In short: the Double Jeopardy Law (McPhee 1963, Ehrenberg 1969) documents that big brands have simultaneously more buyers AND slightly higher loyalty than small brands. The driver of growth is penetration (number of distinct buyers), not loyalty. Light buyers (1-2 purchases/year) generate 70-80% of revenue in many categories. Typical budget allocation: 60-70% acquisition of new buyers, 30-40% retention. Loyalty programs have weak or null effects on real retention.
Double Jeopardy Law: the empirical pattern
William McPhee formulated it in 1963 in "Formal Theories of Mass Behavior". Andrew Ehrenberg demonstrated it empirically in 1969-1972 ("Repeat Buying"). The law: in a category, brands with smaller market share suffer "double jeopardy" — fewer total buyers (penetration) AND slightly lower loyalty (purchases per buyer per year).
The numbers are robust across 50+ categories and 30+ countries. Typical examples (UK FMCG): big brand 60% penetration × 4 purchases/year = 240; small brand 15% penetration × 3 purchases/year = 45. The market share difference (5-6x) is driven by penetration (4x), not by loyalty (1.3x).
Strategic implication: to grow market share, you must increase the number of buyers, not the loyalty of existing customers. Loyalty will follow as a side effect (Double Jeopardy in its positive version: big brand = also more loyal).
Real numbers: big vs small brands
Sharp ("How Brands Grow", 2010) presents extensive tables. In the UK detergent market (Nielsen panel 2007):
| Brand | Market Share | Penetration | Purchases/year |
|---|---|---|---|
| Persil | 22% | 41% | 3.9 |
| Ariel | 14% | 26% | 3.7 |
| Bold | 8% | 17% | 3.4 |
| Surf | 5% | 12% | 3.0 |
The market-share difference Persil vs Surf (4.4x) is almost entirely penetration (3.4x), very little loyalty (1.3x). The same pattern repeats in practically every FMCG, banking, telco, retail category.
Light buyers: who they are and why they matter
Sharp defines a light buyer as a buyer with frequency below the category average. In many categories the light buyer purchases 1-2 times a year, against heavy buyers' 8-12. The distribution is skewed: few heavy, many light.
Pareto is misunderstood: 80/20 (80% of revenue from 20% of customers) is rare in real data. The typical distribution is 60/20 or 50/30 depending on category. Light buyers (50-70% of buyers) still generate 30-50% of revenue, a share too large to ignore.
Sharp shows that focusing only on heavy buyers leads to a strategy paradox: by definition, heavies already buy a lot, so the only lever is trying to make them buy even more (saturation effect). Whereas lights, who are many, can be nudged to buy slightly more, producing a bigger aggregate lift.
Loyalty programs: documented limits
Ehrenberg-Bass has published 30+ papers on loyalty programs. Consistent conclusion: most loyalty programs have a negligible effect on actual loyalty. Loyalty-program "members" are largely customers already loyal before signing up (selection bias).
Sharp et al. study (2002, "Loyalty Programs and Their Impact on Repeat-Purchase Loyalty Patterns") on grocery retail: loyalty-program participants show repeat purchase rate only marginally above non-participants, after controlling for pre-existing buying behaviour.
Loyalty programs have a legitimate function: data collection (CRM), promo tool, perceived emotional retention. They do not have the promised function of "turning casual buyers into heavy buyers".
Evidence-based budget allocation
Given the Double Jeopardy + light-buyer dominance pattern, optimal budget allocation for most categories:
60-70% acquisition: mass-marketing reach campaigns to build mental + physical availability. Goal: increase number of distinct category buyers.
30-40% retention: customer experience, packaging, basic email communication, customer service. Goal: maintain the implicit loyalty that comes with brand size.
Specific cases where allocation changes:
- Subscription/SaaS brands: 50-50 because churn is high and retention is worth as much as acquisition.
- Low-frequency categories (cars, mortgages): 80-20 acquisition because every purchase is significant.
- Brand crisis/decline: 70-30 acquisition + win-back of churned customers.
Case: changing strategy in a mid-market Italian brand
Typical pattern observable in Italian mid-market SMEs: historic brand with loyal customer base (e.g. 30k customers who repurchase regularly), but stagnant revenue for 5-8 years. Current strategy concentrated on loyalty email, points programs, VIP customer events.
Ehrenberg-Bass diagnosis: the 30k base is small relative to the total market (e.g. 2M potential consumers = 1.5% penetration). Current budgets (e.g. 70% retention) do not build mental availability for the 1.97M non-customers.
Recommended strategy: 60% reinvested in acquisition (brand reach advertising + SEO content + retail presence), 40% kept in retention (simplified: transactional email, basic loyalty without complex points programme). Goal: bring penetration from 1.5% to 3-4% in 24 months via mental availability building. Expected result: doubled revenue even with stable loyalty.
Customer base graph: visualising the distribution
Simple diagnostic tool: on your CRM data, plot the distribution of annual purchases per customer. Typically takes the shape of an inverted "L": many customers with 1-2 purchases, few with 8+ purchases.
X-axis: number of purchases/year. Y-axis: number of customers. The Negative Binomial Distribution (NBD) graph mathematically describes this shape and lets you estimate the "true" growth potential.
Ehrenberg-Bass proposes the NBD-Dirichlet model as a simulator: input data (penetration, average frequency, market size), simulate the impact of different scenarios (e.g. "if I increase penetration by 30% while keeping loyalty, what market share?").
FAQ
Is loyalty "dead"?
No, but it is subordinate to penetration. Loyalty exists and has value, but it grows as a consequence of brand size, not as an independent driver. Investing heavily in loyalty while penetration is low = inverting the lever.
How does Double Jeopardy apply to B2B SaaS subscriptions?
The same law holds: large SaaS have more customers and slightly lower churn. The growth driver is acquisition + reduce churn (both correlated with size). Strategies of "expansion revenue from existing customers" have a mathematical ceiling lower than pure acquisition.
Are there exceptions to Double Jeopardy?
Very few. Ehrenberg-Bass has catalogued exceptions (deviation patterns) in specific cases: deliberately niche brands (e.g. cult brands), subscription brands with high switching cost (telco contracts), premium brands with their own rules. Even there, the law works directionally, just with different coefficients.
Should the loyalty program be removed?
Not necessarily. Keep a simple loyalty program if it serves for data collection and CRM. Drop the claim that the program is a growth lever. Redirect the budget of complex programmes (e.g. elaborate points systems) towards acquisition.
How to measure penetration in the Italian market?
Three approaches: (1) NielsenIQ/Circana panel data if available for the category; (2) omnibus survey of 1,500+ respondents with "have you ever bought X?" questions; (3) proxy via market share / average frequency assumption. For SMEs, an annual omnibus survey (€8-15k) is the most realistic setup.
Win-back vs acquisition: which is more efficient?
It depends on the nature of churn. Win-back is efficient for involuntary churn (lapsed customers who stopped without active reason). New-customer acquisition is more efficient for category expansion (reaching consumers who never entered). Typically: 70% acquisition, 30% win-back as starting ratio.
Sources and references
- McPhee, W. — "Formal Theories of Mass Behavior" (1963, Free Press)
- Ehrenberg, A. — "Repeat-Buying: Theory and Applications" (1972, North Holland)
- Sharp, B. — "How Brands Grow: What Marketers Don't Know" (2010, Oxford University Press) — Double Jeopardy chapter
- Sharp, B. et al. — "Loyalty Programs and Their Impact on Repeat-Purchase Loyalty Patterns" (Journal of Consumer Marketing, 2002)
- Romaniuk, J. & Sharp, B. — "How Brands Grow Part 2" (2015, Oxford University Press)
- Ehrenberg-Bass Institute — NBD-Dirichlet model documentation
- Nielsen Catalina — Brand Effect studies on penetration vs loyalty (2018-2023)
- Reibstein, D., Day, G. — "Marketing Metrics" (2010) for complementary metric framework
