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And how do they actually measure those numbers without (i) guessing; (ii) having some JS on the page, or (iii) using Voodoo Black Magic.

I think it's ridiculous to believe ANY company that claims that they can measure traffic of a site accurately without the DIRECT INVOLVEMENT of the site's owners. How are they doing it? Through the ether? Come on! Data, people. Data. Google's figured that out, maybe other companies should too.

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They get clickstream data from the big ISPs. In theory, if the samples are large enough and their models are appropriately calibrated, this ought to be a reasonable way to do it.

Wild guess: maybe they look at the increase in IP ids? On a lot of TCP/IP stacks they are not randomized, and can be measured from the outside by simply looking at 2 successive datagrams from the server. So, make up a reasonable estimation of how many IP datagrams are sent in an average visit. Make sure to do the same thing on all frontend servers. Congratulations, you now have a reasonably credible bullshit number to chart.

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