martes, 17 de mayo de 2011

Estimating Facebook Number of Users with Binary Search

I get tired of marketing people saying "Facebook has 500 million users", "FB has 1 billion users". So I made I little experiment on the estimation of Facebook exact number of users. The results was 1,051,785,857 users! That is a little over 1 Billion users! The result is not surprising if you read that Facebook founder said one year ago that the wanted to reach that number and they receive about 700 thousand new users per day.

Now I detail the details, further work can be done by anyone to make the estimation accurate on any time.

Facebook users are identified by a USERID like 1340269186 or 100011808654570. Apparently the are two possibilities for users ids:
  1. The id is not available, for example user id 666666. In spanish, this is the resultSo the range of available ids can be tracked manually or with a script using binary search. These are the results excepting for some Facebook employees that have ids below 10000. Ranges: [500090001..1777798795] + [100000000000004..100002390891367]. Longer user ids starting with 10000 are the newer ones after reaching 1777798795 (you have to update this number to make the estimation dynamic). If Facebook includes 700 thousand new user per day we expect this number to increase accordingly. The number of aprox. available ids is 3,668,600,157.
  2. Now not all user ids are in-use. Some ids belong in the past to users who closed their accounts. I suspect also that Facebook leaves available id unused for internal debugging and administrative processes. In either case the distribution of used ids inside the ranges we described in 1) is apparently random. So we have to estimate the distribution density assuming a uniform distribution of used ids. This is how unused id look like, like id (spanish locale) 1340269187 The density was 0.286700 used ids per each unused id. The script uses 1000 samples but you can test a bigger batch if you are not confident of the results.
Update!: I found this paper published this year...
[PDF] Estimating Sizes of Social Networks via Biased SamplingFile Format: PDF/Adobe Acrobat - Quick View
by L Katzir - Cited by 1 - Related articles 1 Apr 2011 ... years and their number of users is already measured in many ...... 1, 000, 000 Facebook users and tried to estimate the size of ...