The Change Mariner

Rise of the Power Law in the Blog World

Shirky.com:
... We are all so used to bell curve distributions that power law distributions can seem odd. The shape of Figure #1, several hundred blogs ranked by number of inbound links, is roughly a power law distribution. Of the 433 listed blogs, the top two sites accounted for fully 5% of the inbound links between them. (They were InstaPundit and Andrew Sullivan, unsurprisingly.) The top dozen (less than 3% of the total) accounted for 20% of the inbound links, and the top 50 blogs (not quite 12%) accounted for 50% of such links.

The inbound link data is just an example: power law distributions are ubiquitous. Yahoo Groups mailing lists ranked by subscribers is a power law distribution. (Figure #2) LiveJournal users ranked by friends is a power law. (Figure #3) Jason Kottke has graphed the power law distribution of Technorati link data. The traffic to this article will be a power law, with a tiny percentage of the sites sending most of the traffic. If you run a website with more than a couple dozen pages, pick any time period where the traffic amounted to at least 1000 page views, and you will find that both the page views themselves and the traffic from the referring sites will follow power laws.

The basic shape is simple - in any system sorted by rank, the value for the Nth position will be 1/N. For whatever is being ranked -- income, links, traffic -- the value of second place will be half that of first place, and tenth place will be one-tenth of first place. (There are other, more complex formulae that make the slope more or less extreme, but they all relate to this curve.) We've seen this shape in many systems. What've we've been lacking, until recently, is a theory to go with these observed patterns.

Now, thanks to a series of breakthroughs in network theory by researchers like Albert-Laszlo Barabasi, Duncan Watts, and Bernardo Huberman among others, breakthroughs being described in books like Linked, Six Degrees, and The Laws of the Web, we know that power law distributions tend to arise in social systems where many people express their preferences among many options. We also know that as the number of options rise, the curve becomes more extreme. This is a counter-intuitive finding - most of us would expect a rising number of choices to flatten the curve, but in fact, increasing the size of the system increases the gap between the #1 spot and the median spot.

A second counter-intuitive aspect of power laws is that most elements in a power law system are below average, because the curve is so heavily weighted towards the top performers. In Figure #1, the average number of inbound links (cumulative links divided by the number of blogs) is 31. The first blog below 31 links is 142nd on the list, meaning two-thirds of the listed blogs have a below average number of inbound links. We are so used to the evenness of the bell curve, where the median position has the average value, that the idea of two-thirds of a population being below average sounds strange. (The actual median, 217th of 433, has only 15 inbound links.)