Metcalfe's Law, Reed's Law Revisited: Questioning new Valuation Models

Something tells me that some of today's venture capitalists aren't going to get a great return on their dollars. 

This is based on two observations.  1)The stock market, a few IPOs notwithstanding, doesn't have a large appetite for unproven tech startups; while the alternative endgame, to get acquired by a larger company, isn't really a sustainable strategy.  Large companies will have a limited appetite for buyouts if the stock market itself isn't interested in them.  2)  Reading over at Fred Wilson's blog, it seems that tech companies are actually being valued even more optimistically then the were during the last bubble.

You see, during Bubble1.0 analysts said "CMGI can grow at 150% as far as the eye can see so it makes sense to pay 1000 times earnings for them".  Now the thinking is that if you can grow users 50% per annum, then the value of your user base grows in value even faster--by maybe 200% each year.  Such is EBay's logic behind the $3 Billion price tag for the profitless Skype.  These lofty valuations are based on so-called network effects.  Read on.

Fred talks about something called Reed's law which is Metcalfe's law on steroids.  Metcalfe's Law states that the value of a network is roughly equivalent to the square of its nodes.  IM clients, and p2p file-sharing apps might be examples of this.  Belief in this phenomenon plus new technology enabling collaboration has resulted in boatloads of money being poured into the "social software" space.  Again, lots of folks are looking for the next Skype.  By the way, Reed's Law, which I don't quite understand is even more bold, because instead of a network being valued as n^2, where n is the number of users (nodes), n becomes the exponent, valuing the network as 2^n.  Again, I don't quite understand the rationale, but the theory is based on the idea that each node is in itself a network and thus you have growth within growth.  Who knows.

I see problems with these tools for valuing companies.  First, they take a myopic approach to defining what is Social Software.  Microsoft Windows, while not typically thought of as such, was the ultimate social software when it first came out ("Web 2.0" 1.0?).  For the first time, users with different computers could all share certain standardized software and files.  Remember, in the early days of personal computing there were hundreds of computer companies all with their proprietary operating systems running exclusive software.  Windows, by creating the first common platform made every computer-user much more productive.  One big difference, though between Microsoft, and today's startups is that Microsoft started off by selling their software as opposed to giving it away for free, and then hoping they could provide services.

Another problem is that in all these equations all I see is pluses and exponents.  Where are the Log functions?  Where is the recognition that many kinds of networks degrade with size.  Take an email-listserv for example.  It was nice when it was 5 people in your pottery class trading articles and questions, but if it grew to 50 it would be useless, and then annoying.  Take del.icio.us, which I love.  I subscribe to the finance-tag feed.  So everyday, I see 50 or so headlines to articles that discuss finance.  If, one day, it got bought out by Google, that number turned out to be 500 I'd stop reading the feed.  Perhaps, I'd switch over to del.irio.us.

Even if a network is able avoid degradation, it's inevitable that growth will taper when new nodes start to become irrelevant or redundant.  Such was the conclusion of two economists who discovered that Metcalfe's law overshoots the mark big-time:

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.

Of course, different kinds of networks have different breaking points.  That of a listserv comes relatively quickly, while that of Grokster much later.  Some of them really will be moneymakers...but where is the pessimism? 

The VC industry, I think, suffers from one of the same institutional flaws as Wall St.  In the short term, optimism pays a lot better then pessimism.  BUY calls generate a lot more volume than HOLD calls.  Putting up a Reed's law chart in a presentation will draw bucks into a VC fund a lot quicker than a Log chart.  But in the long term, a healthy skepticism pays better hand-over-fist. 

This points to another problem in Venture-Capital land.  A retail money manager can prudently put large portions of their clients money into cash when he feels that gains will be hard to come by.  VCs, based on the nature of their business, always have to be investing, else their clients would put their money with someone else.  So even when nobody can come up with a viable business-model, like a way to sell a Wiki, you've gotta keep the deals flowing. 

Yes, this blog is unapologetically skeptical about much of the hype over new technologies, or newfangled valuations models and it'll keep banging the drum, encouraging prudence, and at times standing athwart history yelling "stop!".  A lot of the posts recently have been on related topics, the future of computing, Microsoft Vs. Google, what price Skype, etc...it's because we're back to that time, similar to how it felt about 6 years ago, when those who did things "the old way" were being asked to capitulate to the new reality.  We will not...yet.

Comments

[nivi]

2^n comes from the fact that there are 2^n subsets in a set of size n.

For example, if n=2, there are 4 subsets in a set of size 2 (you have to count the empty set).

If n=3, there are 2^3=8 subsets.

Reed's law comes from the fact that if you have n people in a community, you have 2^n possible sub-communities.

Since "value" comes from forming communities, the value of a network that is good at forming communities scales at 2^n.

That's the theory anyway.

If you say that a sub-community is useless when it gets bigger than 150 people, then the right law to use is n^150.

[David Foster]

This kind of valuation model ignores a key factor--competition. It doesn't matter how valuable something is, people will get it from someone other than you if they can get it cheaper. Food is essential, but that's not reflected in stellar margins for farmers and grocery chains.

The idea that one company can fully control the network is, in most markets, naive. AT&Ts network, for example, is not a closed system; you can also communicate with people on MCI or Sprint. Very rarely does one see the kind of closed network that seems to be assumed in this model: Ebay is about as close as it gets.

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