marketing insights
Double Jeopardy Revisited, Again
Many marketers still don't know about this widely occurring phenomenon.
By Andrew Ehrenberg and Gerald Goodhardt
T
he Double Jeopardy (DJ) phenomenon shows that a smaller
brand always attracts somewhat less loyalty than does a bigger brand, and also fewer favorable attitude responses. This
does not signify the small brand is weak and the big one strong.
Instead., DJ is a mere statistical selection effect: There is a mathematical reason why small brands always suffer from DJ.
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. Exhibit 1 illustrates this for fabric conditioners in the United States. Only 5% buy Arm & Hammer in the
year, and they buy it on average 2.1 times, compared with 48%
buying Downy an average of 3.6 times.
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 these few buyers are somewhat
less loyal to the brand. The wide occurrence of DJ has never
been queried because it can easily be checked 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). In other words, large and small
brands often differ greatly in how many people buy them, but
not in how loyal these buyers are. That is plain, memorable, and
startling, but it's a little oversimplified. Big and small brands
often hardly differ in terms of how loyal their buyers are to them.
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 minor variations (e.g., Bounce) by a
factor of less than two.
In theory, DJ 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 oi Marketing Research we reported on the four functional
formats of fabric conditioners as follows:
EXHIBIT 1
Annual buying rates for fabric conditioners
Average number of limes
Brands (by market share)
Buying in year
Downy
Snupgy
Bounce
Cling
Arm & Hammer
Average
34
18
15
Average
purchase rate
3.6
3.1
1.7
2.0
2.1
2.5
Source: Ifll. Phlladfliptiia
Your Check of DJ
Tabulate a loyalty-related measure (e.g., annual purchase rate, 100% loyals, SCR, or %
saying "good value").
Order any competitive brands by their market shares.
Is the measure smaller torltie smaller brands? Yes • No • Not clear •
E-mail your summary result as tollows;
Subject: Double Jeopardy,
From: Your name and number.
To: [email protected] (EdJlor; Markeling Research)
Yes, No, or Not clear
40
Spring 2002
Regular
5,0
Light
3,0
Unscented
2.0
Stainguard
1.7
And in a 1990 fourna! of Marketing article we had reported
DJ for daily newspapers in the United Kingdom, despite strong
segmentation by "height of brow":
Populars
Middle-Brows
Qualities
Read by
(av) 63% p.a.
32% pa.
9% p.a.
issues Der week
3.6
3.2
2.3
DJ AS A MARKETING CONSTRAINT
The data goes against the prevailing view in marketing that
loyalty measures and attitudes can vary freely. In fact, DJ represents a constraint on "Anything Goes" market planning. The
constraint is that marketing inputs cannot increase loyalty by
much or for long unless the brand's penetration is increased—
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 enough. Loyalty-related measures all have
to go up il bit, too. Apart from the occasional technological
upset, market structures are inherently more constrained than
often thought.
On a positive note, knowing about DJ can enable practitioners and academics to interpret their markets better. For
example, if brand X has a low repeat-level, X is probably just a
small brand 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. As David Jenkins, CEO of Kantar (WPP),
recently said, "Clients are increasingly demanding knowledge,
rather than data or even information."
DEVIATIONS AND
ExcEPTroNS
Small deviations from DJ occur, like Bounce's low 1.7 in
Exhibit I. This might seem a golden opportunity for Bounce's
marketing team. But if they can increase its frequency, why do
marketers not similarly increase each and every brand's purchase frequency and get rich?
Some larger exceptions occur, but without profitable marketing implications. Eor example, generics are bought with high
purchase frequency, but this is largely an artifact of their limited
retail distribution.
Higher than predicted purchase rates also can occur for
some market leaders (e.g., 4.1 instead of li.l), though not as regularly as Fader and Schmittlein have recently suggested. Perhaps
some big brands can afford to stock store shelves more regularly
(e.g., on Friday nights)?
According to Garth Hallberg's instant-coffee-analyses, "A//
Consumers Are Not Created Equal,''' Maxim had almost twice
the annual purchase norm of about 3. It turned out this was due
to just two heavy buyers who bought 30 and 32 times. This does
not recur in other instant coffee data (e.g., in our 1990 Journal
of Marketing article).
Doctors' prescriptions follow DJ. A few years ago the
hypertension drug, Capoten, was prescribed on average
10 times a year per prescribing U.K. doctor, instead of the
norm of five times. This happened because doctors were
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 also
follow a regular DJ pattern. But Hispanic channels in the United
States have vastly higher viewing levels (among Hispanics). U.S.
religious stations also can afford exceptional amounts of programming for their few viewers because they are largely funded
by donations.
STATISTICAL SELECTION
DJ 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 more
clever, 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, so ....
A more general case is Simpson's paradox, where combining non-aggregated sub-samples of very different sizes causes big
biases. In two clinical trials, A and B for example, each treated
group improved twice as much as the control group. (See
Exhibit 2.) 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 « = 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%, vs.
Control Av (30%+10%) = 20%.
Eorty years ago, the Columbia University sociologist
William McPhee saw a statistical selection type of explanation
for DJ. He showed mathematically that DJ has to occur when
consumers choose between two similar brands, one big and
one small.
McPhee effectively supposed just two restaurants in town:
W, which is widely known, and O, which is more obscure.
Townspeople who knew both restaurants regarded them as of
equal merit (in terms of food, service, and accessibility). Fewer
people visited O because it was less well-known.
Attitudinal DJ arises, McPhee argued, because relatively
few of the few O customers said that O is their favorite, when
asked. Thus reasoned that, of the many people who choose the
well-known W (many because it's well-known), nearly all will
say it's their favorite because few even know of the more
obscure O.
EXHIBIT 2
Simpson's paradox
TRIAL A
Trealed Group
60 improved out otanof 100 =
Control Group
300 improved out ofanol1000=
30%
TRIAL B
20O improved out ota/i of 1000= 20%
10 improved out olanol 100 =
10%
Total (A+B)
260 improved ouiol an of 1100 = 2n
310 improved out o!anof 100 =
29%
60%
maifceting research 41
But, of the few people who do know O, at most half will say
it's their favorite because 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 DJ, due solely to statistical selection. The same DJ argument applies behaviorally, with
fewer people eating at O and doing so less often.
Since McPhee, DJ also has been found to follow as an automatic by-product from two formal theories of consumer
behavior: (1) the well-established and simple Dirichlet model
and (2) the even simpler "w(l-b)" approximation, which
assumes that buying of any brand X is independent of buying
any substitutable brand Y. The extraordinarily close fit of
these models has already been illustrated over the years.
In contrast to DJ and the Dirichlet, the widely cited Markov
model assumes that consumers' repeat-buying and brandswitching probabilities don't vary with market share, but are
fixed characteristics of each brand. Two theories seldom disagree so unambiguously.
WHY REVISITED AGAIN?
The Dj 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" because 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 a recent in-house seminar at the same company, 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 peo-
ple not knowing about this natural constraint on customer loyalty is like rocket scientists not knowing the earth is round.
Hence, we revisit DJ here "again." •
ADDITIONAL READING
Ehrenberg, Andrew, Gerald Goodhardt, and Patrick Barwise
(1990), "Double Jeopardy Kev'isked^" Journal of Marketings
54,82-91.
Ehrenberg, Andrew and John Bound (2000), "Turning Data
Into Knowledge," in Marketing Research: State-of-the-Art
Perspectives^ Chuck Chakrapani, ed. Chicago: American
Marketing Association.
Ehrenberg, Andrew, Gerald Goodhardt, and Mark Uncles
(2002), "Using Benchmarks to Evaluate Brand
Performance" (e-mail: [email protected]).
McPhee, William (1963), Formal Theories of Mass Behavior.
New York: The Free Press.
Authors' Note: This paper arises from the K&D Initiative
at South Bank (R&[email protected]).
Andrew Ehrenberg is chairman of the R&Dl at South Bank
University, London. He may be reached at [email protected].
Gerald Goodhardt is research associate at South Bank, visiting
professor at the University of South Australia and at Kingston
University, London, and a former dean of the City University
Business School, London. He may be reached at [email protected].
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