Researchers: Metcalfe's Law overshoots the mark

Two University of Minnesota researchers have written a paper arguing that Metcalfe's Law, a rule of thumb that computes the value of communication networks, is overly optimistic.

Metcalfe's Law--a rule of thumb, really, that provided a rationale for aggressive expansion efforts during the dot-com boom--posits that the value of a network increases with the square of the number of devices in the network. But in a preliminary paper (click for PDF) published March 2, Andrew Odlyzko and Benjamin Tilly of the university's Digital Technology Center concluded that the law "is a significant overestimate." In one example, where the law would find a network's value increased 100 percent, their calculations found only a 5 percent enhancement.

The two researchers proposed an alternative formula that heads in the same direction as Metcalfe's Law but doesn't go as far. The differences in the two laws explain why established network powers, such as AT&T, have resisted cooperation with smaller rivals.

Metcalfe's Law was a driving feature of the dot-com boom. Netscape co-founder Marc Andreessen, for example, argued that the law explained the surging amount of time people spent online using services from America Online, his employer at the time.

There is no shortage of laws in the computing realm. Moore's Law, by Intel co-founder Gordon Moore, describes the rate at which more transistor circuitry can be packed onto a single chip. And Amdahl's Law, by IBM mainframe designer Gene Amdahl, governs the performance boost gained by adding new processors to a computer. (Amdahl also is credited for another computing industry innovation, coining the term "FUD," the fear, uncertainty and doubt that one company's propagandists use to undermine a rival's product.)

'Fundamental fallacy'
Metcalfe's Law came from Bob Metcalfe, a founder of networking equipment supplier 3Com and coinventor of the now-ubiquitous Ethernet networking standard. According to the law, a network with 20 telephones--or alternatively, fax machines, instant-messaging teenagers or Internet-phone callers--is four times more valuable than a network with 10. A network with 30 nodes is nine times more valuable than one with 10.

Not so, Odlyzko and Tilly argue.

"The fundamental fallacy underlying Metcalfe's (Law) is in the assumption that all connections or all groups are equally valuable," the researchers report.

If Metcalfe's Law were true, there would have been tremendous economic incentives to accelerate network mergers that in practice take place slowly. "Metcalfe's Law provides irresistible incentives for all networks relying on the same technology to merge or at least interconnect."

The researchers propose a less dramatic rule of thumb: the value of a network with n members is not n squared, but rather n times the logarithm of n. That means, for example, that the total value of two networks with 1,048,576 members each is only 5 percent more valuable together compared to separate. Metcalfe's Law predicts a 100 percent increase in value by merging the networks.

It's not a merely academic issue. "Historically there have been many cases of networks that resisted interconnection for a long time," the researchers say, pointing to incompatible telephone, e-mail and text messaging standards. Their network effect law, in contrast to Metcalfe's, shows that incumbent powers have a reason to shut out smaller new arrivals.

When two networks merge, "the smaller network gains considerably more than the larger one. This produces an incentive for larger networks to refuse to interconnect without payment, a very common phenomenon in the real economy," the researchers conclude.

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Value of a network

I think we should contrast the value of a network to the users vs. the value of a network to the owners. Metcalfe's law not only assumes that each connection has the same value, but also the same cost (or zero cost). The issues of merging disparate networks have more to do with the cost of a connection than the value of a connection. As a network grows bigger, assuming they don't rework new connections to conform to a standard, the cost of adding new connections could also increase as the square of the number of distinct connection types. So there are other possible explanations for large networks charging smaller networks for access.

Also, the larger a network grows, the smaller the % increase in benefit from adding a new node, even assuming Metcalfe's law. The percentage increase in benefit would be

((x+1)^2 - x^2)/x^2, which approaches zero as x increases. Since companies have to grow exponentially to achieve the same returns as compound interest, a company has to add larger groups of nodes to achieve the same percentage increase in revenue.

Only one author was from Minnesota

While Andrew is there, I am currently living in California. To further confuse the situation, I am normally a programmer.

However I am glad to see that the paper is receiving some publicity!