Double jeopardy

The pattern was found somewhere strange. In 1963 the social scientist William McPhee published Formal Theories of Mass Behavior, and in it he described a double penalty he kept meeting in popularity data. Less famous Hollywood actors were known by fewer people, and the people who did know them liked them less. The same held for comic strips and radio presenters. He called it double jeopardy, and he explained it as a statistical selection effect rather than anything about the actors.

Andrew Ehrenberg then spent much of his career showing that brands behave the same way. His 1969 paper and his 1972 book Repeat Buying laid the foundation, and the canonical statement is Ehrenberg, Goodhardt and Barwise, Double Jeopardy Revisited, in the Journal of Marketing in 1990. In any period, a small brand has far fewer buyers than a big one. Its buyers also buy it slightly less often, hold it as a smaller share of their purchases, and are slightly more likely to buy something else next time. The first penalty is large and obvious. The second is small, consistent, and the part nobody expects.

The regularity is what makes it a law rather than an observation. Buying behaviour in a category follows a well-described statistical model, the Dirichlet, and from a brand's size alone the model estimates its repeat rate surprisingly well. The pattern has been documented in over fifty product contexts: packaged goods, retail banking, insurance, luxury goods, cars, political voting, and business markets, and in newer categories such as music streaming and ride sharing.

The mechanism is selection, not psychology. Where competing brands are broadly substitutable and sell to the same kinds of people, the big brand is simply present in more households, more memories and more shops. Most category buyers are light buyers who know little and default to what is mentally and physically available, which is the market leader. Nobody loves the small brand less. Fewer people know it exists, and the ones who do meet it less often.

The known deviations are themselves well documented. A brand with deliberately restricted distribution or a deliberately narrow audience can run unusually high loyalty on a small base, the niche pattern, and private label brands and specialist media are the standard examples. The reverse, unusually high penetration with low repeat rates, appears in seasonal and change-of-pace brands. And the famous counterexample has been tested: Harley-Davidson, cited everywhere as loyalty beating size, shows buying behaviour that broadly follows the pattern once actual purchase data rather than visible enthusiasm is measured.

The honest limits. The loyalty differences are small, so the law says less about loyalty than its name suggests; the real force is penetration. It describes markets where brands compete for the same buyers, and it weakens where a market is genuinely partitioned. And it is a description of a statistical regularity, which explains what loyalty levels are achievable, rather than a mechanism anyone can switch off.

The place this law collides with practice is the annual plan. A small brand reads its own dashboard, sees churn higher than the market leader's and repeat purchase lower, and concludes it has a retention problem. Budget moves to loyalty programmes, win-back campaigns and churn analysis. The law says a good part of that gap was never available to close, because the leader's loyalty numbers come substantially with the leader's size. Comparing your repeat rate to theirs is largely comparing yourself to their market share, and the structural part of the gap does not respond to programmes.

The redirect is penetration. More buyers, reached more often, easier to find and easier to think of. The evidence behind this law is the core of the case that brands grow mainly by acquiring light and non-buyers rather than by deepening existing relationships, and it is why loyalty schemes reliably disappoint as growth engines even when they work as data collection. When penetration rises, the loyalty metrics improve on their own, slightly, as a consequence, which is the direction of causation almost every plan has backwards.

There is a fairness implication worth stating plainly. A manager running a small brand should not be judged against the leader's retention numbers, because the gap is structural. Holding them to it selects for people willing to promise the impossible.

And there is one legitimate escape. A genuinely niche position, narrow audience, restricted distribution, built that way on purpose, can sustain excess loyalty on a small base. The test is the word on purpose. Excess loyalty by design is a strategy. Low loyalty at low share is not a failure of the brand team. It is what small looks like from inside, and the misdiagnosis costs a year of budget aimed at the wrong problem. The larger argument built on this evidence is penetration beats loyalty, and the general pattern of advantage compounding with size is the Matthew effect.

Source: McPhee, Formal Theories of Mass Behavior, Free Press, 1963. Ehrenberg, Repeat Buying: Theory and Applications, 1972. The canonical statement: Ehrenberg, Goodhardt and Barwise, Double Jeopardy Revisited, Journal of Marketing, volume 54, 1990, pages 82 to 91. The Dirichlet benchmarks: Ehrenberg, Uncles and Goodhardt, Understanding Brand Performance Measures, Journal of Business Research, volume 57, 2004, pages 1307 to 1325.

How Brands Grow

Byron Sharp, 2010

The book that took this law and the rest of the Ehrenberg tradition to a general audience. Read it before the next planning cycle, and read the criticisms of its scope alongside it, which the penetration entry here carries.