Economics and incentives
Network effects
A product becomes more valuable to each user as more people use it, which makes leaders grow faster and makes leaving hard.
Understood in telephony a century ago, when AT&T's president Frederick Fish priced home lines below cost to grow the subscriber base; formalised by Jeffrey Rohlfs in 1974. "Metcalfe's law" began as a 3Com sales slide around 1980 and was named by George Gilder in the 1990s.
A telephone with nobody to call is worthless, and each new subscriber makes every existing one worth a little more. The same holds for fax machines, marketplaces, messaging apps, programming languages and file formats: the value to you depends on who else is on it. Metcalfe's law puts a number on it. A network of n members allows n(n-1)/2 pairs, so if every pair is worth the same, value grows with the square of users. Some effects are indirect, running through a second group: more apps draw more users to a platform, and more users draw more apps. The consequences are a hard start, a tipping point, winner-take-most markets and switching costs that hold users in place.
It holds because each new user adds value to all existing users, so growth feeds growth; a network effect is a positive feedback loop. That is why early users get subsidised, why standards wars are fought so hard and why incumbents resist interconnecting with rivals. Facebook is the usual modern case: more than a billion monthly users by October 2012, and in 2013 Bob Metcalfe fitted his own law to its revenue, as the example shows. In practice the question for a new product is where the value comes from before the network exists, because the loop has to be started by something other than itself.
Metcalfe's law is a rule of thumb, not a law, and the square is almost certainly too high. Andrew Odlyzko and Benjamin Tilly argued in 2005 that connections are not equally valuable: most people's valuable links are a small circle, and the rest are rarely used. Their test is interconnection. If value grew as n squared, two equal networks would double their combined value by joining, yet a century ago the Bell System and the independent phone companies resisted interconnection for two decades. They propose n log n, a growth only a little faster than linear, which also explains why so many dot-com business plans built on the square failed. Network effects also run in reverse when users leave, and many firms claim one when they merely have economies of scale.
Example
On 4 October 2012 Mark Zuckerberg announced that more than one billion people were using Facebook each month. In the December 2013 issue of IEEE Computer, Bob Metcalfe plotted Facebook's monthly active users from 2004 to 2013 and its annual revenue over the same ten years, fitted an S-curve to the users and his n-squared law to the revenue, and called it the first application of Metcalfe's law to real data. At the end of 2012 the network had about 1.06 billion users and 150 billion friend connections, about 141 per user. A fit of revenue during a growth phase is weak evidence for the square, which is why the critique in paragraph three still stands.
Where it applies
Choose tools partly by who else uses them: a language, a framework or a model ecosystem with more users has more libraries, answers and hires, and the gap widens. When you build a marketplace, a data platform or an internal tool, solve the empty-network problem first by seeding one side or making it useful to a single user before any network exists.
Think about it
Which product or tool do you use mainly because everyone else does, and what would it take for that to flip?
Applied it to something real? Log it.
Test yourselfWhat observation did Odlyzko and Tilly use against Metcalfe's n-squared law?
If value grew as n squared, two equal networks would double their value by interconnecting, yet Bell and the independent phone companies resisted it for two decades. Connections are not equally valuable; they propose n log n.
Related models
- Feedback loopsA system's output feeds back into its input: balancing loops hold a level steady, reinforcing loops make change grow on itself.
- The Lindy effectFor things that do not wear out, such as ideas, books and technologies, every year they survive raises how long they can be expected to last.
- NonlinearityCause and effect are not proportional: a push can do nothing or everything depending on where the system sits relative to a threshold.
- Supply and demandPrice settles where what sellers will offer meets what buyers will take; hold it anywhere else and a shortage or a glut does the adjusting instead.
- OptionalityPrefer positions that give you the right, but not the duty, to act later, so you can take the upside when it appears and walk away when it does not.
Sources and further reading
- Andrew Odlyzko and Benjamin Tilly, A refutation of Metcalfe's Law and a better estimate for the value of networks and network interconnections (2005)
- Bob Metcalfe, Metcalfe's Law after 40 Years of Ethernet, IEEE Computer 46(12) (December 2013)
- Facebook newsroom, One Billion People on Facebook, 4 October 2012