> As an example, imagine that you are a moderator on a forum and you suspect that a new face is actually a sockpuppet of a user you banned the day prior. You check the IP logs, and despite using different Mullvad servers, both accounts resolve to the overlapping float ranges 0.4334 - 0.4428 and 0.4358 - 0.4423. This gives you a >99% chance that they are the same person.

I don't see how the author is arriving at this ">99% chance" purely from the numbers provided in the article. Assuming the first (banned IP) seed and the second seed are both in the range 0.4423 - 0.4358 (a stronger assumption than is justified by the example), all this tells us is that the first and second IP addresses both have seeds in a range that would contain 0.4423 - 0.4358 = 0.65% of all Mullvad users, which 0.0065 * 100,000 = 650 users. We've eliminated >99% of users as "suspects", but we haven't actually gotten >99% accuracy in identifying an individual across multiple exit IPs.

In more Bayesian thinking, the overlap in potential seeds is great evidence to think these IP addresses represent one and the same person (or Mullvad VPN account at least), but as far as I can tell, that's not what the author is saying.

Say your forum is a big one and has 1000 active users, with 1 joining every day. Most will be a lot smaller/less active.

What are the chances that someone uses this vpn, joins your forum the day after someone was banned, and has an ip in a similar range?

For most small websites this would be strong evidence.