Even leading twitter from atop with 90 million followers, Katy Perry still has
plenty of competition around the corner. Within 15% of 90 million there are a few other accounts (e.g., Justin Bieber, Taylor
Swift, Barack Obama), all North American even though only a small fraction of all twitter users live there. It's also worth noting President Obama has 4 times the followers of Trump and Hillary, combined, but in any event more likely
than not that there will randomly
be a new throne leader at some point.
But don’t feel bad for Katy just yet; this deserving talent should feel proud
of her tremendous achievement and brightly triumphant music. In that spirit we ask: what can we learn at
this very tippity-top of the social media kingdom, about growing our own networking
presence? In this article we’ll take a
rare peek at the tail-end of the twittersphere.
Where über-dominant accounts are measured not in hundreds of thousands of followers (I've worked with many and they are hugely influential), but instead
are measured in a staggering tens of
millions of followers. Sure there is
some luck at play, but it’s not all chance (here). We learn from the mathematics shown here that
wherever you happen to place within the current social pyramid, one needs to
be diligent, insightful, and creative, in order to raise the odds of pushing
their own needle forward.
Now our blog readers will know that a number of models (from the exponential, Pareto or power, Cauchy, Weibull, and other families such as Student-t and a variation of lognormal) can be used to help describe this fatter than normal distribution of followers at the extreme ends of the social media empire (here, here, here, here). Or no model at all, or non-parametric (here, here, here, here). In 2007 before the global financial crisis, black swan connoisseur and NYU professor Nassim Taleb stylishly described this fat-tail phenomenon in his best-selling book. On page 264 of chapter 16, Taleb elaborates on using the power formula to estimate the number of best-selling books sold relative to a given celebrity author's rank. Now social media sites were too nascent at the time of that book, to parameterize them as well, using this simple yet exciting model:
Our third and final point is that our own blog joined twitter (@salilstatistics) this last April and has quickly amassed 11k followers in our fast-growth phase. That’s arguably a vigorous start, since our first year is not over yet. It’s also a strong milestone, for a niche academic mathematics topic.
As noted though, twitter began a decade ago, and so it is unfair to completely contrast 11 thousand followers in couple months, versus someone with tens of thousands of followers after nearly a hundred months. To normalize for the amount of time on twitter (and this applies to other social media such as facebook and LinkedIn) we constructed this simple chart below that shows the expected growth among your followers -relative to the overall growth rate of the twitter network. In other words, having 10k followers after 1 year is considerably more promising versus someone with 30k followers after 8 years (particularly as part of the 30k for the latter comparison is from broad networking growth and not personal excess growth). This is because there is a good chance that this young user may be one of those who quickly surpass the number of followers that the more mature user has taken 8 years to attain (see light blue curve below). On the other hand if two different users have been on twitter for 8 years each (one with 10k followers and the other with 30k followers), it is less likely such a wide chasm is likely to quickly (and perhaps ever) invert since both of these different users have similar maturity and expected growth rates at this point.
There is a lot of compelling things that one (who is in the top quartile or top decile of social media) can research about where they stand relative to their peers. It is clear that at the very highest tail of the twitter followers’ distribution, one must still work increasingly smart in order to gain further influence - ranked against others. And how easy it is to slip in rank, if one is not gaining traction relative to everyone else, particularly incoming stars who are joining social media daily! We’ve seen likeable personalities and great brands, during this economic recovery, lose their way and have an arduous time continuing to have the same influence they once did. In becoming the artistic headliner that she is, Ms. Perry offers this stimulating wisdom in the lyrics of one of her popular songs titled "Fireworks". And it’s easier done than said frankly; keep pushing on those invisible doors impeding your own progress.
Our first point begins by taking a look at the actual number
of followers for the most popular twitter users. We show the chart below, ranked along the
horizontal axis, with the data sized in proportion to the number of followers.
Every user ranked in the top 100 is included, and then a sample of users ranked
up through 1000 is also included. There
are hundreds of millions of real twitter accounts today.
Even though our readers will likely experience greater twitter usage among their own family and friends, most
accounts globally are rarely used (e.g., less than several times annually). Now look at these sampled users:
·
Salman Khan (rank 65) has 18m followers
·
Harry Styles (rank 31) has 29m followers
·
Jimmy Fallon (rank 15) has 42m followers
·
Rhianna (rank 8) has 62m followers
It seems as we start getting near the pinnacle of the
twittersphere, the number of followers gets explosively larger (in order to halve one's rank equates to a having 50% additional followers). Though we
show that this formulaic relationship dismantles as we move into a rank of single digits (as opposed to when
looking at ranks higher up in the double and triple digits). For example, Barack Obama is ranked 4. And he has 76 million followers - just 21% greater
than the number of Rhianna’s followers.
Now our blog readers will know that a number of models (from the exponential, Pareto or power, Cauchy, Weibull, and other families such as Student-t and a variation of lognormal) can be used to help describe this fatter than normal distribution of followers at the extreme ends of the social media empire (here, here, here, here). Or no model at all, or non-parametric (here, here, here, here). In 2007 before the global financial crisis, black swan connoisseur and NYU professor Nassim Taleb stylishly described this fat-tail phenomenon in his best-selling book. On page 264 of chapter 16, Taleb elaborates on using the power formula to estimate the number of best-selling books sold relative to a given celebrity author's rank. Now social media sites were too nascent at the time of that book, to parameterize them as well, using this simple yet exciting model:
base rank * (base books sold / new books sold)-exponent
Now this formula could be reassembled with enough data to
solve for new books sold, given a difference in author ranks. More importantly, it was shown that books
sold and also Americans' net work fits an "exponent" in the low 1’s. While more
exotic phenomena, such as solar flares and war intensities, had an exponent <1. But for this specific formula, applied on the vertical axis of the above data chart, we can fit most of the actual twitter followers using just an exponent
of 2.05. The smaller the exponent, the thicker
the distribution at the extreme tails.
Put differently, the top 1% of people -when using a 1.3 exponent- represents 34% share of success. But when using a 2.0 exponent, it represents a more equitable 10% share. So Ms. Perry and the others in the top dozen don't completely dominate twitter, though they do have a disproportionate share indeed. A more fair distribution could lead the top 1% of people to have something along the lines of a 1%-2% share, while the ubiquitous Pareto principle (the 80 20 rule) follows more of a 1.2 exponent. Note that this analysis could have easily been done on other social media, such as YouTube or Instagram, but recent experiences with twitter made this a good choice to showcase trends. We have learned previously from facebook's deliberate debacles (here, here).
Our second point here is that despite the relative “scrunching”
at the top of social media (and one where the old-guard of Oprah and New York Times have nearly 30 million each and ranking at a less mighty upper 20s), the number of followers is hardly
something that is more lognormal in nature.
We can see in the illustration below that when directly modeling the
number of followers (on the vertical axis), the normal distribution -about the
middle part of this extreme tail of twitter- is very flattish until we get into
the top dozen or so ranked users (in dark blue color). And even then with Ms. Perry and a dozen
other tops users, it is fairly flat relative to a 45 degree angle.Put differently, the top 1% of people -when using a 1.3 exponent- represents 34% share of success. But when using a 2.0 exponent, it represents a more equitable 10% share. So Ms. Perry and the others in the top dozen don't completely dominate twitter, though they do have a disproportionate share indeed. A more fair distribution could lead the top 1% of people to have something along the lines of a 1%-2% share, while the ubiquitous Pareto principle (the 80 20 rule) follows more of a 1.2 exponent. Note that this analysis could have easily been done on other social media, such as YouTube or Instagram, but recent experiences with twitter made this a good choice to showcase trends. We have learned previously from facebook's deliberate debacles (here, here).
Our third and final point is that our own blog joined twitter (@salilstatistics) this last April and has quickly amassed 11k followers in our fast-growth phase. That’s arguably a vigorous start, since our first year is not over yet. It’s also a strong milestone, for a niche academic mathematics topic.
There is a lot of compelling things that one (who is in the top quartile or top decile of social media) can research about where they stand relative to their peers. It is clear that at the very highest tail of the twitter followers’ distribution, one must still work increasingly smart in order to gain further influence - ranked against others. And how easy it is to slip in rank, if one is not gaining traction relative to everyone else, particularly incoming stars who are joining social media daily! We’ve seen likeable personalities and great brands, during this economic recovery, lose their way and have an arduous time continuing to have the same influence they once did. In becoming the artistic headliner that she is, Ms. Perry offers this stimulating wisdom in the lyrics of one of her popular songs titled "Fireworks". And it’s easier done than said frankly; keep pushing on those invisible doors impeding your own progress.
“Maybe a reason why all the doors are closed
So you could open one that leads you to the perfect road
Like a lightning bolt, your heart will glow
And when it’s time you’ll know”
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