# Hertling’s Equation

*I’m a huge fan of William Hertling. His newest book, The Turing Exception, is dynamite. It’s the fourth book in the Singularity Series, so you really need to read them from the beginning to totally get it, but they are worth every minute you’ll spend on them.*

*William occasionally sends me some thoughts for a guest post. I always find what he’s chewing on to be interesting and in this case he’s playing around with doing a Drake’s Equation equivalent for social networks. Enjoy!*

Drake’s Equation is used to estimate the number of planets with currently communicating life, which helps us predict the odds of finding intelligent life in the universe. You can read the Wikipedia article for more information, but the basic idea is to multiply together a number of functions: the number of stars in our galaxy, the fraction of those that have planets, the average percent of planets that could support life, etc.

I’m currently writing a novel about social networks, and one of the areas that’s interesting to me is what I think of as the empty network problem: a new social network has little benefit unless my friend are there. If I’m an early adopter, I might give it a few days, and then leave. If my friends show up later, and I’ve already given up on it, then they don’t get any benefit either.

Robert Metcalfe, inventor of ethernet, coined Metcalfe’s Law, which says “the value of a telecommunications network is proportional to the square of the number of connected users of the system (n^2).”

Social networks actually have a more rigorous form of that law: “the value of a *social* network is proportional to the square of the number of connected *friends*.” That is, I don’t care about the number of strangers using a network, I care about the number of friends. (Friends being used loosely here to include friends, family, coworkers, business associates, etc.)

Drake’s Equation helps predict the success of finding life in the universe because it takes into account the rise and fall of civilizations: two civilizations must exist at the same time and within observable distance of each other in other to “find intelligent life”.

So there must be a similar type of equation that can help predict a person’s adoption of a new social network and takes into account that we’re only willing to try a network for so long before giving up.

Here’s my first shot at this equation:

P = (nN * fEA * fAv * fBE * tT) / (tB * nF) * B

P = probability of long-term adoption

nN = Size of my network (number of friends)

fEA = Fraction of my friends who are Early Adopters

fAv = fraction of those who have available time to try a new network

fBE = fraction that overcome the Barrier to Entry

tT = Average length of time people Try the network

nB = Average length of time it takes to see Benefit of the new network

nF = Number of Friends needed to see benefit

B = The unique benefit or desirability of the network

In plain English: The probability of a given person becoming a long term user of a new social network is a function of the number of their friends who also adopt and how long they remain there divided by the length of time and number of friends it takes to see the benefit multiplied by the size of the unique benefit offered by the social network.

Some ideas that fall out from the equation:

- A network that targets teens, who may tend to have more time and may be more likely to be early adopters, will have an easier time gaining adoption than a network that targets busy executives, all other things being equal.
- A network that has a benefit when even two friends connect will see easier initial adoption than one that requires a dozen friends to connect.
- A network whose benefit applies to distant connections is at an advantage compared to one that only offers a benefit to close friends (because N is larger)
- A sufficiently large unique benefit can overcome nearly any disadvantage.
- Social gaming is interesting, because it provides benefit even when connected to no one, the benefit increases when connected to strangers, and then increases even more when connected to friends.

What do you think?