A model of Twitter growth

A model of Twitter growth

It took 41 days for my Twitter followers to double in number from 50 to 100. It took a further 26 for the number to double again, from 100 to 200. At the moment the growth is slightly faster than exponential, which seems unlikely to continue. Clearly, more followers – especially more followers who are active and engaged – help you to reach a wider audience, so why doesn’t growth continue to be exponential?

Let’s assume that a person’s current number of followers is small compared to the total number of people who would be interested in following them. This seems true for the vast majority of people: perhaps not for someone with tens of thousands or millions of followers, or even for say an MP (there will be a finite number of people in their constituency on Twitter), but certainly for people such as me. Let’s further assume that all followers are equal – which is clearly not true in either number of followers they have or in engagement, but we can assume these things average out for the purpose of this model.

In such a case, growth depends on:

– Scale independent factors – when you like tweets, comment on or retweet others’ tweets or follow them, sometimes they follow you back. Whilst you can increase the amount of activity of this sort you do, there’s no multiplier factor for followers. Call this k.

– Scale dependent factors; i.e. based on how good the content (i.e. the tweets and links) you’re producing is and the number of followers you have – as they are the ones who can retweet it to a wider audience, who may then follow you. Call this tx, where x is the number of followers and t is how engaging your tweets are.

Loss of followers is entirely scale dependent, proportionate to both the number of current followers you have and how much your tweets make people want to disengage (perhaps because they are uninterested in them, or find them irritating or offensive). Call this dx, where x is again the number of followers and d is how disengaging you are.

Therefore, follower gain, G = k + tx – dx, or G = k + (t-d)x. As long as t>d, your followers will keep growing; however, the rate will slow as k becomes less significant.

4 thoughts on “A model of Twitter growth

  1. What I’ve noticed is that the “t” and “d” in your equation are very time dependent – a sudden surge due to tweeting certain things or being mentioned by people.

    The interesting challenge is working backwards – been you see a surge in (un)followers, can you figure out what caused it? Sometimes it’s not from twitter itself (e.g. mentioned on a webpage), so harder to track.

    I would also say it’s dangerous to over-analyse. Twitter accounts that exist purely to increase followers are easy to spot – though I’m not suggesting that’s what yours is! Follower number is a useful barometer, perhaps, but there are enough external factors that reading to much into trends without context is risky. But maybe that’s why my Follower number is fairly constant (I think, I don’t really look at it that often – just now be then spot a milestone).

    P. S. there’s a “+” missing in your last expression.

    1. Oh, definitely! I write these posts more because I find it interesting than as a guide to follower-maximisation: I still don’t really understand why so many accounts stabilise in the mid-hundreds rather than continuing to grow exponentially. But I completely agree I’d rather have a smaller number of active, engaged followers in areas relevant to what I wrote about than hordes of nominal followers who ignored everything I wrote.

      And good point on the time-dependent aspect: I certainly got a dozen or so extra after I posted the TEF game. But that should be broadly averageable (in most cases).

      1. I think there’s also a cap on the number of people most people follows, as well. I rarely add people to my follower list any more – as it is there are far too many posts to see everything, so an account as to be really relevant for me to add them. In practice, that’s often people I know in real life, and I’ve heard of (but have no links to) research that says that’s in the one-to-a-few hundred range.

        You follow ~300 people after a few months, while I follow about 500 after nearly 9 years. I don’t personally do the follow-back thing, though that is more to do with my past life with BBC stuff, where that would have gone a bit crazy (as much as I deliberately didn’t advertise my personal twitter account through the BBC).

        Hypothesis: If the twitter user-base was uniformly and randomly distributed in terms of inter-user connections, and each user followed a few hundred others, then you’d expect each user to have a few hundred followers. Neither of those is likely to be true, and there’ll be “celebrity” twitter users (twilebrities?!), but it might explain the numbers for the “average” user.

        1. That makes a lot of sense: the fact that there is essentially a limited number of ‘follows’ available. I suspect I’ll slow down on following when I’m up to about 500, like you, and probably most people are similar.

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