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scerruti
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PostPosted: Fri Jul 21, 2006 9:16 am    Post subject: Network Value as a Function of the Number of Members Reply with quote Back to top

Throughout the dot com era businesses based decisions on a rough empirical description of network value as a function of the number of members called Metcalfe's law. Robert Metcalfe, as you may or may not recall, invented the Ethernet protocol that has become one of the main pillars upon which the Internet has been built. Metcalfe’s law states that the value of a communication network grows quadratically as the number of members grow.

For example, imagine a phone network with 10 users. Each of those 10 users can call 9 other people. Therefore the value of the network can assumed to be 10(9). Since this can be expressed n(n-1) where n is the number of users, we can roughly estimate the growth curve to be n squared. It is important to note that costs tend to grow linearly with each new customer.

There are two other laws worth mentioning at this point. Sarnoff’s law applies to broadcast networks. Broadcasts network value increases linearly with the addition of new customers. However costs for broadcast networks do not increase linearly for each customer. Reed’s law was intended to be applied to close knit networking groups, email distribution lists or networking sites like http://www.linkedin.com for example. Reed’s law says that network value increases exponentially with the addition of new members. That is the value of the network can be represented not as n-squared, but as 2 to the power n. It is important to understand that all of these laws can’t tell you what a network is worth, but if you know how much a network is worth and how many members it has, you can roughly predict the value as new members are added.


Graphs of Reed's, Metcalfe's and Sarnoff's Laws

If you have read this far you may now be wondering how this applies to Vonage, or perhaps you immediately see where this is going. In the IEEE Spectrum article ”Metcalfe’s Law Is Wrong” authors Briscoe, Odlyzko and Tilly discuss how the dot com failures can be explained by looking at how businesses made decisions based on Metcalfe’s law. They propose that the function n•log(n) more closely models the growth of communication networks.

One mistake to avoid in understanding these mathematical models is to confuse revenue, which grows linearly with customer growth, with value. The other problem here is that while Vonage is itself a network, it is also part of the larger PSTN network and Vonage’s value is affected by the value of the PSTN network. A sidebar to the article, ”Making the Connection” talks about consolidation of networks and how that affects value.

Understanding how customer growth can affect value can assist you in forming opinions about the reasonableness of Vonage’s advertising expenses and their desire for rapid growth. But this article also serves as a cautionary tale warning against repeating the mistakes of the dot com era by overemphasizing network growth based on a flawed model.

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