Last month, I wrote a post entitled “The Network Effect Multiplier, or, Metcalfe’s Flaw“. That post cited a preprint of a IEEE Spectrum article by Briscoe, Odlyzoyko and Tilly that pointed out a key problem with Metcalfe’s law – that the value of a network does not grow proportionally, but rather logarithmically. This paper generated substantial buzz, as a lot of the logic of Metcalfe’s law underlies how we value web applications, particularly socially-enabled web applications.
Metcalfe, in a guest post to colleague Mike Hirshland’s blog, responds to the article. Its a very interesting read, and another wonderful example of how blogs enable conversation. Metcalfe first clarifies his purpose in creating his law.
As I wrote a decade ago, Metcalfe’s Law is a vision thing. It is applicable mostly to smaller networks approaching “critical mass.” And it is undone numerically by the difficulty in quantifying concepts like “connected” and “value.”
This is valuable, as it questions the applicability of Metcalfe to large networks. However, as Metcalfe originally used this law to describe the telecommunication network, I’m confused by his definition of smaller. Nevertheless, he’s absolutely correct about the difficulty in quantifying value – I wrestled with this exact concept when I was analyzing the law. Metcalfe goes on to state:
While they’re at it, my law’s critics should look at whether the value of a network actually starts going down after some size. Who hasn’t received way too much email or way too many hits from a Google search? There may be diseconomies of network scale that eventually drive values down with increasing size. So, if V=A*N^2, it could be that A (for “affinity,” value per connection) is also a function of N and heads down after some network size, overwhelming N^2. Somebody should look at that and take another crack at my poor old law.
Affinity, or value per connection is exactly what I was addressing in my analysis. Metcalfe’s original model was built on the assumption that value was binary – people using a telecommunications network, or an ethernet network, can only experience two states of value – full or none. However, in a social network, value is nuanced and conditional. Of course, in A*N^2, the assumption is A is constant through the network, which is not the case. Nevertheless, I’m enlightened to see this, and I feel that it validates my previous work.
Metcalfe goes on to explain how this notion of affinity can be applied to social networks – and the long tail in general.
Social networks form around what might be called affinities. For each affinity, there is a critical mass size given by N=C/A, as above. If the number of people sharing an affinity is above this critical mass, then their social network may form, otherwise not. As Internet access gets cheaper and the tools for exploiting affinities get better, many more social networks will become viable.
…Let me leave as an exercise for the reader to develop the formulas for how Amazon’s Long Tail grows to the right as the combination of Moore’s and Metcalfe’s Laws biennially halves the critical-mass size of book audiences. Book buying generally shrinks with time, but I’m guessing that Amazon’s per book critical masses, its N=C/As, have been shrinking faster.
Similar formulas could quantify how Moore’s and Metcalfe’s Laws have also driven down the critical mass sizes (N=C/A) of Internet-enabled social networks and extended their Long Tail to the right. Looking more closely, I see that Metcalfe’s Law recurses. Just being on the Internet has some increasing value that may be described by my law. But then there’s the value of being in a particular social network through the Internet. It’s V~N^2 all over again. Down a level, N is now the number of people in a particular social network, which has its own C, A, V, and critical mass N.
Of course the cost (C*N) of getting connected in a social network has been going down thanks to the proliferation of the Internet and its decreasing price. The value (A*N^2) of particular social networks has been growing with broadband and mobile Internet access. Emerging software tools expedite the viral growth and ease of communication among network members, also boosting the value of underlying connectivity.
This is quite interesting. Down the long tail, we see critical masses of decreasingly small sizes, and these critical masses have been enabled by the simplicity of connecting.
VCMike has this very interesting post, and Om Malik is also following the conversation. Good brain food for a Friday morning.
Tags: information, networks
Fred: I think your affinity value is a function of both size and the cost of getting connected. If it’s easy to connect and everyone can do it, the network’s affinity value is going to decline at a faster rate as the number of members increases due to noise. If the social network is harder to connect to (i.e. more restrictive in some way, resulting in a higher “quality” of membership) it will grow more slowly but the affinity may actually increase as the network increases in size. Eventually even a more restrictive network probably reaches a size where noise increases and affinity starts going down…
Maybe the shape of the affinity value curve (affinity vs number of users) might be broadly similar (same class of function) in both cases but the min and max are in different places with respect to size…
But then I’m goog at being dead wrong too ;-)
See you next week for pizza!