Find a good estimate for Tor versions run by clients

When trying to estimate the share of directory requests that any one of our directory mirrors sees, we need a good estimate for the Tor major versions run by clients. 0.2.0.x, 0.2.1.x, and 0.2.2.x all have different weights for picking directory mirrors.

One approach (and maybe the only one) is to assume that clients have the same major version distribution as relays and just use the relay numbers. Are there alternatives?