Published: 17.11.08
Mathematical model

YouTube usage decoded

Why are certain videos on YouTube watched millions of times while 90 percent of the contributions find only the odd viewer? A new study reveals that increased attention in social systems like the YouTube community follows particular, recurrent patterns that can be represented using mathematical models.

Samuel Schläfli

The Internet platform YouTube is a stomping ground for scientists looking to investigate the fine mechanism of the attention spiral in social systems. How is it possible, for example, that one YouTube video of a previously unknown comedian from Ohio can be viewed over ten million times in the space of two weeks and 103 million times during its total two-year running time? The video was aired on the most popular television networks in America and the comedian Judson Laipply has meanwhile become a YouTube star. Social scientists, economists, mathematicians and even physicists are fascinated by this “herding”, as the herdlike behavior in social networks is often termed, on YouTube.

Epidemic-like diffusion

Until two years ago, Riley Crane had been researching supraconductors at the University of California. More specifically, he was examining critical phenomena in quantum systems where, under the right conditions, minor interference can change the whole system. Similar phenomena can also be observed in social systems. This is what Crane now focuses on as a postdoctoral fellow at ETH Zurich’s Chair of Entrepreneurial Risks in the Department of Management, Technology and Economy (D-MTEC). In the latest edition of the scientific publication PNAS, he and his Professor Didier Sornette describe how the “herding” of YouTube users can be represented in simple mathematical models. Crane tracked viewer statistics for five million videos on YouTube for two years with the aid of systems he had programmed himself. In doing so, he was primarily interested in the films that had attracted the most attention, meaning the ones that had been viewed at least 100 times a day. Only 10 percent fell into this category.

Crane then subdivided these into three sub- categories: The first is “junk” videos, which generate a lot of attention unexpectedly, albeit only for a short period of time and which are of no interest as they do not trigger a self-organized development, a “herd instinct”, within the YouTube community; the second category, “viral” videos, is a different story. These videos spread across expansive social networks in an epidemic-like fashion, for example through recommendations via email, blogs and Internet links. In the PNAS publication, Crane cites a trailer for a Harry Potter film that enjoyed an enormous amount of attention through word-of-mouth advertising on the Internet alone as a prime example of this. The third category of videos, the “quality” videos, is not unlike the viral video group. Instead of a gradual rise to popularity, however, they cause a sudden burst of attention on account of their “quality”, their popularity spreading rapidly before gradually ebbing away. The videos of the tsunami in Southeast Asia in 2004 are prime examples of such videos.

Social processes according to physical laws

Crane compared the viewer statistics for “quality” and “viral” videos at the height of their public attention to the total number of viewers over the period of observation. “We illustrated the figures in diagrams and discovered that the graphs for the increase and decrease in viewers had a very characteristic form for both kinds of videos. The capacity of a video to become a mass phenomenon within the YouTube community can therefore be ascertained from the shape of the graph,” explains Crane. For example, he discovered that the fading of attention for viral videos can be described with the mathematics used to model aftershocks in earthquakes, so-called “Epidemic Type Aftershock” models. “I find it fascinating that a social system ostensibly works according to particular rules, just like a physical system, and therefore becomes mathematically comprehensible,” says Crane describing his interest in “sociophysics”. He used deterministic power laws to mathematically reproduce the phenomena observed on YouTube. These are scale-independent, meaning that the function’s basic properties also remain unchanged despite changes to the scale. His model can therefore be used singly to recognize developments that could lead to a mass phenomenon using tendencies in the system – in the case of YouTube, an increase in viewers for a particular video. And all this even before the development has been realized by a critical mass of individuals.

Recognizing potential “blockbusters” early

Crane’s results are especially interesting for marketing purposes. His model could be used, for example, to monitor online book sales in real time. By constantly comparing data, marketing experts could recognize which book has the makings of a blockbuster early on based on the sales graph. The critical point, the so-called “tipping point”, where a viral effect begins and a book’s potential actually leads to a blockbuster, could therefore be consciously provoked with the necessary marketing measures.

In actual fact, Crane and Didier Sornette, Professor of Entrepreneurial Risks in the Department of Management, Technology and Economics, are currently in negotiation with the Internet book seller “Amazon” to integrate their own system in the Internet platform. As the next step, the two scientists are looking to couple their model with existing mathematical ones from the field of epidemiology and thus hone and expand its significance. In the medium term, the two scientists have a kind of trend-monitoring center for the Internet in mind. This would enable phenomena in social systems on different web platforms to be recognized early. “Naturally, we would also eventually like to be able to explain why certain products make the tipping point in social systems whilst others do not. This is still a long way off, however,” admits Crane.


Crane R, Sornette D, Robust dynamic classes revealed by studying the response function of a social system, Proceedings of the National Academy of Sciences, Vol. 105, No. 41. (October 2008), pp. 15649-15653.

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