How Brands Grow, Part 2
Sharp, B., Kennedy, R., & Sharp, A. (2019). How Brands Grow, Part 2: Emerging Markets, Services, Durables, New and Luxury Brands. Oxford University Press.
1 The same laws apply — almost everywhere
“How Brands Grow, Part 2” begins with a striking claim: the empirical patterns revealed in How Brands Grow (2010) are not limited to fast-moving consumer goods. They appear in durables, services, new and luxury brands, B2B, and emerging markets.
The fundamental insight holds:
- Brands grow primarily by increasing penetration — the number of category buyers who buy them at least once in a period—rather than by deepening loyalty.
The second volume provides the evidence and qualifications that make that claim robust beyond supermarkets.
2 Law 1 — Double Jeopardy is universal
Across hundreds of datasets, the familiar Double Jeopardy pattern still appears:
| Measure | Large brands | Small brands |
|---|---|---|
| Penetration | High | Low |
| Average frequency per buyer | Slightly higher | Slightly lower |
Even in airlines, mobile networks, banks, and software subscriptions, smaller brands suffer both fewer buyers and slightly weaker loyalty. The small brand does not have a tribe of super-fans that compensates for its size.
The implication repeats the first book’s logic: if you want to escape double jeopardy, you need to reach more people, not invent a “relationship strategy.”
3 Law 2 — The Duplication of Purchase Law holds across categories
The Duplication of Purchase Law describes how brands share customers. If \(D_{ij}\) is the proportion of Brand i’s buyers who also bought Brand j,
\[ D_{ij} \approx \text{market share of Brand j} \]
So each brand shares its buyers with others roughly in proportion to those others’ size.
In durables, the same logic appears as duplication of ownership or overlap of consideration—for example, people who own Toyota also consider Ford or Honda in roughly market-share proportion.
Managers sometimes call this “brand repertoires” or “multi-brand households.” The law shows that sharing customers is normal, not a sign of weakness. It also means: if you grow your market share, you automatically grow your overlap with everyone else, which is fine.
4 Law 3 — Penetration and purchase frequency scale the same way in services and durables
Services and durables have longer inter-purchase intervals, so “frequency” is measured over years, not weeks. But the underlying shape of buyer heterogeneity still fits the Negative Binomial Distribution (NBD):
\[ P(X = x) = \frac{\Gamma(x + k)}{\Gamma(k)\, x!} \left(\frac{k}{k + \mu}\right)^{k} \left(\frac{\mu}{k + \mu}\right)^{x}, \quad x = 0,1,2,\ldots \]
Here
\(\mu\) is mean purchase rate and
\(k\) captures heterogeneity.
In durables, most people’s \(X = 0\) for several years — exactly what the NBD predicts.
Hence the “zero-class problem” (many non-buyers in a period) is not a data defect; it’s an expected feature of how buying rates are distributed.
5 Law 4 — Light buyers dominate, even in subscription or contractual categories
Managers in telecoms, insurance, or software often believe their base is stable and heavy. The data show that most customers are occasional, churn regularly, and represent the majority of potential growth.
Retention programs tend to benefit existing heavy users but rarely change the shape of the NBD. Because attrition and recruitment are continuous, a brand that stops recruiting declines—even with good retention.
\[ \text{Net Growth} = \text{New buyers} − \text{Lapsed buyers} \] Strategic implication: acquisition and retention are two sides of the same population churn. You cannot trade one for the other; you must feed the pipeline.
6 Law 5 — Physical and mental availability still drive penetration
In services and durables, “physical availability” expands beyond shelf space:
| Aspect | Examples |
|---|---|
| Ease of access | App usability, website loading speed, store hours |
| Distribution breadth | Number of dealerships, delivery coverage |
| Service accessibility | Branch or call-centre availability, local-language support |
Mental availability still means being easily thought of in buying situations, but the category cues differ:
- For durables: “Which car brands come to mind?”
- For services: “Which banks could I open an account with?”
- For luxury: “Which brands fit the occasion or identity?”
Brands with strong and distinctive memory structures — logos, cues, stories — have higher mental availability and, therefore, higher penetration. Luxury does not escape this rule; exclusivity works only if the brand is still salient.
7 Law 6 — Distinctive assets, not abstract differentiation, explain brand identities
Part 2 provides extended evidence on distinctive brand assets — colours, shapes, taglines, characters — that allow buyers to recognise and choose the brand quickly. Testing by the Ehrenberg-Bass Institute shows that these assets differ in:
- Uniqueness (how linked to your brand),
- Fame (how many category buyers recognise it).
Strong assets have both.
Managers are advised to measure and protect distinctive assets as if they were distribution points: they are memory distribution.
A summary table from the Institute’s metrics:
| Asset type | Example | Managerial action |
|---|---|---|
| Colour | Cadbury purple | Consistent use across media |
| Character | Michelin Man | Use frequently to build fame |
| Shape / pack | Coca-Cola contour bottle | Never abandon distinctive geometry |
| Sound | Intel “bong” | Reinforce through repetition |
Distinctiveness works because it fuels mental availability in low-attention environments.
8 Law 7 — Emerging markets follow the same patterns, just compressed
Data from India, China, Indonesia, and Latin America show the same statistical laws—Double Jeopardy, Duplication, and NBD — although:
- Penetrations are lower (distribution still building),
- Purchase frequencies shorter (smaller pack sizes, affordability cycles),
- Brand sets smaller (limited choice).
As physical and media availability widen, these markets converge toward the same mature patterns observed elsewhere.
Hence, marketing “laws” are not Western artefacts; they are behavioural regularities arising from human buying patterns.
9 Law 8 — Luxury and high-involvement categories obey the same mathematics
Luxury brands seem like exceptions: buyers talk of emotion, identity, and status. But when measured, their customer-base metrics follow the same shape:
- Big luxury brands (Rolex, Louis Vuitton) have more buyers,
- Their buyers are only slightly more loyal,
- Purchase repertoires still exist — people own multiple luxury brands.
The difference is mainly in buying frequency (very low \(\mu\)) and in distribution control (selective physical availability). But once you adjust for those, the same equations predict buyer counts and repeat rates.
Thus, luxury marketing’s “exclusivity” rhetoric masks the same behavioural law: growth still depends on penetration—reaching more eligible buyers, even within a narrow elite.
10 Law 9 — Innovation and new brands fit the model too
Launch data show that most new brands follow the same trajectory as established ones scaled down:
Rapid early trial → flat penetration plateau,
Slight loyalty advantage early on (novelty or promotion) → convergence to category norms.
Their penetration decay can be modelled as a special case of the NBD–Dirichlet, where initial awareness is low and physical availability grows over time.
Mathematically, the expected repeat rate \(R\) after first trial relates to mean purchase rate \(\mu\), and heterogeneity \(k\):
\[ R = 1 - \left(\frac{k}{k+\mu}\right)^k \]
As distribution expands, \(\mu\) increases, raising both penetration and repeat rate mechanically — no new psychology required.
Managerial takeaway: most “launch failures” are distribution failures or insufficient reach, not product-love failures.
11 Law 10 — Advertising builds mental availability, not persuasion
Part 2 presents further evidence from single-source media-exposure data: campaign effects come mainly from refreshing memory structures across the whole category, not from converting a narrow segment through argument.
Advertising works when it:
- Reaches as many category buyers as possible,
- Uses distinctive brand assets consistently,
- Is broad, emotional, and recognisable rather than narrowly targeted or rationally persuasive.
Media fragmentation doesn’t change this.
Digital platforms still obey the reach rule: you must be seen, not micro-targeted.
13 Law 12 — Brand extensions behave predictably
When a brand launches a line extension, its sales typically add to the parent’s penetration because many buyers overlap. Duplication analysis predicts the cannibalisation rate.
Under Dirichlet assumptions — that is, assuming category buyers vary in their underlying buying rates but otherwise buy brands independently and in proportion to their popularity — the expected overlap of buyers between a parent brand and its extension is roughly
\[ \text{Expected Overlap} \approx s_i + s_j - (1 - s_j)^{s_i / s_j} \]
where
\(s_i\) = the parent brand’s share and
\(s_j\) = the extension’s share
- Every buyer has a stable long-term buying rate for the category (as described by the Negative Binomial Distribution).
- Each brand has a constant probability of being chosen on any occasion, proportional to its market share.
- Buying decisions are independent across brands and occasions.
- Differences in loyalty or duplication arise naturally from these random-choice probabilities — not from deep psychological attachment.
Empirically, about 60–80 % of extension buyers also buy the parent. So most extensions expand reach modestly but rarely double the brand’s buyer base.
Managerial implication: extensions are safer when they add new physical or mental availability cues (new formats, occasions) rather than simply replicate the parent.
14 The managerial philosophy: build reach and memory, not myths
Throughout Part 2, Sharp and colleagues hammer the same scientific stance:
| Common belief | Evidence-based reality |
|---|---|
| “Services, durables, luxury are different.” | The same buying patterns re-emerge once you control for purchase interval. |
| “Smaller brands have loyal fans.” | Loyalty scales mechanically with size. |
| “Niche targeting builds efficiency.” | It limits penetration and long-term growth. |
| “Premiums prove differentiation.” | They mostly reflect limited distribution, not unique psychology. |
| “Digital breaks the rules.” | Digital is another channel; reach still rules. |
Hence the manager’s task is unchanged:
- Maintain and expand distribution (physical availability).
- Refresh and reinforce memory structures (mental availability).
- Use consistent distinctive assets.
- Measure success in terms of penetration and share, not subjective “relationships”.
15 Summary of key quantitative patterns
| Pattern / “Law” | Short description | Mathematical expression (simplified) |
|---|---|---|
| Negative Binomial Distribution | Purchase frequency across buyers | \(P(X=x) = \frac{\Gamma(x+k)}{\Gamma(k)\,x!}\left(\frac{k}{k+\mu}\right)^k\left(\frac{\mu}{k+\mu}\right)^x\) |
| Zero-class (non-buyers) | Share of non-buyers in period | \(P(0) = \left(\frac{k}{k+\mu}\right)^k\) |
| Double Jeopardy | Small brands have fewer & slightly less-loyal buyers | Empirical linear relation between penetration and loyalty |
| Duplication of Purchase | Brand overlaps proportional to market shares | \(D_{ij} \approx s_j\) |
| Penetration vs frequency | Growth via more buyers, not heavier buyers | \(\text{Sales} = \text{buyers} \times \text{avg. freq.}\) |
These formulae are descriptive, not mechanical “laws of physics”, but they summarise consistent, cross-category regularities.
16 The overall message of Part 2
Human buying patterns are remarkably stable.
Whether buying chocolate, insurance, cars, or luxury goods, most people behave as light, occasional, repertoire buyers.
Marketing laws scale.
The same NBD–Dirichlet mathematics predict market shares, overlaps, and loyalty in categories with radically different frequencies.
Penetration still dominates.
Even in “special” categories, growth comes from reaching more category buyers.
Mental and physical availability remain the growth levers.
Visibility, accessibility, and distinctiveness determine who buys and how often.
Consistency beats novelty.
The assets that buyers can recall and recognise quickly are the engines of growth.
Evidence trumps intuition.
The book continues the Ehrenberg-Bass mission: to replace untested marketing folklore with measurable empirical generalisations.
16.1 Closing thought
If Part 1 dismantled old myths, Part 2 universalised the evidence: the “laws of growth” apply not only to soap and cereal but to software, services, and champagne.
Wherever people choose among alternatives, the same arithmetic of buying behaviour governs success:
- Be easy to think of.
- Be easy to buy.
- Reach everyone in the category.
That is still how brands grow.