How frequently are Android apps in Google Play updated?
From my observations of ~10,000 apps listed at my real-life categorized app-listings, the average app...


requests ~7 permissions
costs USD 0.88
was last updated ~1.5 years (~17 month or 492 days) ago


The last item, a little more detailed:

┌───────────────────────────────────────┬────────┐
| last updated more than 2 years ago    | 24.51% |
| last updated 1..2 years ago           | 20.27% |
| last updated 6..12 month ago          | 17.84% |
| updated within the last 6 month       | 34.87% |
└───────────────────────────────────────┴────────┘


As you've correctly pointed out in your comment, that doesn't sum up to 100%. The difference are apps currently not listed in any of the markets I cater for (i.e. Google Play, F-Droid, Aptoide). As unlistings may be (and sometimes have been) temporary, I still keep those for a few month before removing them finally. Plus add a little "rounding blur" ;)

So I'm afraid I just spoiled your theory...

BTW: Though you didn't ask for: Top categories of "max permissions per app on average" is, after "personal assistants" (31.7 perms/app) cheaper calls (22.2 perms/app – shame to him who thinks evil of it ;)). Only then come apps to remote-control your device (where many permissions make much sense, considered you want to control as much as possible), and "Antivirus", with ~19 perms/app each.

(Statistics as per November 5, 2014)