Yesterday, I posted an open question about the source of network value. Of course, I'm not the first to ponder this question, and thankfully so, because I get to lean on many great minds for the meat of today's post.
A while back, Robert Metcalfe, the inventor of Ethernet protocol, coined the famous Metcalfe's Law, which says that "the value of a telecommunications network is proportional to the square of the number of users of the system." This theory recognized that if the world had only one fax machine, then that machine may as well be a doorstop. Two fax machines? Now you're starting to have something a little more useful. If that fax machine has a million other potential fax machines to talk to, then it is even more useful.
It wasn't so easy for Mr. Metcalfe and his new law, because a bunch of people questioned his math, since he seemed to think that every user you add to the network is equally valuable. Of course, in the real world, there are bunches of people you would just as soon weren't connected to the network. So, the incremental value of adding somebody to the network is highly variable, and sometimes of no value at all. Metcalfe himself conceded this point.
Andrew Odlyzko co-authored a paper that claimed that Metcalfe's Law was wrong, and that the true value of a network is closer to "n log(n)", rather than "n squared", where n is the number of users of the network. It's a good paper, and it seems about right to me, at least for typical interactive network applications like phone calling and faxing.
Other folks came up with other ways of measuring network value based on the number of users or connections, focused on different kinds of networks. For example, David Sarnoff, an executive with RCA Television, believed that the value of a broadcast network grows linearly with the number of subscribers, and that makes sense because the incremental revenue generated when a new broadcast subscriber is added is limited to the subscription and advertising revenue you generate from that one subscriber. This effect is called Sarnoff's Law.
At the other extreme we have Reed's Law, named after David P. Reed, who said that the value of social networks is actually 2 to the nth power, where n is the number of subscribers. As Reed put it in "The Law of the Pack" (Harvard Business Review, February 2001, pp 23-4):
- "[E]ven Metcalfe's Law understates the value created by a group-forming network [GFN] as it grows. Let's say you have a GFN with n members. If you add up all the potential two-person groups, three-person groups, and so on that those members could form, the number of possible groups equals 2n. So the value of a GFN increases exponentially, in proportion to 2n. I call that Reed's Law. And its implications are profound."
Here's a table of the relative value of different network types according to these valuation laws:
| Number of Subscribers |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
| Sarnoff's Law |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
| Odlyzko's Law |
0 |
1 |
1 |
2 |
3 |
5 |
6 |
7 |
9 |
10 |
11 |
13 |
| Metcalfe's Law |
1 |
4 |
9 |
16 |
25 |
36 |
49 |
64 |
81 |
100 |
121 |
144 |
| Reed's Law |
2 |
4 |
8 |
16 |
32 |
64 |
128 |
256 |
512 |
1024 |
2048 |
4096 |
So, you can see how Reed's law starts assigning some pretty outlandish values at even small numbers of subscribers, which seems more than a little bit Internet Bubble 2.0-ish to me. Reed makes the same mistake as Metcalfe makes, where he assumes that just because you CAN make a group on a network, doesn't mean that anybody really WANTS to.
Still, the general idea that group collaboration might be somewhat more valuable to people than bilateral interactivity might be true, so it does lead to a hypothetical rank-ordering of network types by value:
- Social networks (possibly as valuable as 2 to the nth power?)
- Interactive networks (probably about as valuable as n log(n), but possibly as valuable as n squared)
- Broadcast networks (value grows linearly with the number of subscribers).
If the above rank-ordering is true, and I wanted to invest in a network today, what kind of network deserves my investment? An Internet backbone can support all three of the above application types, so that is kind of a slam dunk. How about a Cable TV network? Well if it can only support content broadcasting, then it won't be as valuable as a network that can also do Internet access and voice services, which is exactly why CableLabs developed the DOCSIS and PacketCable standards to extend the cable plant into additional, higher-value services.
Hmmm. If the above rank-ordering is true, which expansion strategy is likley to create more value:
- Telcos offering broadcast television and pay-per-view services?
- Cable companies offering telephone services?
- Wireless phone companies offering content services?
Of course, there is a lot more to think about in this kind of question than a simple rank-ordering of application value. More to come.