you have
to either change the mac address or disconnect for about 20 minutes. You
might also be able to issue a DHCP release command (at least if your
connected directly, but in practice almost nobody is, most people are
connecting through a router of some kind).
In any event none of this really matters. ISPs (and possibly or likely the
NSA as well) generally have at least one persons name and address for the
persons whose paying the bill and by that virtue they have logs that are kept
which can be used later on- after ones IP has changed. They use this data to
associate the subscribers billing with the IP address at a given time.
Obviously there are situations where an ISP may not have this information
(anybody providing free wifi for example), but it's none-the-less useful to
track the majority of users within a degree. And generally sufficient with
further investigation to identify the person (to the extent its recognized by
law).
Unfortunately the courts in the United States seem to be OK with the fact a
person is not actually identified by an IP address. The reasoning is that
because it is likely that the person in question is someone within a
household that is sufficient evidence to get a warrant and terrorize the
innocent within.
What amazes me is that without being able to identify an individual within a
household it means that the warrant issued is going to be for a residence and
not a specific place within (ie they can search any persons
room/computers/etc within the house as opposed to being limited to a
particular person and place, like a persons room or computers). If you think
about that for a minute this is really scary. Any number of people might have
been the reason for the search warrant. Many people have adult (or minor
children) children living with them, flat mates, partners, etc. Based on this
logic it could even a neighbour. They will be getting a warrant to search
everybody until they find what they were looking for (or not). Yes- because
your neighbour did something illegal the cops can actually search your house
based on the reasoning your within distance of the wifi hotspot. And at the
end of the day it might have been any of these people. Somebody might have
been running a Tor exit node, had a friend/visitor over, or had a compromised
machine. At least 90% of systems are infected with malware.
