Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly, writing in IEEE Spectrum, assert that Metcalfe’s Law is wrong ( http://www.spectrum.ieee.org/print/4109). This is shocking news for all the hockey stick business plans of the emerging new dot.com bubble (Bubble 2.0).
To recap, Metcalfe’s Law states that the value growth of a network is a function of the square of the number of users added f(n)**2. The authors propose that instead, the value of a network of size n grows in proportion to n log(n). As they put it:
“Imagine a network of 100 000 members that we know brings in $1 million. We have to know this starting point in advance—none of the laws can help here, as they tell us only about growth. So if the network doubles its membership to 200 000, Metcalfe's Law says its value grows by (200 000**2/100 000**2) 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. In our view, 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).”
In other words, to all practical purposes the network value grows in a far more (near linear) fashion, as opposed to exponentially. Doubling network size by acquiring another player only adds about 5% of value (that should keep the Private Equity boys awake at night). The authors then lightly trip through 2 other Laws:
“The value of a broadcast network is believed to grow linearly; it's a relationship called Sarnoff's Law, named for the pioneering RCA television executive and entrepreneur David Sarnoff. At the other extreme, exponential—that is, 2**n —growth, has been called Reed's Law, in honor of computer networking and software pioneer David P. Reed. Reed proposed that the value of networks that allow the formation of groups, such as AOL's chat rooms or Yahoo's mailing lists, grows proportionally with 2**n.”
In our experience there are a number of implicit assumptions behind any of these laws that need to be watched with care.
Firstly, not all links are equal. The authors tacitly acknowledge this when they say “The fundamental flaw underlying both Metcalfe's and Reed's laws is in the assignment of equal value to all connections or all groups.” We would argue this applies to all these laws, not just Metcalfe’s and Reed's. Anybody familiar with small world/ scale free network theory will know that communication networks (both human and telecoms based) are usually small world networks, and in a small world network not all links are equal, in fact they are massively unequal. (This is now beginning to be discovered even in the “blogosphere”, which it appears may be more feudal than democratic – see Jeff Clavier’s notes on http://blog.softtechvc.com/2006/08/the_revolution_.html)
Secondly, for any of these laws to hold, the expansion of the network into new groups must roughly maintain the overall homogenous value per user assumed . These laws do not hold once you have captured all those groups who desire your service, as from then on you are recruiting groups who value the service less and wish to spend less time and/or money on it, and typically are also more costly to serve. ( An inconvenient fact that was also forgotten in the Great Mobile Licence Rush)
Thirdly, there is an implicit assumption that there are no forces reducing value to the user - such as competition, new technologies, one off benefits etc.
The authors also allude to Zipfs Law in closing, noting that “Zipf's Law is one of those empirical rules that characterize a surprising range of real-world phenomena remarkably well. It says that if we order some large collection by size or popularity, the second element in the collection will be about half the measure of the first one, the third one will be about one-third the measure of the first one, and so on. In general, in other words, the kth-ranked item will measure about 1/k of the first one.”
To be honest I'm not quite sure what their section on Zipf's Law had to do with the Metcalfe's law argument, but it does beg the obvious retort:- one of the areas that Zipf's law may apply to is to the way newly recruited groups value this New New Service.
Group A mayl thus value this New New Thing by Value X, Group 2 by X/2, group 3 by X/3 and so on…so clearly as the extra groups are recruited (either via Metcalfe’ or the n log(n) Laws or whatever), the relative value of user n+1 is falling, thus the value in fact tails off - in fact it starts to look like that old party pooper, the Law of Diminishing Returns (also known as the S curve).
This is exacerbated as, once that fall off in value starts to occur, a number of the positive influences that drove the original exponengtial value increase start to reverse themselves - leading to a good old vicious circle. (as anyone who has looked at system dynamics will quickly understand). This is true whether the fall off in value per user is as draconian as Zipfs law, or a more benign tail off.
In our view, early stage growth is well described in terms of one of these laws of increasing returns (pick the one of your choice for the New New Thing), some grow more rapidly than others. However, in our experience of Real World Networks so far over the last 20 years or so, be they Broadcast, Mobile, Intranet, Internet or good old POTS, the S curve does seem at some point to take a hold.
Somewhere out there, the total number of people prepared to pay top dollar for the New New thing hits its limits, and the good old S curve rears its head. At this point either new services have to be found to capture new users, or a way to increase value to existing users must be found - or both. The trick, as always, is to understand just what that point is. But one thing is for sure, is that that old law has been with us a long, long time.
Maybe its time to bring in Ecclesiastes’ Law – there is nothing new under the sun?
Postscript
In defence of both parties, we must note that:
(i) Bob Metcalfe did not intend his law to be used for pure financial valuation per se – see his rebuttal to this article on http://vcmike.wordpress.com/2006/08/18/metcalfe-social-networks/, and;
(ii) the authors of this paper are mainly arguing for rationality in estimating the true likely values for future investments in the emerging broadband internet space (or bubble 2.0)
Post Postscript
For the last 10 years or so we have been keeping up with the Santa Fe Institute's and others' work on the economics of increasing returns from network effects - it definitely does describe the early stages in any new technological development in our experience - in fact I got interested in it while at McKinseys in the mid 1990's precisely because more conventional theory did not describe what we could see occurring in the emerging Internet at the time.
