The Flawed Metcalfe’s Law & The Power Of Networks

By seeming to assure that the value of a network would increase quadratically—proportionately to the square of the number of its participants—while costs would, at most, grow linearly, Metcalfe's Law gave an air of credibility to the mad rush for growth and the neglect of profitability. It was hot stuff during the Internet bubble. 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. Courtesy of Paul Kedrosky saw this article. The article points out, if a network of 100 000 members that we know brings in $1 million. So if the network doubles its membership to 200 000, Metcalfe's Law says its value grows by (200 0002/100 0002) times, quadrupling to $4 million, whereas the n log(n) law says its value grows by 200 000 log(200 000)/100 000 log(100 000) times to only $2.1 million. In both cases, the network's growth in value more than doubles, still outpacing the growth in members, but the one is a much more modest growth than the other. Much of the difference between the artificial values of the dot-com era and the genuine value created by the Internet can be explained by the difference between the Metcalfe-fueled optimism of n 2 and the more sober reality of n log(n).Incidentally, this mathematics indicates why online stores are the only place to shop if your tastes in books, music, and movies are esoteric. Let's say an online music store like Rhapsody or iTunes carries 735 000 titles, while a traditional brick-and-mortar store will carry 10 000 to 20 000. The law of long tails says that two-thirds of the online store's revenue will come from just the titles that its physical rival carries. In other words, a very respectable chunk of revenue—a third—will come from the 720 000 or so titles that hardly anyone ever buys. And, unlike the cost to a brick-and-mortar store, the cost to an online store of holding all that inventory is minimal. So it makes good sense for them to stock all those incredibly slow-selling titles. This difference will be critical as network investors and managers plan better for growth. The fundamental flaw underlying both Metcalfe's and Reed's laws is in the assignment of equal value to all connections or all groups. At some point, adding one person would theoretically increase the network value by an amount equal to the whole world economy, and adding a few more people would make us all immeasurably rich. Clearly, this hasn't happened and is not likely to happen.