For other uses, consider the vastly less interesting general concept at Long tail (disambiguation).

• For the term specifically used in the realm of statistics, which is a far more precise and less prone-to-marketing-hype definition, one should consult Heavy-tailed distribution.

An illustrative depiction of a power law graph, showcasing the typical distribution of popularity rankings. The expansive, less populated region to the right, often highlighted in yellow, represents what has become known as the "long tail." Conversely, the concentrated area to the left, frequently delineated in green, signifies the dominant few – the "hits" or blockbusters that command significant attention and sales. Recommender systems are, predictably, deeply intertwined with this concept, attempting to navigate the vastness of choice. Concepts

• The rather optimistic belief in Collective intelligence

• The elusive quality of Relevance

• The often-misleading simplicity of Star ratings

• The subject at hand: Long tail

Methods and challenges, because nothing is ever simple:

• The inevitable hurdle of Cold start scenarios

• The often-imperfect art of Collaborative filtering

• The mathematical contortions of Dimensionality reduction

• The subtle art of Implicit data collection

• The specific mechanics of Item-item collaborative filtering

• The linear algebra gymnastics of Matrix factorization

• The attempt to quantify the unquantifiable via Preference elicitation

• The quest for the similar through Similarity search

Implementations, where theory meets the messy reality of application:

• The often-overlooked Collaborative search engine

• The pervasive Content discovery platform

• The structured assistance of a Decision support system

• The rather specific Music Genome Project

• The navigational aid known as a Product finder

Research, for those who insist on understanding things:

• The dedicated efforts of GroupLens Research

• The data haven that is MovieLens

• The now-iconic competition known as the Netflix Prize

• The annual gathering of minds at the ACM Conference on Recommender Systems

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• v • t • e

In the somewhat intertwined realms of statistics and business, the concept of a "long tail" refers to a characteristic feature observed in certain distributions of numerical data. Specifically, it denotes the extended, tapering portion of such a distribution where numerous occurrences are found far removed from the central, most frequently observed values—the "head" or main body. These distributions can represent a myriad of phenomena, from the popularity of various cultural products to the random incidence of events with diverse probabilities. It’s a term that, regrettably, is frequently employed with a certain degree of casualness, often lacking a precise, universally agreed-upon definition, or relying on an entirely arbitrary one. However, for those who prefer clarity over marketing jargon, rigorous statistical definitions are indeed available.

Within the discipline of statistics itself, the phrase "long-tailed distribution" carries a much narrower and more technical connotation. It is, in fact, a specific subclass of what statisticians more broadly categorize as a heavy-tailed distribution. To grasp this concept intuitively, consider a distribution to be (right) long-tailed if, regardless of any fixed threshold you might set, when a measured quantity surpasses a high level, it possesses an almost certain propensity to exceed that high level by at least the specified fixed amount. In simpler, if slightly unsettling, terms: if something is large, it’s probably even larger. It’s crucial to note here that in pure statistical discourse, one typically refers to the property of a distribution being long-tailed, rather than speaking of "the long tail" as a distinct, isolatable segment of a distribution. The distinction is subtle but significant, much like the difference between being perpetually unimpressed and merely being temporarily bored.

In the sphere of business, the term "long tail" is typically applied to rank-size distributions or rank-frequency distributions, particularly those charting the popularity of goods or services. These distributions frequently conform to power laws, which, by their very nature, are long-tailed distributions in the statistical sense. The business application primarily describes a specific retailing strategy: the practice of offering and selling a vast multitude of unique items, each of which sells in relatively minuscule quantities—this collective multitude forms the "long tail." This approach usually complements, rather than replaces, the traditional model of selling a smaller number of highly popular items in massive quantities, which constitutes the "head" of the distribution. Occasionally, an intermediate category is also acknowledged, given various evocative names such as the body, belly, torso, or middle. The precise point at which a distribution transitions from the "head" to the "long tail" is often subjective and arbitrarily chosen, though in certain analytical contexts, an objective specification can be achieved through methods like segmentation of rank-size distributions.

The concept of the long tail, once popularized, has proven to be remarkably adaptable, finding fertile ground for application, intensive research, and practical experimentation across a diverse array of fields. It has become a standard term in the lexicon of online business, significantly influencing strategies in mass media, and even making inroads into the realm of micro-finance—with institutions like the venerable Grameen Bank serving as a notable example. Its principles resonate with theories of user-driven innovation, championed by figures like Eric von Hippel, and inform various mechanisms of knowledge management and social networks, including collaborative models such as crowdsourcing, the more directed approach of crowdcasting, and decentralized peer-to-peer structures. Furthermore, the long tail has implications for modern economic models, innovative marketing techniques (such as viral marketing), and even the rather niche, but increasingly critical, domain of IT Security threat hunting within a Security Operations Center (SOC), where anomalies often reside in the infrequent, long-tailed occurrences.

History

The observation and study of frequency distributions characterized by these extended, tapering tails are by no means a recent development. Statisticians have been meticulously analyzing such phenomena since at least 1946, with foundational work appearing in academic journals. The term itself has also circulated within the more practical, if less glamorous, sectors of finance and the insurance business for many years prior to its mainstream popularization. Indeed, the groundbreaking work of the polymath Benoît Mandelbrot, commencing in the 1950s, was so profoundly impactful in demonstrating the prevalence and significance of these distributions that he is often, and quite rightly, referred to as "the father of long tails." His contributions laid much of the theoretical groundwork for understanding power laws and fractal geometry, which are inherently tied to long-tailed phenomena.

However, the term "long tail" truly exploded into popular consciousness and business discourse through the efforts of Chris Anderson. His influential October 2004 article in Wired magazine served as the catalyst, catapulting the concept into the mainstream. In this seminal piece, Anderson cited prominent internet-era entities such as Amazon.com, Apple, and Yahoo! as prime examples of businesses that had successfully leveraged and applied this burgeoning strategy. Anderson subsequently expanded upon and meticulously detailed the concept in his widely acclaimed book, The Long Tail: Why the Future of Business Is Selling Less of More, which further solidified its place in modern business theory.

Anderson's work, while popularizing the concept, was built upon earlier, rigorous academic investigations. He notably acknowledges research published in 2003 by a trio of scholars: Erik Brynjolfsson, Yu (Jeffrey) Hu, and Michael D. Smith. These researchers were among the first to systematically employ a log-linear curve plotted on an XY graph to visually and quantitatively articulate the intricate relationship between Amazon.com's sales figures and the corresponding sales ranking of its products. Their pivotal findings demonstrated that a substantial portion of the internet's inherent value to consumers did not merely stem from offering lower prices, but more significantly, from unlocking new reservoirs of value by providing unprecedented access to a vast array of products previously relegated to the long tail of obscurity.

Business

The core premise of businesses that successfully implement a long tail strategy hinges on their ability to drastically reduce or even eliminate the distribution and inventory costs associated with offering a wide selection of goods. This economic advantage allows them to derive significant profit from the aggregate sales of a vast number of hard-to-find, niche items, each selling in relatively small individual quantities. This contrasts sharply with the traditional model, which focuses solely on generating large sales volumes from a limited number of popular, high-demand products—the "head" of the distribution. The cumulative sales generated by this expansive collection of "non-hit items" is precisely what is referred to as "the long tail" in a commercial context.

Under conditions where consumers are presented with an adequately diverse array of choices, where there exists a sufficiently large population of potential customers, and critically, where the costs associated with stocking and distributing individual products are negligible, the collective selection and purchasing patterns of that population invariably lead to a demand curve across products that adheres to a power law distribution or a Pareto distribution. These are, by their very nature, long-tailed distributions.

It is absolutely crucial to distinguish why certain distributions tend towards the familiar bell-shaped curve of a normal distribution, while others exhibit the skewed, extended form of a long tail (or power) distribution. Chris Anderson astutely argues that while inherent biological or cognitive attributes such as human height or IQ typically conform to a normal distribution, phenomena within scale-free networks that exhibit preferential attachments are predisposed to generate power law distributions. This occurs because, in such networks, some nodes (or items, or individuals) naturally accumulate more connections or attention than others, creating a disproportionate hierarchy. One might, with a touch of cynicism, recall Malcolm Gladwell's "mavens" from his book The Tipping Point—individuals who, through their innate knowledge and influence, contribute to this uneven distribution of popularity and attention. The implication is that the underlying structure of interaction, rather than inherent quality alone, dictates whether a phenomenon will follow a "normal" or a "long tail" pattern.

Statistical meaning

The tail, as depicted in various models, demonstrably becomes both larger and more elongated in the context of new, digitally-enabled markets. Consider a timeline progressing from left to right: traditional brick-and-mortar retailers historically concentrated their efforts and inventory on the concentrated "head" area to the left of the chart. In stark contrast, online businesses, particularly digital bookstores, have discovered that a substantial and increasingly significant portion of their sales and revenue originates from the extended, less populated area to the right—the very essence of the long tail.

The long tail is not a novel invention; rather, it's a descriptive label for a well-established characteristic of certain statistical distributions that have been known for a considerable time. These include distributions such as Zipf's law, various power laws, Pareto distributions, and the more generalized Lévy skew alpha-stable distribution. In such "long-tailed" distributions, a segment characterized by high-frequency or high-amplitude occurrences is invariably followed by a much larger segment composed of low-frequency or low-amplitude occurrences. This latter segment gradually "tails off" asymptotically, meaning it approaches zero but never quite reaches it, stretching out indefinitely. The events residing at the extreme far end of this tail, by definition, possess an exceedingly low probability of actual occurrence, yet their collective number can be immense.

As a general rule of thumb for these types of population distributions, the vast majority of occurrences—typically more than half, and in cases where the Pareto principle (the 80/20 rule) is applicable, often as much as 80%—are accounted for by a relatively small fraction, specifically the first 20%, of the items within the distribution when ordered by frequency or amplitude. This highlights the inherent imbalance.

Power law distributions or functions are remarkably prevalent, characterizing an important and diverse number of behaviors observed in both the natural world and the vast landscape of human endeavor. This pervasive presence has, quite understandably, given rise to a keen scientific and social interest in understanding these distributions, as well as the underlying relationships and mechanisms that generate them. The mere observation of such a distribution in a given phenomenon frequently serves as a powerful indicator, pointing towards specific kinds of generative mechanisms and often suggesting a deep, sometimes counter-intuitive, connection with other, seemingly unrelated systems. Classic examples of behaviors that consistently exhibit this long-tailed distribution include the frequency of certain words in any given language (a prime example of Zipf's law), the intricate income distribution within an economy or a business, and even the intensity and frequency of earthquakes (famously described by the Gutenberg–Richter law).

The articles by Chris Anderson and Clay Shirky are particularly insightful because they illuminate special circumstances under which we gain the ability to intentionally modify the fundamental underlying relationships that govern these distributions. By doing so, we can directly evaluate the subsequent impact on the frequency of events. In these specific cases, the infrequent, low-amplitude (or, in a business context, low-revenue) events—the very essence of the long tail, represented graphically by the portion of the curve to the right of, say, the 20th percentile—can, remarkably, transform into the largest cumulative area under the line. This profound shift suggests that a relatively minor variation in a key mechanism (such as widespread internet access) or a fundamental relationship (like the dramatically reduced cost of digital storage and distribution) can significantly alter the frequency of occurrence of certain events within the overall distribution. Such a shift carries crucial implications, not only for the probabilities of individual events but also for the fundamental customer demographics and business models of industries like mass media and the burgeoning sector of online sellers.

However, it is essential to draw a critical distinction: the long tails that characterize classic statistical distributions such as the Gutenberg–Richter law or the word-occurrence patterns described by Zipf's law are fundamentally different, if not entirely opposite in nature, from those highlighted by Anderson and Shirky. Anderson and Shirky primarily refer to frequency-rank relations, which plot the popularity (frequency) of items against their rank. In contrast, the Gutenberg–Richter law and Zipf's law are inherently probability distributions. Therefore, in these latter, classical statistical cases, the "tails" actually correspond to large-intensity events—such as major earthquakes or the most popular and frequently used words—which are the dominant elements of their respective distributions. Conversely, the long tails depicted in the frequency-rank plots emphasized by Anderson and Shirky would, paradoxically, correspond to short tails in their associated probability distributions. This means they illustrate a phenomenon that is, in its essence, the inverse of what is described by the Gutenberg–Richter and Zipf's laws, a point often overlooked in the rush to apply the "long tail" label broadly.

Chris Anderson and Clay Shirky

The popularization of the phrase "the long tail" within business contexts, specifically denoting "the notion of looking at the tail itself as a new market" of consumers, is widely attributed to Chris Anderson. This concept did not emerge in a vacuum; it drew significant inspiration, in part, from a perceptive essay published in February 2003 by Clay Shirky, titled "Power Laws, Weblogs and Inequality." Shirky's essay pointed out the inherent imbalance in online attention, noting that a relatively small handful of weblogs garnered an overwhelming number of incoming links, while the vast "long tail" consisting of millions of other weblogs might receive only a paltry few links. Anderson systematically developed and articulated the profound effects of the long tail on both existing and emergent business models, initially through a series of public speeches in early 2004, culminating in the widespread attention generated by his October 2004 Wired magazine article. He subsequently expanded these ideas into a comprehensive book, The Long Tail: Why the Future of Business is Selling Less of More, published in 2006.

Anderson's central thesis posits that products traditionally considered to be in low demand or those with inherently low individual sales volumes can, when aggregated, collectively command a market share that either rivals or even surpasses the sales generated by the relatively few current bestsellers and blockbuster items. This is contingent upon the retail outlet or distribution channel possessing sufficient capacity, breadth, and efficiency. Anderson, in support of his argument, frequently cites earlier academic research conducted by Erik Brynjolfsson, Yu (Jeffrey) Hu, and Michael D. Smith. Their work compellingly demonstrated that a substantial portion of Amazon.com's total sales revenue was derived from obscure books, titles that, due to their limited appeal or niche subject matter, would simply not be economically viable for stocking in traditional brick-and-mortar bookstores. The long tail, therefore, represents a vast, untapped potential market which, as the numerous examples illustrate, can be successfully exploited by businesses leveraging the unparalleled distribution and sales channel opportunities afforded by the internet.

In his influential Wired article, Anderson commences with a particularly illustrative anecdote concerning the creation of a niche market for books on Amazon.com. He recounts the story of a book titled Touching the Void, which detailed a harrowing, near-death mountain climbing accident in the Peruvian Andes. Anderson notes that while the book received critical acclaim, it initially failed to achieve significant commercial success. However, a decade later, with the publication of Into Thin Air by Jon Krakauer—another book about a perilous mountain expedition—Touching the Void experienced a resurgence in sales. Anderson astutely recognized that this unexpected revival was largely attributable to Amazon's sophisticated recommendation algorithms. This mechanism effectively created and served a niche market for readers who enjoyed books about mountain climbing, even though it was not, by conventional metrics, considered a "popular" genre. This observation served as a compelling real-world example supporting the validity and potential of the long tail theory.

An anonymous Amazon.com employee, perhaps with a touch of weary insight, succinctly encapsulated the essence of the long tail with a now-famous quote: "We sold more books today that didn't sell at all yesterday than we sold today of all the books that did sell yesterday." This statement powerfully illustrates the cumulative effect of a vast inventory of slow-selling items, whose combined demand can easily overshadow the daily sales of even the most popular blockbusters.

Anderson himself has further clarified the term, explaining it as a direct reference to the extended, tapering portion of a demand curve. Subsequently, the term has been re-derived and visually represented through an XY graph, typically constructed by plotting popularity (or sales volume) against inventory rank. In such a graph, similar to the example provided, Amazon.com's book sales would be depicted along the vertical axis, while the rank of each individual book or movie (from most popular to least) would be plotted along the horizontal axis. The critical insight derived from such a visualization is that the total cumulative volume of sales generated by the numerous low-popularity items—the long tail—ultimately exceeds the total volume of sales generated by the comparatively few high-popularity items—the head.

Academic research

Effects of online access

The academic trio of Erik Brynjolfsson, Yu (Jeffrey) Hu, and Michael D. Smith conducted seminal research that provided empirical evidence for the long tail phenomenon. Their investigations revealed that a substantial proportion of Amazon.com's book sales were derived from what could only be described as obscure titles—books that, for various reasons, were simply not stocked or readily available in traditional brick-and-mortar retail establishments. Beyond merely identifying this trend, these researchers went further, rigorously quantifying the potential value that the long tail offered to consumers. In a pivotal article published in 2003, these authors demonstrated that, while much of the contemporary discourse surrounding the internet's value to consumers focused predominantly on the obvious advantage of lower prices, the actual consumer benefit (technically termed consumer surplus) accrued from the vastly increased product variety available in online bookstores was, in fact, an order of magnitude larger—ten times greater—than the benefit derived from merely accessing lower prices online. This finding unequivocally shifted the perception of the internet's economic contribution from simple cost reduction to profound value creation through expanded choice.

The longer tail over time

A subsequent and equally insightful study by the same research team—Erik Brynjolfsson, Yu (Jeffrey) Hu, and Michael D. Smith—uncovered a dynamic and evolving aspect of the long tail: it had demonstrably grown longer over time. Their analysis indicated a clear trend where niche books were progressively accounting for an ever-larger share of total sales. Their meticulous statistical analyses suggested that by 2008, these niche books collectively represented a significant 36.7% of Amazon's total sales. Furthermore, the consumer surplus generated specifically by these niche books had increased at least fivefold between 2000 and 2008, underscoring the escalating value consumers derived from expanded access to variety. In addition to these quantitative shifts, their updated methodology also revealed a nuanced insight: while the widely adopted power laws provide a robust initial approximation for the relationship between rank and sales, the slope of this relationship is not necessarily constant across all book ranks. Instead, they observed that the slope became progressively steeper for increasingly obscure books, indicating that the drop-off in sales for the least popular items was even more pronounced than previously assumed, yet their sheer volume remained significant.

In further support of these findings, Wenqi Zhou and Wenjing Duan conducted an in-depth analysis of consumer software downloading patterns, not only corroborating the observation of a longer tail but also identifying a "fatter" tail in their paper titled "Online user reviews, product variety, and the long tail." Their research highlighted that while the overall demand for all products might experience a general decrease, this decline was more pronounced for the "hits" or popular products. This suggests a discernible shift in demand away from blockbusters and towards niche offerings over time. Interestingly, despite this lengthening and fattening of the tail, they also observed a persistent "superstar effect," where a small number of very popular products continued to dominate the overall demand, indicating a complex interplay between broad choice and concentrated attention.

"Goodbye Pareto Principle"

In a compelling 2006 working paper provocatively titled "Goodbye Pareto Principle, Hello Long Tail," Erik Brynjolfsson, Yu (Jeffrey) Hu, and Duncan Simester presented a theoretical and empirical argument for a fundamental shift in market dynamics. They posited that by dramatically reducing search costs—a transformative impact attributable to information technology in general and internet markets in particular—the collective market share commanded by hard-to-find, niche products could be substantially amplified. This, in turn, would lead to the creation of a significantly longer and more impactful tail in the distribution of product sales.

Their research employed a theoretical model to systematically illustrate how a reduction in search costs would inevitably influence the concentration of product sales. To provide empirical validation, they analyzed sales data meticulously collected from a multi-channel retailing company. Their findings offered compelling evidence that the internet sales channel consistently exhibited a significantly less concentrated sales distribution when compared directly with traditional retail channels. Where a conventional 80/20 rule (the Pareto principle) adequately described the distribution of product sales in the catalog channel, this rule required modification to a 72/28 rule to accurately fit the distribution of product sales observed in the internet channel. This difference in sales distribution was not merely anecdotal; it was statistically highly significant, even after carefully accounting for potential differences in consumer demographics and behavior between the channels.

Demand-side and supply-side drivers

The presence and efficacy of a long tail in a sales distribution are critically influenced by a confluence of factors, both from the supply side and the demand side. On the supply side, the paramount determinant is the cost associated with inventory storage and distribution. In scenarios where these costs are negligible or extremely low, it becomes economically feasible to stock and sell a vast array of relatively unpopular or niche products. Conversely, when storage and distribution costs are prohibitively high, retailers are compelled to focus exclusively on the most popular products to ensure profitability. Consider the traditional movie rental store: its physical shelf space is finite and comes with significant overhead costs (rent, utilities, etc.). To maximize its profit per square foot, it must prioritize stocking only the most popular movies, thereby minimizing wasted space. In stark contrast, an online video rental provider, such as Amazon.com or Netflix, operates with vastly different economics. By centralizing its inventory in large warehouses, its storage costs per item are dramatically lower, and its distribution costs (shipping, streaming bandwidth) are largely indifferent to a movie's popularity. This fundamental difference enables it to profitably offer a far wider range of movies than any physical store could. These advantageous economics of storage and distribution then unlock the strategic utility of the long tail: for instance, Netflix famously discovered that, in aggregate, "unpopular" movies are rented more frequently than their blockbuster counterparts.

An insightful article published in the MIT Sloan Management Review, aptly titled "From Niches to Riches: Anatomy of the Long Tail," provided a comprehensive examination of the long tail from both the supply and demand perspectives, identifying several key drivers. From the supply side, the authors underscored how the expanded, centralized warehousing capabilities characteristic of e-tailers enable them to offer an exponentially greater number of products. This expanded inventory, in turn, allows them to cater to an incredibly diverse spectrum of consumer tastes and preferences that would otherwise go unserved.

On the demand side, the proliferation of sophisticated tools such as search engines, advanced recommendation software, and convenient sampling mechanisms empowers customers to discover and access products far beyond their immediate geographic proximity or traditional retail channels. The authors also extended their analysis to anticipate future trends, discussing the "second-order, amplified effects" of the Long Tail, including the predictable growth of specialized markets specifically designed to serve ever-smaller and more granular niches.

However, it is crucial to recognize that not all recommender systems are created equal when it comes to fostering the expansion of the long tail. Some recommenders, particularly certain types of collaborative filters, can unfortunately exhibit an inherent bias towards already popular products. This can create a positive feedback loop, paradoxically leading to a reduction in the long tail rather than its expansion. A detailed study conducted by the Wharton School of the University of Pennsylvania meticulously documented this phenomenon and proposed several innovative ideas designed to actively promote the long tail and enhance overall sales diversity.

A 2010 study by Wenqi Zhou and Wenjing Duan further illuminated the complex interplay between demand-side factors (specifically, online user reviews) and supply-side factors (product variety) in shaping the formation of the long tail in consumer choices. They found that consumers' reliance on online user reviews as a decision-making heuristic is significantly modulated by the sheer quantity of available products. More specifically, their research indicated that the impacts of both positive and negative user reviews are attenuated as product variety increases. Furthermore, the increase in product variety had a more pronounced dampening effect on the influence of user reviews for popular products compared to niche products. This suggests that while reviews remain important, their decisive power shifts as the long tail expands, making discovery more complex.

Networks, crowds, and the long tail

The extensive "crowds" comprising customers, users, and numerous small companies that populate the long-tail distribution are increasingly capable of engaging in collaborative and distributed work, fundamentally altering traditional production models. Some of the most pertinent and transformative forms of these new production paradigms include:

• The highly effective peer-to-peer collaboration groups, famously responsible for the development of open-source software and the creation of vast communal knowledge repositories like wikis, with Wikipedia standing as a preeminent example of aggregated, decentralized effort.

• The crowdsourcing model, a business strategy where a company strategically outsources tasks or projects to a large, undefined group of market participants, leveraging collaborative online platforms to tap into a distributed workforce.

• The more targeted model of crowdcasting, which involves the deliberate process of cultivating and building a network of users, and subsequently issuing specific challenges or tasks to this network with the explicit objective of garnering diverse insights, innovative ideas, or creative solutions.

• The increasingly recognized phenomenon of work performed by individuals within commons-like, non-market networks, a concept meticulously described in the seminal work of Yochai Benkler, which highlights the power of decentralized, voluntary collaboration outside traditional economic structures.

The demand-side factors that contribute to the emergence and expansion of the long tail can be significantly amplified by the intricate "networks of products" that are forged through hyperlinked recommendations and cross-promotions between various items. An MIS Quarterly article by Gal Oestreicher-Singer and Arun Sundararajan provided compelling evidence for this. Their research demonstrated that categories of books on Amazon.com that occupied more central positions within and were thus more profoundly influenced by their recommendation network exhibited significantly more pronounced long-tail distributions. Their extensive data, spanning over 200 subject areas, revealed a powerful correlation: a doubling of this network influence translated into an impressive 50% increase in revenues generated specifically from the least popular one-fifth of all books. This underscores how digital infrastructure can not only facilitate the long tail but actively enhance its economic viability.

Turnover within the long tail

While the concept of the long-tail distribution provides a valuable snapshot of market dynamics at any given moment, it is crucial to recognize that this distribution is not static. Over time, the relative popularity and sales performance of individual products within this vast tail will invariably shift and change. Although the overall shape of the sales distribution may appear superficially similar across different time periods, the actual positions of individual items within that distribution are in constant flux. For instance, new items are continuously introduced into the majority of fashion markets, perpetually altering the landscape of what is considered "in" or "out." A recent fashion-based model of consumer choice, which possesses the inherent capability to generate power law distributions of sales strikingly similar to those observed in real-world practice, explicitly incorporates this dynamic element of turnover. This model accounts for the constant shifts in the relative sales performance of a defined set of items, as well as the continuous process of innovation, where entirely new products are introduced for sale.

Given the inherent dynamism, there may exist an optimal inventory size, carefully balancing the potential for sales with the ongoing costs associated with managing and keeping pace with this perpetual turnover. An analysis grounded in this pure fashion model suggests that, even for ostensibly digital retailers—who benefit from seemingly infinite virtual shelf space—the optimal inventory might, in many practical scenarios, be considerably less than the millions of items they could theoretically offer. In other words, as one delves deeper and deeper into the long tail, the sales figures for individual items can become so infinitesimally small that the marginal cost of merely tracking and managing them in rank order, even at an automated digital scale, might be optimized well before reaching a million distinct titles, and certainly long before attempting to stock an infinite number. This sophisticated model offers further predictive insights into markets characterized by long-tail distributions, providing, for example, a robust framework for optimizing the quantity of each individual item ordered, taking into account its current sales rank and the total number of different titles currently stocked.

Long-tailed distributions in diplomacy

In an intriguing and somewhat unexpected application, the dynamics of long-tailed distributions have also been observed in the realm of international relations. From the perspective of any given country, its diplomatic interactions with other sovereign states likewise exhibit a distinct long-tail pattern. Strategic partners, naturally, command the lion's share of diplomatic attention and resources, receiving the largest volume of communication and engagement. However, there exists a lengthy tail comprising numerous remote states, each of which typically obtains only an occasional, often symbolic, signal of peace or amicable interaction. The compelling argument has been made that the very fact that even these allegedly "irrelevant" countries receive at least rare, friendly overtures from virtually all other states creates a kind of "societal surplus of peace." This surplus acts as a latent reservoir of goodwill and potential connections that can be mobilized should a state suddenly find itself in need of diplomatic support or alliance. In this context, the diplomatic long tail functionally resembles the concept of "weak ties" in interpersonal networks, where infrequent connections can nonetheless prove invaluable in times of need.

Business models

Competitive impact

In the era preceding the widespread adoption of the long tail model, market dynamics dictated that only the most popular and commercially viable products were generally offered by retailers. This was largely due to the prohibitive costs associated with inventory, storage, and distribution. However, as these costs have progressively diminished—a transformation largely driven by digital technologies and online retail—a vastly expanded range of products has become economically viable and readily available to consumers. This fundamental shift can, in turn, have the profound effect of paradoxically reducing the concentrated demand for the formerly ubiquitous "most popular" products. Consider, for example, a small, specialized website that meticulously curates niche content. It faces a significant competitive threat from a much larger, more generalized website (such as Yahoo) that offers an immense variety of information. While the smaller site focuses on a few specific niches, the larger site blankets a far broader spectrum of interests, offering an overwhelming choice.

Historically, the competitive threat posed by these numerous niche sites was mitigated by the considerable cost and effort required to establish and maintain them, as well as the logistical burden placed on readers to track multiple small, disparate websites. However, these barriers have been dramatically eroded by the advent of easy-to-use and inexpensive website software, coupled with the pervasive adoption of content syndication technologies like RSS. Similarly, traditional mass-market distributors, such as the now-defunct Blockbuster, found themselves increasingly vulnerable to agile, digitally-native distributors like LoveFilm. These newer players could profitably supply an extensive catalog of titles that Blockbuster simply could not offer, precisely because those titles were not already wildly popular. The ability to cater to unfulfilled demand in the tail ultimately became a significant competitive advantage.

Internet companies

It is no coincidence that many of the most profoundly successful internet businesses have strategically integrated the long tail as a core component of their overarching business strategy. Prominent examples among the major corporations include eBay, which thrives on its vast marketplace of unique auction items; Yahoo! and Google, whose web search capabilities effectively organize and make accessible the immense long tail of online information; Amazon.com, the retail behemoth whose success is deeply rooted in offering an unparalleled selection; and the iTunes Store, which revolutionized music and podcasts distribution by providing access to millions of tracks. Beyond these giants, smaller, more specialized internet companies like Audible.com (audio books) and LoveFilm (video rental) also demonstrate the viability of this model. A key advantage for these purely digital retailers is their near-zero marginal cost for each additional item offered or stored digitally, a benefit largely unavailable to physical retailers who face hard limits on their product offerings due to physical space constraints. The internet has not only removed these physical perimeters but has also opened up vast new territories for selling and distributing products, freeing businesses from the confines of "local markets" that restrict physical retailers such as Target or even Walmart. With the rise of digital and hybrid retailers, the traditional boundaries on market demands have effectively been dissolved, allowing for an unprecedented expansion into the long tail.

Video and multiplayer online games

The burgeoning adoption of video games and massively multiplayer online games (MMOs), such as the virtual world of Second Life, as potent tools for education and professional training is increasingly exhibiting a clear long-tailed pattern. The economic calculus here is compelling: modifying an existing game platform to create a specialized training application is demonstrably and significantly less expensive than developing entirely unique, bespoke training applications from scratch. This cost efficiency applies across diverse sectors, including business training simulations, commercial flight instruction, and complex military mission rehearsals. This trend has led some observers to envision a future where game-based training devices or simulations will become readily available for thousands of distinct job descriptions, catering to highly specific vocational needs that were previously uneconomical to address with custom-built software. The long tail here represents the vast array of specialized training requirements that can now be met through adaptable, game-based solutions.

Microfinance and microcredit

The banking business, traditionally conservative and risk-averse, has undergone a significant transformation through the strategic leveraging of internet technology, allowing it to reach an ever-expanding number of customers. However, arguably the most profound shift in business model driven by the long tail concept has manifested in the various innovative forms of microfinance that have emerged globally.

In stark contrast to the high-tech operations of e-tailers, microfinance is, at its heart, a distinctly low-technology business. Its fundamental objective is to extend very small credits—"microcredits"—to individuals belonging to the lower-middle, lower, and indeed, the poorest segments of society, individuals who would otherwise be entirely overlooked and underserved by conventional banking institutions. Banks that have courageously adopted this strategy of offering services to the low-frequency, long-tail segment of the market have discovered a surprisingly robust and vital niche, one that had been largely ignored by traditional consumer banks. Counter-intuitively, the recipients of these small credits tend to exhibit remarkably high rates of loan repayment, despite their often non-existent formal credit histories. Furthermore, they are frequently willing to accept higher interest rates than those offered to standard bank or credit card customers, reflecting the profound value of access to capital where none existed before. This model not only proves financially viable but also fulfills a crucial developmental role within an economy, fostering entrepreneurship and stability where traditional finance fails.

The Grameen Bank in Bangladesh stands as a globally recognized exemplar of successful adherence to this microfinance business model. In Mexico, institutions like Compartamos and Banco Azteca have similarly carved out significant market share by catering to this underserved customer demographic, albeit with a greater emphasis on consumer credit. Kiva.org offers a contemporary, digitally-enabled variation, functioning as an organization that facilitates microcredits to individuals worldwide. It achieves this by partnering with intermediaries, known as small microfinance organizations (S.M.O.'s), which efficiently distribute crowd-sourced donations made by Kiva.org's global network of lenders, effectively extending the long tail of charitable finance.

User-driven innovation

According to the increasingly influential user-driven innovation model, forward-thinking companies can strategically rely on the very users of their products and services to undertake a significant portion of the innovation work. The underlying premise is simple yet powerful: users inherently desire products that are meticulously customized to their specific needs and preferences. Crucially, they are often not only willing but eager to communicate to manufacturers precisely what they genuinely want and how it should ideally function. Companies can shrewdly leverage a suite of tools, particularly interactive and internet-based technologies, to effectively empower their users, giving them a voice and enabling them to actively participate in innovation efforts that directly benefit the company.

Given the dramatically diminishing cost of communication and information sharing—a phenomenon analogous to the low cost of storage and distribution that benefits e-tailers—the importance of long-tailed, user-driven innovation is poised to grow exponentially for businesses across all sectors.

By embracing a long-tailed innovation strategy, a company effectively utilizes this model to tap into the vast, distributed intelligence of a large group of users who typically reside in the low-intensity area of the demand distribution. It is their collective collaboration and the aggregation of their individual contributions that culminate in a potent and dynamic innovation effort. These emergent social innovation communities, formed by self-organizing groups of users, are uniquely positioned to rapidly execute the iterative trial and error process inherent in innovation, efficiently share valuable information, and rigorously test and disseminate the resulting solutions.

Eric von Hippel, a distinguished scholar at MIT's Sloan School of Management, meticulously defined and elaborated upon the user-led innovation model in his seminal book, Democratizing Innovation. Among his profound conclusions is the insight that as innovation increasingly becomes user-centered, the imperative for information to flow freely and democratically intensifies. This process naturally fosters the creation of a "rich intellectual commons," a shared pool of knowledge and ideas, and, in doing so, fundamentally "attacks a major structure of the social division of labor," blurring the lines between producers and consumers.

In the contemporary landscape, consumers are not merely passive recipients; they are increasingly eager to articulate their opinions and actively shape the products and services they utilize. This presents an unparalleled opportunity for companies to strategically leverage interactive and internet-based technologies to grant their users a powerful voice and empower them to participate directly in the innovation process. By embracing this paradigm, companies can glean invaluable insights into their customers' nuanced needs and evolving preferences, which, in turn, can serve as a potent catalyst for driving product development and continuous innovation. By proactively establishing platforms that enable users to freely share their ideas and provide constructive feedback, companies can harness the immense power of collaborative innovation, thereby maintaining a crucial competitive edge. Ultimately, the integration of users into the innovation process represents a mutually beneficial scenario for both companies and their clientele, leading directly to the creation of more precisely tailored, highly effective products and services that more accurately meet the genuine needs of the end user.

Marketing

The relentless drive to cultivate new markets and extract revenue from the consumer demographic residing within the long tail has spurred businesses to adopt and implement a diverse array of long-tail marketing techniques. The overwhelming majority of these strategies are predicated upon the extensive and sophisticated use of internet technologies. Among the most representative and widely employed approaches are:

• New media marketing: This encompasses the strategic development and ongoing management of social networks and online or virtual communities. The primary objective is to extend the reach of marketing efforts to the low-frequency, low-intensity consumer in an exceptionally cost-effective manner, often achieved through the judicious use of blogs, RSS feeds, and podcasts.

• Buzz marketing: This technique involves the deliberate and strategic deployment of word of mouth communication and the organic transmission of commercial information from person to person, whether within an online environment or through real-world interactions.

• Viral marketing: This is the intentional dissemination of marketing messages through the leveraging of pre-existing social networks. A key emphasis is placed on the casual, non-intentional, and low-cost nature of the spread, commonly facilitated through engaging YouTube videos, easily shareable viral emails, and self-contained microsites.

• Pay per click (PPC) and search engine optimization (SEO): This involves the marketing of websites on prominent search engines such as Google, Yahoo! Search, and Bing. The strategy here is to focus on "long-tail keywords"—highly specific, often multi-word search queries—which, despite having lower individual search volumes, benefit from significantly less competition, making them a cost-effective route to targeted traffic.

• Demand-side platforms (DSPs): Analogous to how search engine marketing effectively monetizes the long tail of keywords, auction-oriented buying and selling mechanisms have proven equally viable in helping to monetize the long tail of available ad impressions across numerous niche publishers within the display advertising ecosystem. Publishers actively utilize these ad exchange environments, such as Right Media or AdECN, to efficiently sell display inventory that might otherwise remain unsold through traditional direct sales force operations. As a direct consequence of these sophisticated mechanisms, by January 2011, a substantial 20–25% of all US ad spending was attributed to long-tail advertisers, demonstrating their collective economic power.

Cultural and political impact

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The profound implications of the long tail extend far beyond mere economic considerations, potentially reshaping fundamental aspects of culture and politics. In environments where the opportunity cost associated with inventory storage and distribution remains high, the market inevitably gravitates towards offering only the most popular and commercially viable products. However, in scenarios where the long tail model thrives—facilitated by diminished costs—a vast spectrum of minority tastes and niche interests becomes accessible, thereby presenting individuals with an unprecedentedly wider array of choices. The long tail, by its very nature, creates fertile ground for a multitude of suppliers to introduce products catering to these niche categories. This economic enablement, in turn, actively encourages the diversification of products across various markets. These niche offerings simultaneously open up new avenues for suppliers while fulfilling the previously unmet demands of countless individuals, thus perpetually extending the tail portion of the long tail. In contexts where popularity has historically been dictated by the lowest common denominator, a long-tail model holds the promise of fostering a significant improvement in a society's overall level of cultural sophistication and diversity. The opportunities that arise directly from the long tail profoundly impact societal cultures because suppliers, no longer constrained by physical limitations, possess virtually unlimited capabilities due to infinite digital storage and the ability to meet demands that were previously impossible to satisfy. At the extreme end of the long tail, the conventional profit-making business model often ceases to be the primary driver; instead, individuals are frequently motivated to create and offer products for a myriad of reasons, such as pure self-expression or community contribution, rather than solely for monetary gain. In this transformative way, the long tail effectively opens up an expansive and invaluable space for authentic, uncommercialized works of creativity.

Cultural diversity

Television serves as an excellent case study to illustrate the long tail's impact on cultural diversity. Chris Anderson defines "long-tail TV" specifically in the context of "content that is not available through traditional distribution channels but could nevertheless find an audience." Consequently, the advent of innovative services such as television on demand, pay-per-view options, and even premium cable subscription services like HBO and Showtime, has created unprecedented opportunities for highly specialized, niche content to successfully reach its intended audiences. This occurs even within what was once considered an archetypal mass medium. While these niche programs may not always attract the highest absolute levels of viewership, their innovative business and distribution models render mass appeal of significantly less importance. As the opportunity cost of offering diverse content diminishes, the available choice of television programs proliferates, leading directly to a discernible increase in overall cultural diversity.

Distribution of independent content

Often framed as a phenomenon primarily of interest to mass-market retailers and sprawling web-based businesses, the long tail also carries profound implications for the myriad producers of content. This is particularly true for those whose creative products—for compelling economic reasons—could not previously secure a place within the tightly controlled, pre-Internet information distribution channels dominated by established book publishers, record companies, movie studios, and television networks. Viewed from the creators' perspective, the long tail has catalysed a veritable flowering of creativity across virtually all fields of human endeavor, providing unprecedented avenues for expression and dissemination. YouTube stands as a prime example of this democratization of content: thousands upon thousands of diverse videos—whose content, production value, or sheer lack of mainstream popularity would render them entirely unsuitable for traditional television broadcast—are now effortlessly accessible to an incredibly wide and global range of viewers.

Contemporary literature

The intricate intersection of viral marketing, burgeoning online communities, and the disruptive new technologies that operate within the vast long tail of consumers and businesses is vividly explored and depicted in the acclaimed novel by William Gibson, Pattern Recognition. Gibson's work often presciently captures the zeitgeist of technological and cultural shifts, and this novel serves as a literary reflection on the fragmented, niche-driven digital landscape that the long tail helps to define.

Military applications and security

In the realm of military strategy and security thinking, John Robb has compellingly applied the concept of the long tail to analyze developments within insurgency and terrorist movements. Robb's analysis demonstrates how readily available technology and pervasive networking capabilities empower the long tail of disgruntled groups and criminal enterprises to effectively challenge established nation-states, and in certain contexts, even possess a tangible chance of achieving their objectives. This application underscores how distributed networks and low-cost tools can aggregate the power of numerous small, disparate actors into a formidable force, mirroring the economic dynamics of the long tail in a geopolitical context.

Criticisms

Despite its widespread acceptance and application, the long tail theory has not been without its detractors and rigorous academic scrutiny. A significant 2008 study led by Anita Elberse, a distinguished professor of business administration at Harvard Business School, presented findings that directly called the core long tail theory into question. Citing extensive sales data, her research suggested that, contrary to the theory's central premise, the web actually tends to magnify the importance and dominance of blockbuster hits rather than diminishing it. Chris Anderson, ever the proponent, responded to Elberse's study on his blog. While he commended Elberse for her academic rigor and the intellectual challenge she posed, he drew a crucial distinction regarding their respective interpretations of where the "head" of a distribution truly ends and the "tail" begins. Elberse defined these segments using percentages (e.g., the top X% are the head), whereas Anderson's conceptualization often relied on absolute numbers, leading to different conclusions about the relative dominance of hits versus niches. Similar results and arguments were subsequently published by Serguei Netessine and Tom F. Tan, who further advocated for defining "head" and "tail" using percentages rather than absolute numerical thresholds.

Also in 2008, a meticulous sales analysis of an unnamed UK digital music service, conducted by economist Will Page and high-tech entrepreneur Andrew Bud, yielded results that further complicated the narrative. Their study found that sales data for digital music exhibited a log-normal distribution rather than the power law distribution often associated with the long tail. Perhaps most strikingly, they reported that a staggering 80% of the music tracks available through the service sold absolutely no copies whatsoever over a one-year period. Anderson, in response, acknowledged the study but noted that its findings were inherently difficult to fully assess and contextualize without direct access to the underlying data, highlighting the complexities and nuances inherent in empirical validation of such broad theories.

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References

Citations

•

• ^ Alpheus Bingham and Dwayne Spradlin (2011). The Long Tail of Expertise . Pearson Education. p. 5. ISBN 9780132823135 .

• ^ • Asmussen, S. R. (2003). "Steady-State Properties of GI/G/1". Applied Probability and Queues . Stochastic Modelling and Applied Probability. Vol. 51. pp. 266–301. doi:10.1007/0-387-21525-5_10. ISBN 978-0-387-00211-8 .

• ^ Levine, David M.; Stephan, David; Krehbiel, Timothy C.; Berenson, Mark L. Statistics for Managers using Microsoft Excel . 3rd edition. Prentice Hall, 2002, p. 124.

• ^ • John Verzani (2004). Using R for Introductory Statistics . CRC Press. p. 62. ISBN 978-1-58488450-7 .

• ^ A search for the phrase "long tail" in the database MathSciNet yielded 81 hits, the earliest being a 1946 paper by Brown and Tukey in the Annals of Mathematical Statistics (volume 17, pages 1–12).

• ^ Bessis, Jöel "Risk Management in Banking". Wiley, 1995

• ^ a b • Quinion, Michael (24 December 2005). "Turns of Phrase: Long Tail". World Wide Words. Retrieved 25 December 2011.

• ^ Obrist, Hans Ulrich "The Father of Long Tails. An interview with Benoît Mandelbrot", Edge.org, 2008

• ^ Anderson, Chris. "The Long Tail" Wired , October 2004.

• ^ • Brynjolfsson, Erik; Hu, Yu (Jeffrey); Smith, Michael D. (2003). "Consumer Surplus in the Digital Economy: Estimating the Value of Increased Product Variety at Online Booksellers". Management Science . 49 (11): 1580–1596. doi:10.1287/mnsc.49.11.1580.20580. hdl:1721.1/3516. ISSN 0025-1909.

• ^ Carr, Nicholas "The shape of the tail.", roughtype.com, 2006

• ^ • Anderson, Chris (2006). scifoo: A problem with the Long Tail . New York, NY: Hyperion. ISBN 978-1-4013-0237-5 .

• ^ See The origins of "The Long Tail"

• ^ "Power Laws, Weblogs and Inequality" Archived 2004-07-07 at the Wayback Machine, by Clay Shirky. February 8, 2003.

• ^ The Long Tail: Definitions: Final Round!, comment #3 by Josh Petersen.

• ^ • "The Long Tail". NPR. 5 November 2004. Retrieved 25 December 2011.

• ^ Brynjolfsson, Erik; Yu (Jeffrey) Hu, and Michael D. Smith, "Consumer Surplus in the Digital Economy: Estimating the Value of Increased Product Variety at Online Booksellers", Management Science , 49 (11), November 2003. working paper version, April 2003

• ^ Bynjolfsson, Erik; Yu (Jeffrey) Hu, and Michael D. Smith, 2010, "The Longer Tail: The Changing Shape of Amazon's Sales Distribution Curve"

• ^ a b • Zhou, Wenqi; Duan, Wenjing (21 November 2010). "Online User Reviews, Product Variety, and the Long Tail: An Empirical Investigation on Online Software Downloads". Electronic Commerce Research and Applications . 11 (3): 275–289. doi:10.1016/j.elerap.2011.12.002. S2CID 23070895.

• ^ Brynjolfsson, Erik; Yu (Jeffrey) Hu, and Duncan Simester, 2006, "Goodbye Pareto Principle, Hello Long Tail: The Effect of Search Costs on the Concentration of Product Sales"

• ^ • Brynjolfsson, Erik; Hu, Yu "Jeffrey"; Smith, Michael D. (Summer 2006). "From Niches to Riches: Anatomy of the Long Tail". MIT Sloan Management Review . 47 (4): 67–71. SSRN 918142.

• ^ • Anderson, Chris (1 July 2006). "The Rise and Fall of the Hit". Wired . Vol. 14, no. 7.

• ^ • Fleder, Daniel; Hosanagar, Kartik (May 2009). "Blockbuster Culture's Next Rise or Fall: The Impact of Recommender Systems on Sales Diversity". Management Science . 55 (5): 697–712. doi:10.1287/mnsc.1080.0974. SSRN 955984.

• ^ • "Benkler, The Wealth of Networks". Benkler.org. Retrieved 25 December 2011.

• ^ • Oestreicher-Singer, Gal and Arun Sundararajan (2012). "Recommendation Networks and the Long Tail of Electronic Commerce". MIS Quarterly . 36 (1): 65–83. doi:10.2307/41410406. JSTOR 41410406. SSRN 1324064.

• ^ • Bentley, R. Alexander; Lipo, Carl P.; Herzog, Harold A.; Hahn, Matthew W. (2007). "Regular rates of popular culture change reflect random copying". Evolution and Human Behavior . 28 (3): 151–158. CiteSeerX 10.1.1.411.7668. doi:10.1016/j.evolhumbehav.2006.10.002.

• ^ • Highfield, Roger (16 June 2004). "Why are they so popular?". The Daily Telegraph . Archived from the original on 23 February 2006. Retrieved 25 December 2011.

• ^ • Bentley, R.A.; Hahn, M.W.; Shennan, S.J. (2007). "Random drift and culture change". Proceedings of the Royal Society . 271 (1547): 1443–50. doi:10.1098/rspb.2004.2746. PMC 1691747. PMID 15306315.

• ^ • Bentley, R. Alexander; Madsen, Mark E.; Ormerod, Paul (2009). "Physical space and long-tail markets". Physica A: Statistical Mechanics and Its Applications . 388 (5): 691–696. arXiv:0808.1655. Bibcode:2009PhyA..388..691B. doi:10.1016/j.physa.2008.11.009.

• ^ • Nishikawa-Pacher, Andreas (2023). "Diplomatic complexity and long-tailed distributions: the function of non-strategic bilateral relations". International Politics . 60 (6): 1270–1293. doi:10.1057/s41311-023-00510-3.

• ^ • Anderson, Chris (13 December 2004). "The Long Tail" (PDF). ChangeThis . Vol. 10, no. 1.

• ^ • McDonald, Scott (September 2008). "The Long Tail and Its Implications for Media Audience Measurement". Journal of Advertising Research . 48 (3): 313–319. doi:10.2501/S0021849908080379. ISSN 0022-2437.

• ^ • "Microcredit and Microfinance". The Global Development Research Center. Retrieved 25 December 2011.

• ^ • "Vision and Mission Statement for Building Inclusive Financial Sectors". United Nations Capital Development Fund. Archived from the original on 31 December 2011. Retrieved 25 December 2011.

• ^ • "Democratizing Innovation". MIT Press. Retrieved 25 December 2011.

• ^ • "'Long Tail' Advertisers Are Back, U.S. Ad Expansion Reaches '03 Levels". MediaDailyNews. 2011-01-04. Retrieved 2014-01-20.

• ^ Chris Anderson. The Long Tail TV: Conclusion. The Long Tail Blog . January 17, 2005.

• ^ • Elberse, Anita (July 2008). "Should You Invest in the Long Tail?". Harvard Business Review .

• ^ • Anderson, Chris (27 June 2008). "Excellent HBR piece challenging the Long Tail". The Long Tail Blog.

• ^ • "Rethinking the Long Tail Theory: How to Define 'Hits' and 'Niches'". Knowledge@Wharton. 16 September 2009.

• ^ • Anderson, Chris (8 November 2008). "More Long Tail debate: mobile music no, search yes". The Long Tail. Retrieved 25 December 2011.

• ^ • Foster, Patrick (22 December 2008). "Long Tail theory contradicted as study reveals 10m digital music tracks unsold". The Times . Times Online.

General and cited references

• • Anderson, Chris (2006). The Long Tail: Why the Future of Business Is Selling Less of More . New York: Hyperion. ISBN 978-1-4013-0237-5 .

• The Long Tail—a computer model by Fiona Maclachlan, The Wolfram Demonstrations Project

External links

• Media related to The Long Tail at Wikimedia Commons