### The Limits to Growth

I’ve been thinking lately about the dynamics of gaining and losing followers on Twitter. The distribution of Followers each account has is such that a lot of accounts have few followers, a few have a lot of followers, and a medium number of accounts have a medium number of followers. What could give rise to that structure in this particular case? How does the number of followers change over time? Even, what are the biggest days to gain (or lose) followers?

I follow Avinash Kaushik (@avinashkaushik), the author of Web Analytics: An Hour a Day, one of those people with a lot of followers (and deservedly so) and who follows few other people (none of whom are me). As of today, about 23,400 people follow him and he follows about 89. (UPDATE, Aug 9, 2010: Today Mr, Kaushik changed his Twitter account to @avinash.)

The graph below shows the number of followers Mr. Kaushik has had each day from October 1, 2009 through August 4, 2010:

The number of followers seems to follow Gompertz’s equation, though I’m not certain if there’s a good reason for this or if it’s just because I’ve got Gompertz-on-the-brain and I am trying to fit his equation to everything I can get my hands on. (I’ve written previously about Gompertz’s equation in relation to the growth of my chickens. It’s not really chickens I’m interested in – I’m more interested in how all sorts of systems grow and change over time.)

If present trends continue, Mr. Kaushik should crack 25,000 followers somewhere around Thanksgiving of this year. I’ve also graphed the number of new Followers he has gained each day. (This is not the net change in the number of Followers, which would be the number of new Followers minus the number of people who ‘unfollowed’ him on that day. This is just the number of new people who started following him each day.) I’ve broken up the data by day-of-week to find out which days are the most popular to gain followers:

(The biggest day he gained new followers was Tuesday, October 27, 2009, though most days were considerably lower.) I’ve checked this with other individuals and some corporate accounts like @amazon, one of the official accounts of Amazon.com, which also has about 25,000 followers. It seems to be that Tuesdays are the days when accounts tend to gain the most new followers, on average. And, similar analysis shows that Fridays tend to be the days with the highest number of cases where people ‘unfollow’ a given account.

I have not gathered a large sample of accounts yet, though, so I’m trying to be careful about not making any statements that are not justified by the amount of data I have so far.