  The competition for the attention of users is a central element of the
Internet. Crucial issues are the origin and predictability of big hits, the few
items that capture a big portion of the total attention. We address these
issues analyzing 10 million time series of videos' views from YouTube. We find
that the average gain of views is linearly proportional to the number of views
a video already has, in agreement with usual rich-get-richer mechanisms and
Gibrat's law, but this fails to explain the prevalence of big hits. The reason
is that the fluctuations around the average views are themselves heavy tailed.
Based on these empirical observations, we propose a stochastic differential
equation with L\'evy noise as a model of the dynamics of videos. We show how
this model is substantially better in estimating the probability of an ordinary
item becoming a big hit, which is considerably underestimated in the
traditional proportional-growth models.
