Power Laws Describe the \"Power

Power Laws

Describe the "power law" - what does it imply for sales of a) "superstars" and b) "underdogs."

The Power Law specifically refers to the behavior of specific natural, financial, and operational attributes or variables to distribute themselves inversely to the power of the value being measured. This results in disproportionately high level of activity on a few select variables in the analysis, generating a long, thin tailed distribution of the other variables throughout the overall distribution of the population or sample of interest. The Power Law is often referred to as being comparable to Zipf's Law or Pareto distribution, where the 80/20 Law is typically referenced. The Power Law is more precise in its effects, and has been prevalently found in biology, sociology, psychology, economics, linguistics, geography, and physics. Given the prevalence of the Power Law throughout all these areas, scientists are beginning to look for links between each of these disciplines at the network level. Power Laws are in marked opposition to Poisson distributions which are the well-documented in statistical research. The essentials of Power Laws are shown in Figure 1. Figure 1: Essentials of Power Laws

The Power Law's implications for superstars and underdogs are quite different, and in the research completed by Elberse and Oberholzer-Gee (2006), the galvanizing effect of superstars is statistically significant and differentiates these few, high-selling products from the majority of other products that have sporadic and light order rates over time. The work from these two authors in comparing DVD and VHS sales shows what intuitively what would be expected: more recent titles with "theatrical" in the title and abiding by the Motion Picture of America rating system do better than X-rated or unrated videos where the customer has fewer cues to trust the DVD or not. For superstar products over time, these cues become stronger and according to Newman (2005) in his excellent article Power laws, Pareto distributions and Zipf's law, shows conclusively the behavior of Power Laws relative to Zipf's Law and Pareto Analysis. Power Laws become illustrated over time in online sales, regardless of the use of up-selling, cross-selling and online catalog management or web-based navigational tools, as superstar products have more of a community of customers who seek them out than those cross-sold or up-sold from them, according to Elberse and Oberholzer-Gee (2006).

Contrary to these finding, those "underdog" products typically struggle to gain any market traction and despite the ubiquity of the Internet and the argument that cross-sell, up-sell, and online merchandising strategies can increase sales of the products that comprise the "long tail" of a product sales distribution, this in fact hasn't been the case. The implications for underdog products is much more aligned with Pareto's Analysis that 80% of revenues are typically generated from 20% of the products, and even with global distribution made possible with the Internet, there still exists a significant challenge to companies looking to move their underdog products to superstar status.

What precise reasons do the authors' offer for video CD sales to be distributed according to power law? Which of those reasons can be argued to arise from ecommerce?

Elberse and Oberholzer-Gee (2006) state that DVD sales are distributed according to the Power Law due to the following factors emanating from the broader, non-online aspects of the product's sales strategy:

Length of DVD and VHS product lifecycles as measured in months since initial release to distribution on the Web.

Distribution costs through brick-and-mortar stores, which translates into a smaller overall selection in retail stores. This cost factor forces a right-shifted distribution of sales as retailers must focus only on the highest selling DVDs.

Higher search costs in the brick-and-mortar sales channel vs. online.

Higher probability of a customer purchasing a searched for product when they have sought information through multiple channels. The impact of multi-channel retailing on the selection and purchasing process is significant.

Arising from the use of e-commerce strategies for selling DVDs and VHS entertainment, the following factors emerge:

According to Columbus (2001) there is a statistically significant relationship between the successful use of guided selling and online search strategies with the price elasticity and long-tail attributes of any given product. Guided selling has become the strategy of choice for competing cost effectively when a product becomes part of the long tail of its given market.

The lower search costs also inherent in using the online stores as a distribution channel make it economically possible for online retailers to virtually stock a given DVD, despite its sales level. The crux of this challenge however is the distribution and fulfillment system, an area Amazon.com for example had streamlined for low-quantity orders before ever launching their website and online store. This equates to what Elberse and Oberholzer-Gee (2006) mention as the ability of online retailers to in effect feed the creation of long-tail markets by representing thousands of products online and fulfilling them through synchronized order management and supply chain systems.

According to Newman (2005) the network centricity of the Power Law is a contributing factor to its efficiency. From the standpoint of online retailers, this network effect is illustrated by the level of supply chain integration, synchronization, and the use of real-time shared data to create stronger hub-like efficiencies within a Power Law-dominated industry. One assumption and area of future research is in the definition of velocities of information throughout a Power Law network. Figure 2 shows a graphical representation of a Power Law-dominated network, and the hubs have definite velocities of information associated with them.

Finding these velocities and their effects to force a market into a long-tail dynamic is worth a primary research effort.

Figure 2: A Graphical Representation of a Power Law-based Network

In a table, list the hypotheses in one column and the method used to test the hypotheses in the second column.

Long-tail market characteristics emerge year-over-year based on sales mix of products

Inter-Quartile and Kolmogorov-Smirnov Statistics

Selling results of each quartile of DVD sales; also the hypothesis that DVDs would move across quartiles over time, filling out the long tail distribution of the market

Qauntile Regression

Measuring the best-sellers vs. those titles that comprise the long tail

Negative Binomial Regression Model.

Hypothetical) Suppose a student wants to test to see if power law pattern holds for books purchased online. Discuss a) his research question, b) data collection and b) model he should test in order to conduct such research.

To test if the Power Law exists for books purchased online, the following research questions and hypotheses would be used:

Research questions and hypotheses

Research questions:

Quantify the influence of the hub-based structure to Power Law networks and define the relative level of information velocity necessary to attain the Long Tail in product sales over time.

What are the implications of search costs being nearly zero on the price elasticity of the good being searched for? This has implications for forecasting the impact of pursuing a long-tail strategy within online retailing.