Compared to a large competitive brand, a small brand typically has far fewer buyers. But in addition, fewer of its buyers like the small brand (e.g. say “Good Value” or “Tastes Nice”). And they buy it less often. Table 1 illustrates this for fabric conditioners in the US. Only 5% buy Arm and Hammer in the year and they buy it on average 2.1 times, compared with 48% buying Downy on average 3.6 times.

The numbers buying, the brand penetrations, go down by a factor of 10. The average number of times each brand is bought also goes down (with some small wobbles, e.g. Bounce), though much less so − by a factor of less than 2.

This pattern is ubiquitous and has long been called Double Jeopardy (DJ). The small brand is “punished twice” for being small: it has fewer buyers, and its fewer buyers also buy the brand somewhat less loyally.

The wide occurrence of DJ has never been queried. One reason is that DJ can easily be seen in one’s own data.

In many markets even the biggest brand has a fairly low penetration (say 20% per year, instead of 48% for Downy). In such cases, the DJ variation in the buying rates is generally very small (e.g. from 2.8 down to 2.3). This is often condensed into:

Large and small brands differ greatly in how many people buy them, but not in how loyal they are.

That is plain, memorable, and startling. But it is a little oversimplified: big and small brands often hardly differ in terms of how loyal their buyers are to them.

In theory, Double Jeopardy holds for functionally substitutable brands that cannot be told apart in a blind product test.

In practice, DJ also holds for differentiated competitors, like the powder, liquid and tablet forms of detergents. For example, in the Fall 2001 issue (p38) of the AMA Marketing Research we reported on the four functional formats of fabric conditioners as follows:

And in our 1990 DJ Revisited paper in Journal of Marketing we had reported DJ for daily newspapers in the UK, despite strong segmentation by “Height of brow”:

There are innumerable other published examples of DJ.

DJ as a Marketing Constraint, with Marketing Implications

The data go against the prevailing view in marketing that loyalty measures and attitudes can vary freely.

Double Jeopardy in fact represents a constraint on “Anything Goes” market planning. The constraint is that marketing inputs cannot increase purchase frequency (loyalty) by much or for long, unless the brand’s penetration is also increased and usually by much more.

The back-to-basics message is that sales can increase only by selling to more people: you just have to recruit more customers. But that’s not quite all: loyalty-related measures all have to go up a bit too. Apart from the very occasional technological upset, market structures are inherently more constrained than is often thought.

On a more positive note, knowing about Double Jeopardy can enable practitioners and academics to interpret their markets better. For example, if brand X has a low repeat-level, they need not immediately rush into remedial action: if they look, X is probably just a small brand and behaving normally. DJ also provides grounded benchmarks and insights for planning and evaluating new brands, for monitoring established ones, and for understanding the lack of dramatic sales boosts from loyalty schemes, advertising, and CRM.

Clients are increasingly demanding knowledge, rather than data or even information.

(David Jenkins, CEO Kantar [WPP])

Deviations and Exceptions

Small deviations from DJ occur, like Bounce’s low 1.7 in Table 1. This might seem a golden opportunity for Bounce’s marketing team. But if they can increase its purchase frequency, why not similarly increase each and every brand’s purchase frequency and get rich?

Some larger exceptions also occur, though so far without many profitable marketing implications:

• Generics are bought with an apparently high purchase frequency. But this is largely an artefact of their limited retail distribution.
• Higher than predicted purchase rates can also occur for some market leaders, e.g. 4.1 instead of 3.2 for example (though not as regularly as Fader and Schmittlein suggest in the 1996 JMR).
• Perhaps some big brands can afford to stock store-shelves more regularly (e.g. on Friday nights)?
• In Garth Hallberg’s instant coffee- analyses, “All Consumers Are Not Created Equal”, Maxim had almost twice the annual purchase norm of about 3. It turned out that that was due to just two very heavy buyers (buying 30 and 32 times). This does not recur in other instant coffee data (e.g. in our 1990 “DJ Revisited”).
• Doctors’ prescriptions follow DJ. A few years ago the hypertension drug, Capoten, was prescribed on average 10 times a year per prescribing UK doctor, instead of the norm of 5 times. This happened because doctors had been offered a free PC if they prescribed Capoten often enough to be able to evaluate it. When the incentive was withdrawn, the blip disappeared.
• The weekly reach and hours viewed of TV channels follow a regular DJ pattern. But Hispanic channels in the US have vastly higher viewing levels (amongst Hispanics). And US Bible stations can afford exceptional amounts of programming for their few viewers, being largely funded by donations.

The Causal DJ Mechanism: Statistical Selection

Double Jeopardy comes about as mere statistical selection. The traditional example (told for many nationalities) is that when a Scotsman migrates to England, the average intelligence in both countries goes up. This is not caused by each nation becoming cleverer but as a form of statistical selection:

1. Only a rather dumb Scot would migrate to England. The average intelligence of those remaining in Scotland is therefore higher.
2. But even a dumb Scotsman is more intelligent than is the average English. Therefore…

A more general case is Simpson’s Paradox, where combining non-aggregated subsamples of very different sizes n causes big biases: In two clinical trials A and B say, each Treated Group improved twice as much as the Control Group. But the figures didn’t when combining the individual results for A+B (24% is lower than 29%):

This form of statistical selection bias arises when, as we say, heavily weighted samples (n = 100 and n = 1000 for the Treated Group, the reverse for the Control) are aggregated at the individual level. Combining the (average) results of each test instead preserves the 2:1 ratio − Treated Avg (60% + 20%) = 40%, versus Control Av (30% + 10%) = 20%.

Forty years ago, the Columbia University sociologist William McPhee saw a “statistical selection” type of explanation for Double Jeopardy. He showed mathematically that DJ has to occur when consumers choose between two similar brands, one big and one small.

McPhee effectively supposed that there are just two restaurants in town: W, which is widely known, and O which is more obscure. Those townspeople who knew both restaurants regarded them as of equal merit (food, service, accessibility, etc). Fewer people visited O because it was less well-known.

McPhee argued that in addition, attitudinal DJ arises because relatively few of the few O-customers said that O is their favorite, when asked. His reasoning was that:

• Of the many people who choose the well-known W (many because it is wellknown), nearly all will say it’s their favorite if asked (because few even know of the more obscure O).
• Of the few people who do know O, at most half will say it’s their favorite since most of them will also know the wellknown W which is of equal merit. They therefore split their vote (with some “Undecideds”).

That is classic Double Jeopardy, due solely to statistical selection. The same DJ argument applies behaviorally, with fewer people eating at O and doing so less often.

Since McPhee, Double Jeopardy has also been found to follow as an automatic by-product from two formal theories of consumer behavior:

• The well-established and simple Dirichlet model.
• The even simpler “w(l-b)” approximation which assumes that buying of any brand X is independent of buying any substitutable brand Y (which is very nearly so in practice).

The extraordinarily close fit of these models has already been illustrated over the years. (The models are reviewed in our Report 1 for Corporate Members and later in our Journal of Business Research article).

In contrast to DJ and the Dirichlet, the widely-cited Markov model assumes that consumers’ repeat-buying and brand-switching probabilities do not vary with market-share but are fixed characteristics of each brand. Two theories seldom disagree so unambiguously.

Why revisited “Again”?

The Double Jeopardy phenomenon, although long established, is still not widely known. When a leading company chairman came across it some years ago, he said

Very very interesting. We must research that. But of course it has to be confidential.

He had to be told: “Too late”, since DJ had already long been in the public domain. It was just that he (like most marketing people) did not yet know about DJ or use that knowledge.

In an in-house seminar in the same company recently, only two people had heard about DJ. One was the seminar organizer, the other a colleague whom she had told the day before. In our experience that is about par for the course. Yet marketing people not knowing about this natural constraint on customer loyalty is like rocket scientists not knowing that the earth is round. Hence we revisit Double Jeopardy here “again”.