Metacalfe's law is wrong

Models for Network Externalities.

Sarnoff’s Law: V ∝ N (Broadcast Networks)

Metcalfe’s Law: V ∝ N²(Communication networks)

Reed’s Law: V ∝ pow(2, N)(Group forming networks)

Widely Used: V ∝ N Log N

Metcalfe’s law is proposed by Robert Metcalfe — Inventor of Ethernet, founder of 3COM.

Metcalfe’s law: It states that the value of a telecommunications network is proportional to the square of the number of connected users of the system N².

Critical Mass crossover

Metcalfe’s Law points to a critical mass of connectivity after which the benefits of a network grow larger than its costs. The number of users at which this critical mass is achieved can be calculated by solving C*N=A*N², where C is the cost per connection and A is the value per connection. The N at which critical mass is achieved is N=C/A.

Metcalfe’s law assumes that all people in the network are connected .In a case of network with n users, each is connected to (n-1) users and so on for all n people.

Total no of connections is n * (n-1) ∝ n²

In the real world scenario, the observed increase in the value of any communication network with n users is found to be close to N log N.

For example: Let the users in an X and Y network be N, M.

According to Metcalfe’s law: Total value of two networks is N²+M².

When both the networks combine then the value of the network will be (N+M)². (Which is not observed in the real world scenario and contradicting the above statement).

So this states that Metcalfe’s law is just an empirical law like Moore’s law which states that No of transistors in a chip will double every 18 to 20 months. Metcalfe’s law is not a physical law.

The value of Interconnecting

A network grows not only by the addition of single members. It can jump in size by interconnecting or merging with another network. If N log N holds good the smaller network would gain more than larger one. For Example: If the larger network is eight times as large as smaller one, its gain would be less than half of the smaller one. This reduces the incentive for the owners of the larger network to interconnect without compensation.

N log N law for valuation of Skype and Whatsapp

For c3 = 2.89$(mean C) Present Valuation of Whatsapp = $26.1 billion. For c3 = 4.88$ Present Valuation of Whatsapp = $43.92 billion.

For c3 = 5.5155$(mean C) Present Valuation of Skype = $14 billion.

For c3 = 7.185$ Present Valuation of Skype = $18.27 billion.

The above calculations are the estimated calculations by taking the constants from C NlogN =valuation for Whatsapp and Skype at the time of Acquisitions.

Good Content + Good Network = Great results.