Bass diffusion model
The quantitative member of cluster F — the mathematical counterpart to Rogers’ qualitative technology-adoption-curve. Published by Frank Bass (1969), it models how a new product’s cumulative adoption F(t) grows over time as the sum of two forces:
- Coefficient of innovation
p— external influence (advertising, media); adopters who buy independent of others. Typical p ≈ 0.03 (range ~0.01–0.03). - Coefficient of imitation
q— internal influence (word-of-mouth, social contagion); adopters pulled in by those who already adopted. Typical q ≈ 0.38 (range ~0.3–0.5).
The governing equation is dF/dt = (1 − F)(p + qF), which produces the familiar S-shaped cumulative curve (slow start → acceleration as imitation compounds → plateau at saturation). It is widely used for new-product and technology sales forecasting (consumer durables, medical devices, services).
How it relates to the rest of cluster F
- Maps onto Rogers.
p-driven early buyers ≈ Rogers’ innovators; theq-driven bulk ≈ the early/late majority whose adoption is socially mediated. Bass adds math to Rogers’ categories — you can fitp,qto early data and project the curve. - It is a continuous/aggregate model. This bears directly on the wiki’s standing
continuous-vs-discontinuous tension (Moore posits a sharp
chasm; Rogers insists adoption is a continuous variable): Bass sits
firmly on Rogers’ side — a smooth aggregate S-curve with no discontinuity built in.
Moore’s chasm would appear, in Bass terms, as a regime where
qfails to ignite for the pragmatist majority — something the basic model doesn’t predict, which is exactly the refinement Moore added by hand. - Sentiment is a separate axis. Bass models adoption share, not expectation — the gartner-hype-cycle‘s territory; pairing the two (adoption × sentiment) stays more informative than either alone.
Limitations
The basic model covers only the introduction + growth phases (not full life-cycle), assumes a fixed market potential, and — like all of cluster F — is a useful lens, not a validated law (parameters are fit retrospectively; forecasts are sensitive to early-data noise).
Related
technology-adoption-curve · everett-rogers · crossing-the-chasm · geoffrey-moore · gartner-hype-cycle · tech-adoption-curve-twenty-years