# 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.