Double Jeopardy Law

The Double Jeopardy Law is a structural phenomenon in marketing science stating that brands with lower market share suffer twice: first, by having fewer buyers (low penetration), and second, by those fewer buyers purchasing the brand slightly less often (low loyalty). Conversely, market leaders enjoy both the largest customer base and the highest average purchase frequency. This law proves that 'loyalty' is not a result of clever retention strategies or emotional bonding, but a mathematical byproduct of market share. For marketers, this means that attempts to grow a brand through loyalty-focused 'retention' strategies are statistically doomed. Growth is almost exclusively driven by increasing penetration—reaching more light and non-buyers—which naturally drags loyalty metrics upward as a side effect. It is a law of market structure, not a choice of brand strategy.

The phenomenon was first identified and named by social scientist William McPhee in 1963 in his work 'Formal Theories of Mass Behavior.' McPhee observed this pattern while studying the popularity of radio presenters and comic strips, noting that the less popular options were not only known by fewer people but also liked less by those who did know them. However, it was Professor Andrew Ehrenberg and his colleagues at the Ehrenberg-Bass Institute for Marketing Science who rigorously applied this to consumer goods. Over several decades, Ehrenberg developed the Dirichlet model of repeat buying, which provides the mathematical foundation for Double Jeopardy. The law was later popularized for a mainstream marketing audience by Professor Byron Sharp in the seminal book 'How Brands Grow' (2010), which synthesized decades of Ehrenberg-Bass research to challenge the prevailing 'loyalty-first' marketing paradigms.

The Double Jeopardy Law is not a 'suggestion'; it is a statistical regularity described by the Dirichlet distribution, a mathematical model that predicts how frequently people buy different brands within a category. The mechanism is rooted in the nature of 'repertoire buying' behavior. Most consumers are not 'monogamously loyal' to one brand; instead, they buy from a small set of acceptable brands (a repertoire). Larger brands have higher market share because they are more 'mentally available' (easier to think of) and 'physically available' (easier to find). Because they are more available, they are included in more consumer repertoires.

Mathematically, the 'loyalty' part of Double Jeopardy—the purchase frequency—is a function of the brand's penetration. As a brand's penetration increases, it naturally attracts more buyers who have the brand in their repertoire. Because these buyers encounter the brand more often in stores and in their own minds, they buy it slightly more frequently. Small brands suffer 'Double Jeopardy' because their lack of availability means they are in fewer repertoires, and even those few customers who do buy them will inevitably buy the market leaders more often simply because the leaders are more available. There is very little variation in loyalty across brands once you control for market share. If you have a 5% market share, you cannot have the loyalty levels of a brand with 40% market share. The math simply won't allow it.