The same way you know how many times a show was watched legitimately, you take a sample of known data and extrapolate it from there. It's basically guesswork but it's educated guesswork.

BitTorrent, even though it's decentralised, is still operating on the public internet using public, known protocols. You can join a swarm and get an idea of how big that swarm is with a small amount of data inspection. I mean, your torrent client knows how many seeders and leechers there are, right? Just watch the swarms and extrapolate from there.

Any time you read these articles, they're always caveated with something similar to "The number could be much higher than that" too because it's not just torrents, you've got newsgroups, file shares, streaming sites, even old school IRC, people putting titles on a USB stick and so on. Hence there's a lot of guessing, but it's not entirely plucked from thin air.

Where it does get more bullshitty is when they try to translate those numbers into lost sales. That is just made up numbers as far as I'm concerned.

That may be the point, but it doesn't mean its true. I doubt even half of the "pirates" who download shows and movies ever take the kind of precautions you'd need to to be untrackable.