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The Fundamentals of Market Share | Kyle Findlay

by Social Physicist

4,258 views

This presentation outlines how market share forms from a network perspective. ...

This presentation outlines how market share forms from a network perspective.

It is based on an oldish paper I wrote for the 2009 Southern African Marketing Research Association (SAMRA) Conference. It subsequently won the WPP Atticus "Research in Practice" award.

Please drop me an e-mail if you have any questions, comments or would like a copy of the deck.

Note that the SlideShare conversion process has corrupted some of the slides (e.g. slides 20, 26)

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Bilal Sununu, Founder at ThinkOut Marketing Hi, I am very interested to get this PowerPoint, and i know it is your intellictual property, is it possible to send it to bilalsununu@gmail.com
Bilal 2 years ago
Are you sure you want to
Social Physicist, R&D at N/A Hey Aygul,

You make some interesting comments. If you would like to continue the conversation, please feel free to drop me an email.

K 2 years ago
Are you sure you want to
Aygul Umurzakova at Aygul Umurzakova Hi again,

I shared with the recent news from the world’s richest people (that they are giving money to charity)
in a response to your Pareto Principle and the notion that the Rich-is-Getting-Richer and The poor are getting poorer effects. I think billionaires are very smart people who were able to build fortunes, inspiring brands(IPhone, Microsoft, Oracle, epic movies like Star Wars, etc) and create thousands of workplaces for hard-working people all over the world. And they help the world economy and balance it. So, not so rich people’s well-being depend on the well-being of the richest people directly. And now the rich people are going to give at least $150 billion to charity.

It’s Simply Wonderful! :-)

Then, about the Generic Products. I meant about daily consumer goods. In today’s tough economy many people prefer to choose generic products over just Big Name Brands. And there are cheaper version of almost every product from toilet papers to cereals and basic baking products.
So, consumers can save from $200-$1,500 per year by purchasing generic products. These amounts are taken from the recent article about saving money.

You are speaking a little bit in a technical language. So, it’s a little bit confusing about specific scientific terms.

According to the recent news the US has the risk of Deflation currently. It means prices of gasoline, food, health-care, education are all getting more expensive. So the Federal Reserve is afraid of double-dip recession. :-( :-(

And according to the recent data from the Reuters news articles:
’Weak consumer demand forces a steady fall in prices of goods... Deflation could be as high as 50 percent.’ :-(

There are inflation in some areas and the deflation in others.
So, it’s no wonder that many people choose to save over paying just for the brand name.

Have a Nice Day!

Best Wishes, Aygul 2 years ago
Are you sure you want to
Social Physicist, R&D at N/A Aygul, thanks for the comments :)

In response to your question, here's what I think:

Just to reiterate, power laws form in the presence of a biasing factor such as social influence. On the topic of generics, are the products differentiated from each other so that I can meaningfully distinguish between them or are we talking about commodities? If they are differentiated, what is influencing which product I ultimately choose? If the answer is friends and family, or 'it's the one my mother always bought' or something like that, I think you are going to TEND towards a power law-like inequality.

Market factors such as price and availability are confounding variables which play against this tendency towards a visible inequality in market share by undermining the scale-free nature of the system.

Cheers,
Kyle 2 years ago
Are you sure you want to
Aygul Umurzakova at Aygul Umurzakova Dear Kyle Findlay,

I like this very well-organized and inspiring presentation about my favorite area: social media. It's very very cool!

I just want to add that I like plain cheese: Mozzarella and Gouda.
'And on August 4, 2010 the US billionaries pledged to give at least half their fortunes to charity. Based on Forbes magazine's estimates of the billionaires' wealth, at least $150 billion could be given away.'
So, they are not so greedy any more! Cool...
Source:http://www.reuters.com/article/idUSTRE6733F520100804?rpc=59
And the last but not the least question:
What about essential Generic Products which are popular without any additional marketing?
Thanks for creating such informative presentation!

Best Regards, Aygul 2 years ago
Are you sure you want to

This paper was presented at the 2009 Society for Chaos Theory in Psychology and Life Sciences conference in Milwaukee, Wisconsin, USA and at the 2009 Southern African Marketing Research Association Conference in Cape Town, South Africa. See notes pages for more detail on the topics discussed on each slide…
In order to start down the road of understanding how systems such as markets work, we first have to agree on some basic aspects of the human condition. First and foremost, we are not isolated beings, devoid of all contact. Rather we are agents swirling around within a complex environment full of many other agents. According to Mark Earls (2007), some have suggested that during the course of our day, while commuting to and from work, passing people on the street or chatting via instant messaging, we experience as many as 10,000 social interactions (a crude estimation I am sure, but it makes the point). All these other agents have a role to play in our lives whether directly or indirectly, passively or actively. For example, parents’ purchase decisions might be made based on the advice of so-called ‘experts’, children’s decisions are often made based on media exposure and prevailing trends within their social group, and we are all influenced by the opinions and perceptions of our friends and family around us whether we realise it or not. We want to belong, or at the very least, know where we fit in. We want to be seen wearing the right jeans, driving an acceptable car, sporting the latest cellular phone or ensuring that we are adorned with the correct collective trappings of one’s chosen counter-culture (goths, emos, skaters and punks all spring to mind here). We like to think of ourselves as autonomous individuals, but a large amount of what we do is influenced by those around us. Either we tend towards the majority, or define ourselves in opposition to it, but we still react to it. Short of removing ourselves from civilization and living as a hermit, there is not much we can do to escape the influence of peers, friends, family, colleagues, community and media.
Social influence is evident everywhere online
Social influence is evident everywhere online
Unsurprisingly, it seems that I am not the only one noticing this. The above picture comes courtesy of Joshua Porter of Bakardo Social Design. http://bokardo.com/archives/how-social-is-amazon/
Continued from “Markets are social” slide… … This phenomenon extends to customer markets. Functional features undoubtedly play a role in the product one decides to purchase, and this makes up for the rational perspective of a purchase. But, perceptions of self-esteem, belonging and power also play a large (mostly subconscious) role in many purchases. We use our purchases as symbolic badges of association and statements about ourselves, as much as for their functional benefits. Generally, this is done without realising it. Unwittingly, we align ourselves with our own self-image and the groups that we think we belong to (or don’t want to belong to). We do this in numerous ways: the way we dress, the cars we drive, the stores we choose to shop at, and the types of food we keep in our fridges. This is the emotional side of the purchase decision, and a very large part of it relates to how we perceive ourselves in relation to others. A huge aspect of our purchase decisions - one that, arguably, colours all our decisions - is purely social. It is important to keep this in mind when we start looking at the runaway success of market-dominant brands.
Goths, emos, punks – all reactionary groups to societal norms and pressures?
“ Sheeple” 
Don’t even try and escape… ;)
Skittles eventually toned down its level of social media integration on its website as undesirable brand mentions began to show up. This opens up an interesting debate on the pros and cons of their approach and subsequent reaction that is beyond the scope of this presentation. Read more: http://www.mediapost.com/publications/?fa=Articles.showArticle&art_aid=101402 http://www.socialcustomer.com/2009/03/skittles-social-media-experiment.html
Let’s take a step back and examine how markets form from a purely analytical point of view. Let us start off with a thought experiment. Imagine we have five brands in a new market, none of which have any users yet. Imagine that ten shoppers approach the new brands on the store shelf. Assuming that each brand is lined up in a row on the same shelf, there is little basis for a shopper to choose any one brand over another. Thus, the probability of any one brand being chosen is 0.2 (a 1-in-5 probability – see Round 1 ). Now imagine that Brand 1 pays the retailer for an additional shelf facing ( Round 2 ). The retailer has a finite amount of shelf space, which means that one of the other brands must lose a facing for Brand 1 to receive it (let’s assume that Brand 5 loses out in this case). In our simplistic example, with this single act, Brand 1 has increased the probability that a shopper will choose it over a competitor brand. Brand 1 now has a 0.3 probability of being chosen, while Brands 2 to 4 have a probability of 0.2, and Brand 5 of 0.1. Brand 1 is now more likely to be chosen by future shoppers. Where all brands initially started off with an equal probability of being chosen, Brand 1 now has an advantage (and Brand 5 a disadvantage); and, this advantage is not necessarily due to Brand 1’s functional superiority over the other brands. In another scenario, Brand 1 might have gained an initial boost by some non-commercial means. A bulk shopper may have arrived and, deciding that all the brands looked about the same, bought all of Brand 1’s units on a whim. The retailer, seeing that Brand 1 appears to be the top seller, might give it an additional shelf-facing in future. Whatever the case may be, for the purposes of our thought experiment, Brand 1 is now more likely to be bought than any of the other brands despite being qualitatively very similar to the others.
Let’s assume that a second wave of shoppers enters the store. Brand 1 fares much better this time, with higher sales than its competitors. Now, as it turns out, Brand 1 isn’t all that bad. It does what it promises on the back of the box and it fills a need in shoppers’ lives. So, Brand 1 purchasers start talking to their acquaintances and making recommendations when asked for their opinion, just as the purchasers of Brands 2 to 5 are doing. Unfortunately for Brands 2 to 5, they have fewer advocates working on their behalf. Word spreads about the supposed virtues of Brand 1, just as word is spreading about Brands 2 to 5; however, word of these brands is spreading slower. With just a single additional advocate, word of Brand 1 is reaching increasingly more people with every additional person that is being told about the brand.
The Ego image taken from Duncan Watts’ fascinating book, Six Degrees: The Science of a Connected Age (2003) , does a great job of illustrating the theoretical boost in word-of-mouth a brand can attain over its rivals from initially having just a single additional advocate. The bar chart gives you an idea of the accelerating rate at which word of Brand 1 spreads. Initially, Ego starts off as the only advocate. He then tells five people, who in turn tell another five people. In three easy steps, Ego has reached 105 people, which implies that the rate at which Ego is reaching people is not increasing linearly. It is increasing at an accelerating rate as the chart below illustrates. Brand 1 now has a clear advantage. Not only does it have a greater chance of being bought, but its chances of being bought are growing at a greater rate than those of its competitors. This means that awareness of Brand 1 is crowding out awareness for the other brands. More people are hearing about it, talking about it, and going out to buy it. As more and more people buy it, word spreads even more, and subsequently, more and more people buy it. Brand 1 has just become the most popular brand in our thought experiment and all it took was an additional shelf-facing.
http://en.wikipedia.org/wiki/Steven_Pinker “ Steven Arthur Pinker (born September 18, 1954 in Montreal, Quebec) is a prominent Canadian-American experimental psychologist, cognitive scientist, and author of popular science. Pinker is known for his wide-ranging advocacy of evolutionary psychology and the computational theory of mind. Pinker’s academic specializations are visual cognition and language development in children, and he is most famous for popularizing the idea that language is an "instinct" or biological adaptation shaped by natural selection. On this point, he partly opposes Noam Chomsky and others who regard the human capacity for language to be the by-product of other adaptations. He is the author of five books for a general audience, which include The Language Instinct (1994), How the Mind Works (1997), Words and Rules (2000), The Blank Slate (2002), and The Stuff of Thought (2007). Pinker's books have won numerous awards and been New York Times best-sellers.”
Sometimes big brands make the choice easy for us by removing/minimising said choice!
NOTE: There are many candidate generative mechanisms that produce power law distributions. For the purposes of this paper/presentation, we only focus on preferential attachment.
As a new customer, who am I most likely to pay attention to? We may have many brands shouting for our attention, but the biggest brands often shout the loudest because they have the biggest budgets for marketing and advertising.
Ranking brands in terms of brand size, an inequality in terms of “shouting strength” amongst brands becomes evident…
” "What's in a name? That which we call a rose / By any other name would smell as sweet." ~ William Shakespeare, Romeo and Juliet (II, ii, 1-2) We now have a basic understanding of the mechanism that seems to be at play (this inequality in terms of brand size). The next question that springs to mind is what do we call this mechanism? It actually already goes by many names (since nothing is ever really new): cumulative advantage, preferential attachment, the Pareto Principle, the Rich-Getting-Richer Effect, the Matthew Effect, double jeopardy, Zipf’s Law, power laws, etc. These names are invoked whenever one is trying to describe some quantity that… “… is distributed among a number of individuals or objects according to how much they already have” [Wikipedia, 2009] In other words, a quantity is distributed with a probability distribution proportional to the size of the existing entities in the environment [Dorogovtsev & Mendes, 2001; Barabási & Bonabeau, 2003; de Menses, et. al., 2005].
Some of the earliest versions of a preferential attachment mechanism (the most descriptive name in my opinion) were described by the Pareto Principle and Zipf’s Law. The Pareto Principle (which went on to much fame and success as the Pareto Distribution) is sometimes referred to as the 80/20 Rule. In 1906, Italian economist Vilfredo Pareto observed that 80% of Italian property was owned by 20% of its population [Wikipedia, 2009]. The distribution fell out this way (80/20) due to the preferential attachment mechanism just discussed – the rich accumulated property at a faster rate than their less wealthy countrymen. The more land they had (a proxy for wealth), the more land they were likely to acquire . More anecdotally, 80/20 is used as a rule of thumb for the equilibrium balance that arises due to this mechanism (that is, the trend seems to slow down once the disparity in the environment reaches an approximate 80/20 split) and it has spawned an entire sub-category of self- and business-help books, seminars and lectures.
This is probably the most simple and widely recognised application of a preferential attachment mechanism at work. We are all familiar with the saying, “you need money to make money”, and this is a perfect example of agents being allocated a quantity (money) based on how much they already have. The more money one has, the easier it is to make even more money as you are able to invest your cash for increasing returns and pay for the allegiances of others. This accounts for why the few wealthiest people in the world are unlikely to diminish in wealth any time soon, and why their collective wealth dwarfs that of the vast majority of the world’s population. Preferential attachment tells us that this gap isn’t likely to decrease if markets are left to their own devices (a debate outside the scope of this paper). This is the universal truth that Vilfredo Pareto struck upon.
A passage from the Christian Bible has been borrowed to describe another version of the rich-getting-richer effect: “ For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath.” - Matthew 25:29, King James Version The term was coined by sociologist Robert K. Merton in 1968. Essentially it is another take on the distribution of a quantity within a population based on how much each agent already has. Merton coined the term to describe, among other things, why eminent scientists tended to receive more credit for their work in comparison to similar work by less well-known scientists [Merton, 1968, 1988].
Chart description: An example of the long tail distribution. Traditional brick and mortar retailers are only capable of carrying the few well-known products in their catalogue, while warehouse and digital retailers are able to carry more due to the lower cost of keeping stock [Image: Wikipedia, 2009] In 2004, Chris Anderson wrote an article for Wired Magazine in which he coined the term “the Long Tail” to describe the business strategy adopted by companies such as Amazon.com, Netflix and the iTunes Store. A large part of these companies’ revenue comes from the frequent small sales of the less popular items in their catalogues, which collectively add up into a sizeable chunk of these businesses’ overall revenues. Traditional business wisdom says that most of your sales come from a few popular items since it is costly to keep inventory of, and distribute, rarer items. However, thanks to the internet, it is now cheaper for retailers to hold a greater variety of stock without having to maintain a physical presence and it is easier for customers to exercise their freedom of choice by discovering and purchasing ‘rarer’ items. A few items still tend to dominate though (a quick glance at Amazon.com at the time of writing this, February 2009, shows that the top spots belong to the likes of Coldplay, U2 and Bruce Springsteen), and this consistent inequality in popularity is another example of preferential attachment at play. Anderson (2004) even describes the value of a preferential attachment mechanism in the formation of the Long Tail. He describes how customers require a non-random initial entry point, or how they need to be swayed in their purchase decisions, for the Long Tail to form. MP3.com proved that giving customers a random entry point did not work (note my emphasis in italics at the end): “ In 1997, an entrepreneur named Michael Robertson started what looked like a classic Long Tail business. Called MP3.com, it let anyone upload music files that would be available to all. The idea was the service would bypass the record labels, allowing artists to connect directly to listeners. MP3.com would make its money in fees paid by bands to have their music promoted on the site. The tyranny of the labels would be broken, and a thousand flowers would bloom. Putting aside the fact that many people actually used the service to illegally upload and share commercial tracks, leading the labels to sue MP3.com, the model failed at its intended purpose, too. Struggling bands did not, as a rule, find new audiences, and independent music was not transformed. Indeed, MP3.com got a reputation for being exactly what it was: an undifferentiated mass of mostly bad music that deserved its obscurity. The problem with MP3.com was that it was only Long Tail. It didn't have license agreements with the labels to offer mainstream fare or much popular commercial music at all. Therefore, there was no familiar point of entry for customers, no known quantity from which further exploring could begin .”
Double jeopardy is a generally accepted term in the marketing world. It was coined by William McPhee in the 1930s. McPhee noticed that popular radio stations had more listeners than their less popular rivals, and that popular stations’ audiences listened to them for longer on average than their rivals. He also noticed a similar effect among newspaper comic strips. Popular strips had more readers and their readers read the strips more frequently. He termed this ‘double-whammy’ effect that worked in favour of big brands and against small brands the ‘double jeopardy’ effect [Ehrenberg, et. al., 1990; Sharp, 2003 ]. The bar charts recreates McPhee’s original double jeopardy finding. It is a contemporary example of double jeopardy in action using data from a modern newspaper market. One of the foremost researchers and proponents of the double jeopardy effect is Australian market researcher, Andrew Ehrenberg, who seems to hint at a preferential attachment mechanism with the statement that: “ Double jeopardy trends have been reported for a variety of loyalty or liking measures when customers choose between items that are similar but differ in their popularity” [Ehrenberg, et. al, 1990] Indeed, McPhee had his own explanation for why Double Jeopardy occurs (as summarised by Ehrenberg, et.al., 1990) that closely mirrors our earlier thought experiment: “ McPhee’s (1963) theoretical explanation for DJ arose from his noting an asymmetry in people’s familiarity with, or exposure to, items that are similar but differ in popularity. For instance, suppose there are just two restaurants in town, one widely known and the other more obscure. Suppose also that people who know both restaurants regard them as being of equal merit (equal in quality, service, value for money, accessibility, etc.). If people are asked which is their favourite, a DJ effect is bound to occur. The reason is that of the many people who know the popular restaurant, most do not know the more obscure one exists and cannot mention it if asked for their favourite. In contrast, of the few people who know the obscure restaurant, most also know the popular one. Hence they will “split their vote” – they are equally likely to mention either restaurant as their favourite (or say “undecided”) because we have supposed the two restaurants are of equal merit to those who know both. Of the many people who know the popular restaurant, most therefore will rate it their favourite, whereas of the few who know the obscure one, only about half will say that it is their favourite. This is a classic double jeopardy effect.” [Ehrenberg, et. al., 1990] Finally, Ehrenberg, et. al. (1990) draw a parallel between double jeopardy and gravity, which I think is perhaps a truer comparison than they might have realised at the time: “ Trying to buck the DJ trend might look suspiciously like trying to make aeroplanes fly by waiting for breakdowns in the law of gravity.”
Cumulative advantage has become a buzz word recently. Somewhat surprisingly, it was first coined as far back as 1976 by physicist and information scientist, Derek J. de Solla Price. Price noticed that the number of citations scientific papers received followed a Pareto distribution, or power law (see subsequent slides). Some papers received many citations, while most received relatively few. The phrase ‘cumulative advantage’ neatly describes how an idea, brand or celebrity accumulates an advantage over time based on its initial popularity. It is another example of our initial definition of preferential attachment – popularity is distributed among individuals or brands based on their existing popularity. The effect has been shown to apply to the popularity of musicians [Watts, 2007] and people’s preferences for artworks [Campbell & Liddle, 2008], but it can be transplanted into other diverse areas (for example, economic bubbles, which rely on traders taking their cue from other traders). What is particularly interesting about the cumulative advantage phenomenon is that it has been demonstrated that by arbitrarily assigning entities with ratings, one can affect the subsequent popularity of the entities. This process does not bias established perceptions, it actually creates perceptions. If I see that those around me love a product, I am more likely to actually like it myself. Social interactions are the stuff that perceptions are made of (at least partly).
Let us look at Campbell and Liddle’s experiment as an example. Group 1 (control) was not exposed to any social influence, Group 2 saw others’ ratings of the artwork and Group 3 saw the ratings and user comments ( Appendix 1 summarises their experimental design). Simply by displaying the ratings (out of 10) for several artworks featured on a website on-screen, it was found that it was possible to amplify or dampen the popularity of any specific artwork. Artworks with initially high ratings (e.g. 9 out of 10) ended up being rated higher overall than artworks with low initial ratings (e.g. 4 out of 10). This pattern was consistent across the control and experimental groups, even when the initial ratings and comments were randomly and arbitrarily assigned and varied between experimental groups. This tells us that people are subconsciously biased by cues like ratings when forming their own preferences. This has implications today more than ever, as so much of our communication and socialising is done online and via social networking platforms where ratings and preferences are particularly easy to communicate to (and thus influence) others. As the saying goes, “first impressions count”. In fact, as Campbell, Liddle and Watts have found, they could potentially be the make-or-break factor for your brand. As we discussed earlier, markets are social and it is social interaction that reinforces the popularity of entities, feeding the cumulative advantage effect, which takes hold due to social cues such as people’s brand ratings. In this way, we see that cumulative advantage essentially represents the same preferential attachment mechanism (the strength of a rating is given based on its existing strength). However, the only difference is that the term has until now only been narrowly applied within the context of popularity. The basic, underlying mechanism is the same though.
In 1932, Harvard University linguist, George Kingsley Zipf published Selected Studies of the Principle of Relative Frequency in Language. Part of his research consisted of counting how many times each word appeared in the English dictionary. His surprising finding was that the frequency with which the words appeared followed a pattern. He noticed that the most popular word in the dictionary (“the”) appeared about twice as often as the second most popular word (“of”) and roughly three times as often as the third most popular word (“and”) [Pfanner, 2007]. Table 1 is an example of a frequency table that ranks the top ten words in the English language based on how often they occured in a specific corpus [Croft, 2002] . This is done in a similar manner to how Zipf would have done so as part of his original research published in 1932.
A preferential attachment mechanism can result in a multitude of distributions that, while they all follow the same fundamental principle, differ in their scale. Zipf’s Law is one example of a specific preferential attachment distribution that always results in the same scaling exponent (more on that in the next section). Many other examples of distributions with a specific scale exist, most of which are named after the person who first identified the consistent pattern in their field. Considering the ubiquitous nature of this class of distributions, it is unsurprising that so many researchers have stumbled across specific examples in such a diverse range of interests.
The Pareto Distribution and double jeopardy move us in a slightly more empirical direction in contrast to the loose rules of thumb described by the likes of the 80/20 rule, the Rich-Getting-Richer Effect, the Matthew Effect, the Long Tail or cumulative advantage. All these approaches have one thing in common though – they describe a non-linear tendency towards an inequality that forms over time. However, there is a more technical name for this class of non-linear distributions that is used in disciplines as varied as physics, mathematics, biology, economics, linguistics and finance. Such inequitable distributions are technically referred to as ‘ power laws’ . They are so named due to the formula that describes a power law distribution: f(x) = ax k + o(xk) … where k (in super-script) is the scaling exponent (or the ‘power’) that defines the slope of the curve and the only number you really need to worry about. Power law curves differ from the traditional Bell Curve which underlies many statistical assumptions. Unlike a Bell Curve, where most of the individual observations are very similar and outliers are treated as less important anomalies, a power law curve focuses on these so-called ‘outliers’, with its few very large observations (the ‘outliers’) and many smaller observations (which are sometimes referred to as “the Long Tail” and are the traditional domain of the Bell Curve).
The above maps of the USA give us an idea of how networks with normal distributions differ from networks with power law distributions. Normally distributed networks tend to have a grid-like layout, where nodes all have relatively low degrees, while the overall average path length is long. An example of such a network might be road networks. In contrast, networks with power law distributions tend to have a few highly connected nodes, and many poorly connected nodes. Despite this, the average path length is low as the few highly connected nodes act as hubs capable of connecting all other nodes in a relatively few number of steps. Such a network is more characteristic of an airport network, where a large amount of traffic is routed through a few particularly busy airports (e.g. JFK, O’Hare, etc.).
And in so many other areas of nature… !
NOTE: Taleb warns that many of these are only very rough estimates of the various scaling exponents and should be used for illustrative purposes only.
It is very easy to spot what appears to be a power law by inspection, but it is more difficult to prove that a specific distribution is, in fact, a power law. The first step to identifying a power law should be to rank the data based on size or frequency. This should uncover the characteristic few large observations to the left and many small observations to the right.
The next step would be to perform a log-log linear transformation on the distribution. If a power law exists, you should get a straight line, with a slope of k.
Getting a straight line with slope k after performing a log-log transformation is a good starting indicator that you are dealing with a power law. However, this is still not enough as other similar distributions can also give you straight lines (e.g. exponential distribution). In order to be thoroughly rigorous, you need to fit a curve to the data and ensure that no other distribution type gives you a better fit. I will not go into the details of how this is done here (see Appendix 3 ), suffice it to say that it can be challenging if you come at it from a standing start, as we discovered, especially when dealing with discrete data.
So far we have laid out the theory behind how markets (and many other natural environments) form. The next question is, do markets form based purely on preference or attitude like many other environments? The answer may seem obvious as we have just discussed, but we all know where assumptions lead us, so the remainder of this paper deals primarily with this question.
The first port of call when identifying whether a dataset follows a power law curve or not is to rank the brands by size and see whether there is a non-linear relationship between the largest and the smaller brands in the market. Below are two examples of this approach. From the charts on this slide, we can see that the mustard market displays what looks like it might be a power law, while the cheese market does not (it doesn’t display the characteristic steep drop-off between the first two ‘brands’).
Next, we perform a log-log transformation on the dataset [Goldstein, et. al., 2004; Newman, 2005; Clauset, et. al., 2008] to see if we end up with a straight line (with a slope of k , the scaling exponent). The figures seem to support our initial hunches. The mustard market looks somewhat like a straight line, while the cheese market does not. There are several likely explanations for why the cheese market looks the way it does: perhaps the market is relatively new and thus still in a state of flux, or, perhaps market entrants have created disruptive innovation and thus the established structure has been shaken up. What may also be the case is that research-specific issues are to blame. Collecting reliable and representative data is always a challenge so it needs to be clear that the correct sampling methodology was used and that it was strictly adhered to by field workers. In addition, the second research-specific question that springs to mind is has the market been correctly defined? Do all the cheese types in the brand list really compete against each other? For example, when visiting the store to buy cheese for my children’s school lunches am I really going to agonise over the choice between Gouda and Camembert? If the answer is “no”, then they should not be included in the same brand list. When one starts reading the literature on the subject, many are happy to stop at a log-log transformation when identifying a power law. Unfortunately, while getting a straight line in your log-log transformation is a necessary criterion, it is not a sufficient one for pronouncing the existence of a power law since other distributions might also give you similar results.
In order to be truly thorough (and even here there is still some debate as to whether this is thorough enough), you need to indulge in some curve fitting, which is exactly what we did with the gracious help of Aaron Clauset of the Santa Fe Institute and Michel Goldstein, currently at Yahoo [Goldstein, et. al., 2004; Newman, 2005; Clauset, et. al., 2008]. We took 46 datasets that covered a diverse range of categories from around the world and fitted a power law curve to each one. The results show that a pure power law is seldom present, with goodness of fit scores tending to range between 0.1 and 0.4 (in this case, the lower the score, the better, since we are measuring the distance the actual curve is from our best fitting power law curve, and you want the distance to be small - see Appendix 2 for a summary of our results).
So far we have spoken about the ubiquity of power laws, but do we really see them everywhere? The answer is “no”. If we refer back to our original definition - that of ‘a quantity being distributed based on how much each entity already has’ - it is clear that this doesn’t always happen in nature. If we think of areas where we do see power laws forming, we realise that one of the defining characteristics of each environment is that the ‘cost’ of distributing a quantity to any of the entities in the environment (whether in the context of proteins, people, computers or meteorites) is low. Putting it another way, it is similarly efficient to distribute a quantity to any entity because there are few environmental ‘barriers’ making it more costly in terms of the energy, time or money to distribute to one entity over another. Where there are costs, we see distributions that might tend towards inequality, but do not reach the expected state described by a power law. This means that, although the potential for a power law seems to always exist, we only see power laws actually forming in relatively ‘frictionless’ environments. The presence of barriers in the environment skews this natural tendency.
Returning to the example of the internet, we see that few websites tend to have many links, while most websites have few. Similarly, in the physical world, we see that a few servers, dotted around the globe, tend to act as internet hubs, re-routing a disproportionately large amount of network traffic, while most servers deal with a relatively low amount of traffic. Kottke (2003) went so far as to plot the distribution of incoming links to the top 100 most linked to blogs as defined by the blog tracking website, Technorati. The result followed a power law distribution. This is consistent with what we would expect as the cost of adding an additional link to one’s blog is relatively low. And, we know that the internet environment is teeming with social influence in every facet of its make-up, so it is unsurprising that a few blogs end up being the most popular. The more inter-connected an environment is (in this case via social networking), the greater the chance that the agents in the environment will fall into lock-step. As a result, the internet is a good example of an environment where social influence is high and transaction costs are low, resulting in power law distributions forming naturally. In summary, power laws form when there is some kind of non-random, generative selection process at play - in this case preferential attachment. This is most likely to occur in a small-world network, particularly one wherein the cost of creating new links is relatively low, or, to put it in marketing-speak, in which the market is relatively frictionless.
The internet is a good example of an environment that is particularly prone to falling out in a power law distribution [ Barabási and Bonabeau, 2003]. Such environments, or ‘networks’, have been named ‘small-world networks’ by network theorists Duncan Watts and Steven Strogatz (1998). One of the properties of a small-world network is its “scale-free” nature. Describing a network as scale-free implies that there is no consistency in the scale of the network. A few nodes (re: servers or websites) have an almost unlimited number of connections, while most have very few, which makes looking at the average or median number of connections misleading as they do not accurately describe the topology of the network. Hence, we describe such environments as ‘scale-free’ – they have no scale . Power laws form when the cost of distributing a quantity - or in network terms, the cost of creating new links between nodes - is low. As Watts (2003) puts it, “ the essential limitation of scale-free networks is that everything is assumed to come for free …without regard for the difficulty of creating or maintaining them [links between nodes]”. This brings us back to what we have just said about where power laws form. They form when the cost of distributing the quantity is low, or when it “comes for free”.
One of the most common alternatives to a scale-free, small-world network is a random network. Random networks form the basis of much of the field of graph theory, the foundations for which were laid by Paul Erdős and Alfréd Rényi in 1959. Random networks tend to have a scale. That is, the mean number of links to individual nodes acts as a decent description of the network. This is because links tend to be fairly uniformly distributed across all nodes in a random network [ Barabási and Bonabeau, 2003]. The figures in the previous chart show the differences between a random network and a scale-free network. The earlier network illustrations of the U.S. continent may also help with your conception of the differences. The difference between small-world networks and random networks is betrayed by the word ‘random’. Small-world networks are not random. So, if links are not made at random in small-world networks, what is the non-random process at play? The most popular candidate put forward is none other than our preferential attachment mechanism [ Barabási, 2002 and Watts, 2003 ]. In a small-world network, links are more likely to form based on the number of existing links a node has. This is why certain celebrities end up being more popular – because individuals’ preferences for celebrities are influenced by the people (re: nodes) around them. In much the same way, an individual’s brand choice is influenced by existing brand popularity among the people around them. On a related note, this process can be extended to (at least partially) explain the popularity of a political ideology or religion over its rivals.
I subscribe to a framework that informs my philosophy about brands. I, along with my colleagues, believe that a brand’s market share is influenced by a few elements – the brand’s power in customers’ minds and its power in the market place, onto which we overlay the power of execution (how effectively your actions are executed). A brand’s power in the mind is a purely attitudinal concept while its power in the market (in terms of market factors) is more functional. The framework says that the interaction of these concepts results in a brand’s actual business results. A brand’s power in the mind describes the share a brand would receive if customers were able to act purely on their preferences in a frictionless market – one in which customers are able to purchase their first choice of brand, regardless of price, distribution or any other form of impeding factor. For example, my preferred make of car is a Porsche. If I was able to go out today and purchase one without any consideration for price or availability, I would be acting purely on my attitudinal preference. However, in reality, we know that this is often not the case. There are many factors which modify customers’ purely attitudinal brand preferences and these elements are captured by a brand’s power in the market. I refer to elements that affect a brand’s power in the market as ‘market modifiers’ (for example, price, availability of the brand, distribution channels, contractual obligations or even the length of queues at outlets).
In a frictionless market - in other words, a market in which customers are able to act perfectly upon their preferences and buy their brand of first choice– customers’ purchase decisions are more likely to align with the preferences of others, for as discussed, we do not create our preferences in isolation. Rather, they are, at least partly, influenced by the opinions of others in their network environment. However, when faced with market factors, customer purchase decisions stand the chance of being modified. While my original intention was to buy a Porsche, upon checking my bank balance (price), I realised that this decision is not viable. Thus, market modifiers prevent market share from forming based purely on preferential attachment. The implication of this is that markets have a tendency toward inequality as defined by a preferential attachment mechanism, but environment-specific modifiers prevent a perfect power law distribution from forming as they raise the ‘cost’ of creating purely attitudinal attachments.
It is worth remembering that preferential attachment often kicks in accidentally (as we saw in our initial thought experiment). The initial success of Crocs shoes is a good example (before the trend ran its course). However, it also appears possible to manufacture success to some extent, as illustrated by the success of pop stars like Britney Spears and Justin Timberlake.
Some researchers have assumed that power laws exist as a matter of course [Hofmeyr, 2007, 2008]. I agree with the belief that all markets tend towards a power law as I think the literature on this is consistent and robust. However, we do not yet have the hard numbers to prove it. It is likely that researchers that already subscribe to this theory have been looking at markets which are already intuitively more homogenous (e.g. fruit juice). This makes it easier to confirm the theory. However, research samples and market definitions often are not as homogenous as we would like, and there is still much research to be done in the area of identifying homogenous surfaces. What our explanations do show however is that most markets, while they tend towards inequality, as evidenced by the wide-ranging prevalence of the double jeopardy effect, do not follow perfect power laws and are thus not fully scale-free. The next step in the process is to quantify the factors that are modifying our markets, and thus preventing pure power law formation. Again, some have already started down this road, but lack hard, quantitative evidence for this approach. This is not to discount these approaches, but rather to say that right now we are working on the basis of well-informed and heavily supported conjecture.
Considering that power laws are more likely to form in markets where customers are able to act on their purely attitudinal preference, we would expect to see a correlation between: 1. How closely a market’s structure follows a power law (i.e. its goodness of fit), and, 2. The level of friction in the market (i.e. are customers able to ‘slide’ into their brand choice, or do market factors modify their final destination?) Some previous work has been done in this area, at least in terms of examining the level of friction in the market. Patel (2005) discovered that the strength of relationship a brand has with its users predicts market share even better in low-friction markets than higher-friction markets, which seems to lend credence to the hypothesis that attitudinal measures predict best in low friction markets. --- In order to minimise some of the guess work, our next step would be to see whether there is a correlation between the level of friction in a market and how closely it resembles a power law curve. As mentioned in our initial hypothesis, we would expect lower-friction markets to more closely resemble a power law curve. Unfortunately, time did not allow us to pursue this unanticipated branch of our research. However, this area definitely warrants further research, with top priorities being the development of an accurate friction measure and the identification of more homogenous datasets. Based on what we know at this point though, what does the role of friction in market share formation appear to be? Purely attitudinal choices have a high signal-to-noise ratio. That is, decisions made on the basis of personal preference are more likely to translate directly into power law distributions when aggregated. However, market modifiers reduce the signal-to-noise ratio, thus diminishing the likelihood of a power law forming. They essentially ‘interrupt’ the one-to-one translation of choices based on preference into power law distributions.
This paper/presentation is about how market share forms. We looked into one of the potential mechanisms at play and summarised the disparate early attempts at articulating what a power law is. Terms such as the Pareto Principle, Zipf’s Law and cumulative advantage have all been coined to describe a consistent pattern of inequality that seems to pop up in many areas of society and nature. We have also touched on a strong candidate mechanism for why this inequality arises in the first place, called preferential attachment. We looked at how preferential attachment applies to markets and the role that market factors play in modifying pure power law formation. It appears that power laws are more likely to form in the absence of impeding market factors; however, it also seems that the ‘ghost’ of a power law exists in all markets, waiting to fully manifest itself. This understanding gives us an insight into how people behave, how we are influenced by our environment and why markets do not always fall out in a 100% rational manner – why the best product doesn’t always win and why the gap between the haves and the have-nots always emerges in society. I started out this paper with a definition of systems thinking, which I believe is the necessary mindset one must have in order to understand something as complex as a market. Great strides have been made in recent years towards the creation of a toolbox for understanding complex systems. The tools in this toolbox have been donated from a diverse range of inquiry, which itself is a reflection of the complex, interacting systems we are trying to understand. In order to truly understand the systems we are dealing with, whether as marketers, policy makers, scientists or human beings, it is absolutely necessary to adopt an inter-disciplinary approach to research and knowledge that acknowledges the limitations of our individual domains and recognises the value a different perspective can bring to a potentially myopic point of view. Understanding some of the concepts touched upon in this paper, such as power laws and network theory, is vital to the understanding of complex systems such as markets, and the agents that act within them. While this paper is by no means the final word on the topic (or even the first), hopefully, it serves as a teaser to the new possibilities currently being raised by contemporary scientific thought. Finally we are at a point where we can actually start understanding how the complex systems that make up nature and life really work.

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