As already mentioned, my take on Tumbler's popularity was that it was primarily (hard to give an exact percentage) a function of their providing Dofollow links in their content sections.
My hypothesis on their slow transition to a site with nofollow rather than do follow, was, at the time, their avoiding a Google SERPS death penalty and therefore increasing the probability for a success public offering.
Well, they did not go the public offering route, instead opting to sell out to a public company, Yahoo.
The technical issue of the recently announced Yahoo purchase deals, again IMHO, in how many of Tumblr's email addresses that Yahoo can add to their roles as "sincere Yahoo users" rather than the strategic reason (i.e., dofollow links) underpinning Tumblr's success.
If, for example, 90% of Tumblr's traffic was for strategic reasons, i.e., getting dofollow backlinks, then it sounds reasonable to suggest that those same 90% of Tumblr's users have no need for the Yahoo version of Tumbler because there's nothing in it for them.
Without access to forensic analysis of Tumblr log data, it's hard to put a number on the sincere versus strategic users of Tumblr, and therefore its long term utility to Yahoo.
Home page temporarily offline. Please check the navigation menu for assistance.