Was Metcalfe Wrong?

Much of the anticipated growth of the New Economy in the 1990s was predicated on a simple formula known as Metcalfe's Law. It stated that that the value of a network would increase quadratically—proportionately to the square of the number of its participants—while costs would grow linearly, for all practical purposes. It was the mathematical underpinning to the bromides of the Internet Bubble such as: "first-mover advantage," "Internet time," and, of course, "build it and they will come." Now, along come a trio of researchers who claim that Metcalfe was off all along. They lay out their case in this month's feature "Metcalfe's Law Is Wrong".

IEEE Medal of Honor recipient Robert M. Metcalfe is the co-inventor of the Ethernet protocol, a co-founder of 3Com, a longtime industry analysts and author, a general partner at Polaris Venture Partners, and, of course, the creator of the eponymous Metcalfe's Law.

The lead author of our article, Bob Briscoe, is the chief researcher at Networks Research Centre BT (formerly British Telecom), in Ipswich, England. Joining him are: Andrew Odlyzko, a professor of mathematics and the director of the Digital Technology Center at the University of Minnesota, in Minneapolis; and Benjamin Tilly, a senior programmer at Rent.com, in Santa Monica, Calif. (Odlyzko and Tilly have written on this subject before.) They argue that Metcalfe's Law seriously overestimates the importance of overall connections to the ultimate value of a network.

Instead of Metcalfe's original formula (where value is proportional to the square of the number of users of the system), they propose that a more accurate expression of value would be the number of users multiplied by the logarithm of that number, yielding a lower result.

"Remarkably enough, though the quaint nostrums of the dot-com era are gone, Metcalfe's Law remains, adding a touch of scientific respectability to a new wave of investment that is being contemplated, the Bubble 2.0, which appears to be inspired by the success of Google," they write. "That's dangerous because, as we will demonstrate, the law is wrong."

Whether we use the word wrong or the phrase historically inaccurate (which certainly sounds kinder to Metcalfe), it would seem that now is a good time to revisit Metcalfe's Law and perhaps upgrade it, as information technology seems poised to proceed with another growth spurt. And a good place to start would be this article by Briscoe, Odlyzko, and Tilly.

As they conclude: "At a time when telecommunications is the key infrastructure for the global economy, providers need to make fundamental decisions about whether they will be pure providers of connectivity or make their money by selling or reselling content, such as television and movies. It is essential that they value their enterprises correctly—neither overvaluing the business of providing content nor overvaluing, as Metcalfe's Law does, the business of providing connectivity. Their futures are filled with risks and opportunities. We believe if they value the growth in their networks as n log(n), they will be better equipped to navigate the choppy waters that lie ahead."

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