Large and small brands differ greatly
in how many people buy them, but not
in how loyal they are.
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Double Jeopardy
Revisited
Andrew Ehrenberg and Gerald Goodhardt
Report 26 for Corporate Sponsors (January 2002)
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.
Table 1 : Annual Buying Rates for
Fabric Conditioners
(Five typical larger and smaller brands)
Brand (by
% Buying Average Purmarket share) in Year
chase Rate
Downy
48
3.6
Snaggy
34
3.1
Bounce
18
1.7
Cling
8
2.0
Arm & H
5
2.1
Average
15
2.5
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:
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:
Brought
by
Av. no. of
times
Regular:
63% p.a.
5.0
Light:
32% “
3.0
Unscented:
9% “
2.0
Stainguard:
9% “
1.7
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”:
Populars:
Middle-Brows:
Qualities:
Read by:
Issues
per wk:
(av) 35%
3.6
“ 23%
3.2
“ 9%
2.3
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 coffeeanalyses, “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
•
•
•
•
•
Simpson’s Paradox
Treated Group
TRIAL A
60 improved out of a n of 100 = 60%
Control Group
300 improved out of a n of 1000 = 30%
TRIAL B
200
“
n of 1000 = 20%
10
“
n of 100 = 10%
Total (A+B)
260
“
n of 1100 = 24%
310
“
n of 1100 = 29%
•
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
currently reviewed in our “Grounded
Benchmarks”, while the historical development of DJ has been rehearsed by
John Bound, as noted in the Additional
Readings.)
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”.
Key References
McPhee, William (1963). Formal Theories of Mass Behavior. New York:
The Free Press
Ehrenberg, Andrew, Gerald Goodhardt
and Patrick Barwise (1990). “Double Jeopardy Revisited”. Journal of
Marketing, 54, 82-91
Ehrenberg, Andrew and John Bound
(2000). “Turning Data into Knowledge”. In: Marketing Research
(Chuck Chakrapani, ed). Chicago:
American Marketing Association
Ehrenberg, Andrew, Gerald Goodhardt and Mark Uncles (2001).
“Grounded Benchmarks to Evaluate Brand Performance” (email:
[email protected])
www.marketingscience.info
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