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Justin Bieber, Social Networks and How Numbers Can Lie

2010 May 23

What do you know about Justin Bieber?  If you’re not a teenage girl, the answer is probably not much.  Yet if you want to a glimpse at the future of business, you should take another look.

He is a prime example of how our world is changing and how we’ll have to change with it.  Understand Justin Bieber, and you’ll know why business statistics have a serious flaw and how numbers often lie.

The Justin Bieber Story

I’ve been living outside of the US since 1997, when Pearl Jam was still cool.  I get back every few years and, from what I gather by the rolling eyes of my teenage nieces, I’ve become decidedly less hip in the interim.

However, even I couldn’t escape Justin.  Apparently, what started out as his mother posting videos on YouTube became an internet sensation.  His videos were viewed millions of times even before he released his first album, which has sold nearly a million copies.  (For the full story, see here)

That makes Justin the first true social media star.  He says he feels like he won the lotto, but actually his story is far less likely than that.  According to the way today’s businesses are run, his story is more than unlikely, it’s inexplicable.

Justin Bieber in a “Normal” World

Most of business statistics are based on the “normal” distribution, which assumes that events are independent and randomly distributed.  It looks like this:

Normal Distribution

Normal distributions are especially convenient because we know a lot about them.  When things really do happen this way we can predict the probability that a potential event will happen with amazing accuracy

Gauss first used this model to predict the movement of celestial bodies (which is why it is often called a Gaussian curve).  Einstein used it to prove the existence of atoms.  In the 1960’s and 1970’s wizards used it to revolutionize the financial industry (in hindsight, with mixed results).

Statistics based on this “normal curve” have been employed extensively in risk management, financial engineering, confidence testing and a lot of other things.  We use these statistical models to make our businesses more predictable, and therefore more valuable.

However, the normal curve has some problems with young Justin.

Let’s take twitter:  The average twitter user (in the middle of the curve) has 126 followers, while Justin has 2.5 million.  He’s what statisticians like to call an “extreme outlier.”  Unfortunately, normal curves don’t account for the extraordinary.

In other words, according to the statistics of Gaussian curves, Justin Bieber doesn’t really exist mathematically.  He’s just “one of those things.”

Justin Bieber in a Skewed World

Of course, statisticians aren’t that unreasonable.  They have ways of dealing with unruly young data points like Justin Bieber.  It’s called a skewed distribution and it looks like this:

Skewed Distribution

This makes a lot more sense.  There is a lower limit to twitter followers: zero.  After all, you can’t have negative followers.  On the other hand, there is no limit on how many followers you can have, so we can expect a curve skewed towards large numbers.

Unfortunately, we know much less about skewed data sets.  All we can do is use some integral calculus to evaluate young Justin’s chances based on existing twitter users.  However, we would conclude that the probability of Justin Bieber is so unlikely he’s not worth paying attention to.

The smart business move would to be to leave poor Justin by the curb.  Or, if your preferences are more Dickensian, let him sweep out coal chimneys 18 hours a day.  That’ll teach him some character!

Have You Declared Independence?

Now we get to the tricky part.  Math is highly subjective. It involves assumptions.  In this case we assume that events are random and independent.  Make the wrong assumptions and you use the wrong math which will lead to the wrong conclusions. Your numbers will lie.

For the most part, business statistics have worked over the past decade because the independence assumption served as a useful fiction.  The models predicted well enough, as long as you didn’t take them too literally.

That’s what’s fundamentally changed.  Globalization and an interconnected world have made the independence assumption untenable.  Interdependence creates feedback loops and a much more volatile and dangerous world.

The problem is that the normalized world has become so pervasive that we don’t even think about it any more.  Every time you expect things to “average out” or believe a poll or bet a billion or two on derivatives, you are declaring independence.

(Multi-million dollar bonuses can help to inspire such beliefs).

Yet, there is an alternative.  In the late ’90’s, some very smart people started to unravel the interconnected world and successfully explained how networks work. That’s where we’ll find Justin Bieber starts to make more sense.

The Fitness of Justin Bieber

Let’s imagine for a moment that Justin Bieber is a very talented young man and that talent counts for something.

Talent doesn’t figure into conventional statistics, but Albert-László Barabási found that the numbers don’t work without it.  He calls his method the fitness model of networks (and his paper describing it is one of the most cited ever).

In this model, there are two key variables: fitness and links per node, both of which are mutually reinforcing.  When you have a node that is “fit” or good at its function, it attracts links.  The more links it has, the more probable it is that it will gain new ones (the rich get richer).

It also works the other way, a new more fit node will attract links from an existing one, which will diminish the size of the incumbent and decrease its ability to gain a following even further.   Feedback loops are integral to a functioning network.

The more complex and interconnected the network is, the more feedback loops and volatility.  Technologies like the Web and Social Media accelerate the process. The Semantic Web will propel it even further and faster.

In this model, Justin Bieber isn’t an anomaly, he’s a natural consequence (as are market boom and busts as well as other forms of turbulence).

How To Conquer Bieber’s World

Understand the New Forces: Michael Porter’s old five forces framework needs to be updated.  The new forces of chaos, networks and the semantic web are mutually reinforcing and will drive the future.

The old reductionist methods of isolated variables and predictability are no longer effective (if they ever were).

Develop New  Metrics: It’s difficult, if not impossible, to manage what we can’t measure.  While there is still much work to be dome, some basic models have been developed to help us better understand financemarketing and organizations.

Learn to live with uncertainty: The biggest change is that the new models are fat-tailed, meaning that they allow for considerably more extreme values than the old “normal” statistics assumed.  Outliers can no longer be a considered uncomfortable curiosities, but must be incorporated into any strategic process.

Which brings us back to young Justin who, for all his newfound fame and fortune, is still a sixteen year old boy with a great deal of trials and tribulations in front of him.

Let’s wish him luck.

– Greg

14 Responses leave one →
  1. May 24, 2010

    Great post. Having just finished an MBA and survived corporate strategy framework overload, I agree that some previously held (revered, even) assumptions fail to capture the changing dynamics of business in the internet age.

  2. May 25, 2010

    Thanks Dan. Congratulations on your degree and good luck!

    – Greg

  3. May 25, 2010


    I enjoyed your post and thanks for sharing the Justin B story. My daughter has the “Beiber Fever” and so does all her friends. I asked her about him and she said “Come On Dad” he’s all over Youtube. You could imagine how I felt.
    A light bulb turned on when she showed me the video. It was at that moment I realized just how powerful this social media/Youtube thing is and how the marketing and sales landscape is changing, and methodology used today will be obsolete in a few years if not months.

    The companies that can understand how to navigate in these un-chartered waters will be the ones that survive the rough seas of competition. It’s going to be a place for ingenuity and innovativeness in the marketing arena. People like you should thrive in this environment.

    One more thing, “Statistics and Probability Does Not Make It So” It’s the outlayers, the fringe, the edge and to even despise logic. It is the understanding and working at that level which will result in novel creative and game-changing endeavors. It is my hope our leaders and and educational system picks up on that course to truely tap our collective potential.

    Again thanks for the post,
    You can read my ramblings at


  4. May 25, 2010

    Thanks, Tony.

    Good luck with your blog!

    – Greg

  5. harold permalink
    July 14, 2010

    as a statistics graduate, it’s all about how you read them. i realize one can make numbers say whatever you want them too…

  6. August 7, 2010

    Does anyone still think this is a “normal world?” 😉

    Normal distribution models are irrelevant in any large scale networked system.

    The mathematical model for social networks (and a staggering number of natural and man-made phenomena) is power law. Specifically, here’s an article by Clay Shirky from seven years ago describing the inevitability of “Justin Bieber’s.”

  7. August 8, 2010

    Thanks for the tip, John.

    Have a great week.

    – Greg

  8. August 8, 2010

    Super post Greg!! My statistic muscles are weak and dusty – you’ve done a great job of jarring my perspective in a fun and engaging way. Thanks.

    Take care,

  9. August 9, 2010

    Thanks Terrence. Have a great week!

    – Greg

  10. Adrian Goodsell permalink
    August 10, 2010

    Hi Greg

    Firstly, great post.

    I’m certainly not in Master Bieber’s target demographic and must confess that as a result I haven’t scratched beneath the surface of the ever-present social media phenomenon that is ‘Biebermania’. There are some really interesting learnings here.

    The point about fitness resonated with me and I agree with it entirely. Are we meant, then, to assume that Bieber’s fitness as a node is a consequence of talent? 😉

    Also, interested to know where the 126 followers average (on Twitter) figure came from?

    Keep up the good work,

  11. August 10, 2010

    I am many things for sure…

    Opinionated. Loud. Very Loud. Coffee-addict. Did I mention loud? Creative. Writer. Idea instigator.

    One thing I am not and NEVER will be is a “numbers guy.”

    It’s that whole right side/left side brain thing. It’s one of the reasons I married a former bookkeeper. That and she’s pretty damn amazing and way too beautiful for a slug like me… but I digress.

    Folks like you Greg (and my brother Joe) always impressed the hell out of me. How you can make sense out of stats, numbers, charts and so on… I will never understand. I am simply not wired that way.

    I do appreciate you taking the time to explain so even a dolt like me can understand.

    Steve O

  12. August 10, 2010


    Thanks. To be honest, I don’t remember where I got that figure from. Usually I provide a link, but I didn’t with that one for some reason.

    In any case, it’s been widely cited, here for instance:

    Thanks again for your comment.

    – Greg

  13. August 10, 2010


    Thanks. I’m glad you liked it. Best to your wife and Joe:-)

    – Greg

  14. August 11, 2010


    Ooops! I forgot to respond to your point about “fitness.” I don’t think it can be described as “talent.” In fact, it is just a name given to a mathematical variable that neatly fits into Bose-Einstein statistics which happened to have extremely good explanatory power for networks and made a lot of sense conceptually.

    Most likely, it is most related to meme fitness, which I wrote about recently:

    I hope that’s helpful.

    – Greg

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