Physics model predicts book sales

By Kimberly Patch, Technology Research News

When UCLA physics professor Didier Sornette looked at the way his 2003 book on stock market crashes sold, he saw something that needed further investigation.

A few days after Sornette gave an interview in mid-January 2003 to a high-diffusion Internet news network his book reached number five on Amazon, then quickly moved down the rankings, disappearing from the top 50 within a week.

Using the same statistical physics methods they used to study complex systems like earthquakes and financial markets, Sornette and his colleagues set out to explain the book-ranking behavior. They used the Epidemics-Type Aftershock Sequence model, which draws on statistical techniques for studying how diseases spread through populations in order to model earthquake aftershocks.

The model is very simple, said Thomas Gilbert, a University of California at Los Angeles researcher who is now at the University of California at Berkeley. "The idea is that information about a book travels through the network of potential buyers in two possible fashions: exogenous [and] endogenous."

Exogenous shocks come from sources outside the system they affect; endogenous shocks come from internal forces. An exogenous shock hits the entire system like a hammer, said Gilbert. It is like seeing a billboard while driving, or a New York Times article. "Everyone is influenced in the same fashion from an exogenous source," he said. This shock is big enough that it pushes the book to the bestsellers' list.

An endogenous shock is the sum of very small exogenous shocks that happen in a coordinated fashion, said Gilbert. For instance, "I find a book in the bookstore. I read and like it. I tell my family and my friends, of whom maybe half will buy it, and then they'll spread the word, and so on," he said. "It reaches the bestsellers' list in a slow fashion, through word-of-mouth."

The model predicts how sales will decline after they peak according to how the peak occurred. The method could be used to predict book sales in order to better coordinate printing, and to time the market, said Gilbert.

The decline after an exogenous shock is fairly steep, while the decay after an endogenous shock is more gradual. Exogenous shock decline is quick "because the information has not really penetrated the network, since it was only transmitted as a huge hit on the system," said Gilbert. Endogenous shock decline is slow "since the information has penetrated the network much more: people talking to people is a much more credible information transfer then just billboards and adverts," he said.

The researchers collected data on real books in order to confirm the theory. One of the researchers wrote a program that automatically logged onto the Web site to collect book rankings. They also used data from a researcher who had been collecting this type of data over a longer period of time. Between the two sources they were able to glean the rankings of thousands of books over a two-year period.

They identified 138 bestsellers from this list, then sorted the growth patterns into an exogenous class that showed very fast growth over less than four days, and an endogenous class that showed slower growth. They measured the slopes of the book sales declines after the sales peaks of the bestsellers.

When they used the model to predict sales of the 138 books, the predictions matched the way the book had actually sold 84 percent of the time." For something that may seem as random and unpredictable as book sales, we find that a simple generic model can give a very good prediction as to how customers will behave," said Gilbert.

The power-law pattern the book sales exhibited is common in the natural sciences, including the study of earthquakes, and has been more recently shown in financial markets, said Gilbert. Power-law patterns plot as straight lines on a log-scale graph were each successive scale number is 10 times the one before. "It seems to be a general type of pattern," he said. "We have shown that it even appears in simple customer behavior."

There are books that fall between the two classes as well. "The perfect example is the classic series Lord of the Rings," said Gilbert. Movies based on the book came out at Christmas 2001, 2002 and 2003. Peaks in the sales of the books occurred around those periods, but it is not clear whether those peaks were exogenous or endogenous, he said. "People expected the movies to come out, and everyone was talking about how good they were going to be -- sounds endogenous -- but the movies did come out and did hit everyone in the face -- sounds exogenous." In these cases it's difficult to tell which type of growth is occurring in order to predict sales.

Book publishing houses and marketing firms could use the method to precisely quantify how books will sell post-peak as a function of how the peak occurred, said Gilbert. "One can measure the total sales very precisely, since it is just the area under the curves" of the graph showing the peak, he said.

It could also be used to time the market, said Gilbert. "[Publishers] need to figure out exactly when the network will be ready for a new advertising campaign... and they want to know how much to print for the next months," he said. "Our method can tell them just that."

The idea of exogenous and endogenous shocks can be applied to a variety of other events, said Gilbert. Epidemics can be modeled, and also events like 9/11, he said. "Did 9/11 cause the airline industry to go down the tubes -- exogenous shock -- or were there beforehand some structural problems that lead to all the recent bankruptcies -- endogenous crash."

Using the method to study complex non-physical systems like markets could, in turn, help scientists understand complex physical systems like living beings, whose divisions between exogenous and endogenous shocks are difficult to distinguish, according to Gilbert.

The method could be used in practical applications within six months to a year, said Gilbert.

Gilbert's research colleagues were Didier Sornette, A. Helmstetter and Y. Ageon. The work appeared in the November 26, 2004 issue of Physical Review Letters. The research was funded by the James S. McDonnel 21st Century Science Award.

Timeline:  > 1 year
Funding:   Private
TRN Categories:   Physics
Story Type:   News
Related Elements:  Technical paper, "Endogenous Versus Exogenous Shocks in Complex Networks: An Empirical Test Using Book Sale Rankings," Physical Review Letters, November 26, 2004


December 15/22, 2004

Page One

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Physics model predicts book sales

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