Bass Diffusion Forecaster · iPod — Minkyu Sung
Tools I built · New Product Diffusion

Bass Diffusion Forecaster.

The classic Bass model projects how a new product spreads through a market — a race between innovators (p) who adopt on their own and imitators (q) who follow the crowd. It loads with the coefficients I fit to Apple's real iPod sales — move the sliders to see the adoption curve, the sales peak, and when the market saturates.

Parameters

Coefficient of innovation (p){{ pLabel }}
External pull — ads, launch buzz, early adopters.
Coefficient of imitation (q){{ qLabel }}
Word-of-mouth — social contagion from existing users.
Market potential (M){{ mLabel }}
Total eventual adopters (thousands of units).
Horizon{{ horizonLabel }}

The ratio that shapes the curve

q/p = {{ qpRatio }}. When imitation dwarfs innovation, adoption starts slow, then accelerates hard once social proof kicks in — exactly the iPod's shape.

Peak sales
{{ peakSales }}
in {{ peakWhen }}
Total adopters
{{ mLabelShort }}
market potential
Saturation
{{ saturation }}
adopted by horizon

Adoption over time

per-period sales + cumulative
{{ yTop }} 0 {{ xStart }} {{ xEnd }}
New adopters per period Cumulative adopters

Model

St = p·(M − Yt−1) + q·(Yt−1/M)·(M − Yt−1)

Coefficients estimated by regressing St on Yt−1 and Yt−1², then solving for M, p, and q — the method from the iPod mini-project. Simulation runs live in-browser.

The project behind it

iPod: the story of a lifecycle.

For a graduate New Product Marketing project, my team reconstructed Apple's iPod unit sales from 2002–2014 out of 10-Q and 10-K filings, then fit the Bass model to it. The annual fit put market potential near 403M units, with imitation (q ≈ 0.52) roughly 19× stronger than innovation (p ≈ 0.028) — the signature of a product carried by word of mouth. The predicted peak lands around 2007, matching the real growth peak before the iPhone took over.

Why it matters: the same two coefficients turn a launch guess into a plan — when to build inventory for the peak, when maturity will flatten, and when to line up the next product. The recommendations followed the curve: invest hard in the slow introduction phase to recruit early adopters, plan for the Q1 holiday spike, and stage the end-of-life transition early — which is exactly how Apple handed the baton from iPod to iPhone.