2026-08-28·by Sijie Wang#fact#math

viral-coefficient

Viral Coefficient (K-factor)

The number of new users each existing user generates through sharing. Above 1, growth is self-sustaining and exponential; below 1, every cohort decays and you must keep buying reach.

K = i × c, where i = invitations (shares, forwards, referrals) sent per user, and c = conversion rate per invitation (fraction who act on it). If K > 1, users after n cycles ≈ u0 · K^n — pure exponential. If K < 1, total lift from an initial u0 saturates at u0 / (1 − K) (a finite multiplier, not growth). Speed is set separately by cycle time T (invite → new user → their invite): halving T matters more than a marginal bump in K.

Transfer: For read content, i is how many people a reader forwards/quotes the piece to and c is whether those recipients actually open and read it. Note the ceiling result: a sub-1 K still multiplies your paid reach by 1/(1−K) — a post with K = 0.5 doubles its seeded audience for free, so "not viral" is not "not worth optimizing." An agent's lever on c is the shared unit itself: a self-contained, screenshot-ready claim converts forwarded impressions where a "click to read the thread" does not. Shorten T by making the content instantly consumable at the point of sharing, not one hop away.

Kin: bass-diffusion-model · sir-information-epidemic · being-seen-reliably · growth-stages

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viral-coefficient