Takeaway

The Bass model explains adoption curves via innovators (external influence) and imitators (word-of-mouth), producing an S-shaped cumulative adoption over time.

The problem (before → after)

  • Before: Adoption forecasting is ad hoc.
  • After: A simple differential equation with two parameters (p, q) fits many product lifecycles.

Mental model first

Early adopters try new tech on their own; later adopters follow others. The more who adopt, the stronger the imitator effect—until saturation.

Just-in-time concepts

  • Hazard of adoption: p + q F(t), where F is cumulative adoption fraction.
  • Differential equation and analytic solution for N(t).
  • Estimation from time-series sales data.

First-pass solution

Fit p and q by nonlinear regression on sales time series; forecast peak timing and saturation.

Iterative refinement

  1. Extensions: Marketing mix, pricing, and heterogeneity.
  2. Competition: Multi-product diffusion and substitution.
  3. Network-aware diffusion and contagion models.

Principles, not prescriptions

  • Separate innovation push (p) from social pull (q).
  • Validate forecasts against cohort and channel data.

Common pitfalls

  • Overfitting with short histories; parameter instability.
  • Ignoring supply constraints or channel effects.

Connections and contrasts

  • See also: [/blog/network-effects], epidemic SIR models.

Quick checks

  1. What shapes the S-curve? — Interaction of p and q.
  2. What is peak sales timing? — When imitator effect starts to wane near saturation.
  3. How to extend? — Add covariates for marketing spend and price.

Further reading

  • Bass (1969), subsequent empirical studies