The Analytical badge is retired, presumably because it is no longer possible to obtain it. If this is not the case, please let me know. If it is the case, shouldn't the Precognitive and Beta badges be retired as well?
From this MSO post:
The Precognitive badge appears in the badge list on every site to announce the presence of Area 51, and its primary function.
Since Area 51 is itself about creating new sites that don't exist yet, the thought process is supposed to be:
hmm, I can't get [the precognitive badge] on this site, but I could get it on some hypothetical future site I might be interested in.
Yes! Thus, based on seeing this badge and reading about it, a user is incentivized to:
- visit Area 51 (and we provide a handy link in the badge description itself) -- win
- look at upcoming site proposals -- win
- follow likely proposals, which requires reading them and deciding if they have a chance -- win.
So in conclusion it seems that Stack Exchange knows these badges (or at least Precognitive) aren't possible on this site, but still thinks their presence on the Badges page is a net positive. I'm not sure I agree, but in any case this isn't likely to get changed.