why modeling averages is not good enough

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Why Modeling Averages Is Not Good EnoughA Critique of the Law of Doubie Jeopardy

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For more than 40 years, Andrew Ehrenberg and others have demonstrated thevalue of the Dirichlet and related distributions as a method for modeling typicalbrand performance measures (BPMs) in markets. This work has led to trenchantcritiques of many attitudinal measures related to brandingspecifically, brandstrength, differentiation, and persuasion. Using panel data, we show that thoughthe Dirichlet leads to accurate BPMs for fixed time-slices, its assumptions aboutindividual behavior are wrong. We therefore challenge the way the law-of-double-jeopardy theorists use patterns identified by the Dirichlet to generalize about brandperformance, the psychology of consumer preference, and the role of advertising. Farfrom being problematic, attitudinal measures may be the only path to the successfulunderstanding of the effects of marketing initiatives.

INTRODUCTiONAccording to the law of double jeopardy (DJ) inmarkets, b i g brand s benefit do ubly: They have m oreusers, and their users use them m ore. More formally:"In all markets, all convenfionally used bran d per-formance measures (BPMs) can be predicted frommarket share using theDirichlet distribution (oncecalibrated)" (Chatfield and Goodhardt, 1975).

The law challenges many marketing-researchapproaches. Consider brand equity. Most attitu-dinal systems are based on some sort of commit-ment or engagement "ladder" (Keller and Lehman,2004). Th ese areused to identify strong and weakbrandstypically by quantifying the percentageof people found at various "levels." Ehrenberg andothers have argued repeatedly, however, that allcan be accounted for by bran d size alone. To quo te"... there are clearly big brand s and smaller brand s,(but) there is no evidence... that over and abovethis there are 'strong' and 'weak' ones" (Ehrenbergand Goodhardt, 2004).

Consider also loyalty programs, or customerrelationship and customer experience manage-ment. Most commercial approaches focus on

relationships with existing customers as the mosefficient way to increase profits (e.g., Reichheld1993). Yet DJ implies that retention and share ofwallet increase only if penetration also increases. Inother words, a narrow focus oncurrent customerswill work only if it also leads, whether intention-ally ornot, to the creation of new customers.

This research does not question the many pat-terns that scholars have identified using the Dirich-let distribution. The evidence is overwhelm ing. Yetone must ask wh y some m arketers often behave asif D J does no t exist.

There is at least one reason. As Ehrenberg andUncles note (1995), the law holds "... for competi-tive markets which are in a near-steady state"in other words, so long as market shares do notchange too much. Market shares do change, how-ever. And so marketers persist in using tools thatignore the law because they hope that by doing so,they will develop fortune-changing brand strate-gies. The result is an unsatisfactory standoffbetween thepatterns revealed by the Dirichlet onthe one hand and attitudinal brand performance asmeasured bymarketers on the other.

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WHY MODELING AVERAGES ISN'T GOOD ENOUGH

This article examines the empiricalveracity of DJ by comparing the statisti-cal assumptions that underpin it withreal behavior in panels. We show thatthe Dirichlet is based on assumptionsabout individual behavior that are false.In so doing, we show that although DJaccurately describes aggregate marketbehavior, it does so in a limited sense.Additionally, the authors argue that itsempirical flaws can best be resolved bymeans of attitudinal measures.A BRIEF INTRODUCTION TOTHE DIRICHLET MODEL OF MARKETSScopeComm ercial o perators (Nielsen, IRI, TNS,Gfk, etc.) typically report a wide range ofbrand performance measures (BPMs)market share, penetration (i.e., percentbuying in a specified time period), theaverage number of purchases of the brandper buyer, the percent who buy the brandabove a certain threshold, and the like(Ehrenberg and G oodh ardt, 2004).

Over the years, Ehrenberg and othershave shown that all these measures can bepredicted by using the Dirichlet distribu-tion with very little market measurement.Implementation takes just two steps: first,a calibration or mo del estimation step and ,second, a calculation step. To estimate amod el, you need to specify a "base period"(typically six months or a year) and thenmake four measures:

The percen t of all con sum ers (panelists)wh o buy in the category at least once The average number of purchases each

category user makes The penetration of just one of the bigger

brands The average number of purchases each

of the bigger brand's bu yers makes.These inputs are used to estimate themodel's parameters for the time period

and market of interest. Once those dataare in place, all BPMs for all brand s can b eestimated with remarkable accuracy justby entering the brand market shares orpenetrations.

In terms of reach, Dirichlet patternshave been found across multiple geogra-phies for a mu ltitude of different kind s ofmarket including goods with a very highpurchase frequency (e.g., gasoline), dura-ble goods (e.g., PCs and au tomob iles), andcategories in which loyalty programs arethou ght to play an impo rtant role (e.g., air-lines, retailers).

Statistical UnderpinningsThe model is based on the followingassumptions about behavior in markets: Each person buys in the category at a

steady, long-run rate (e.g., mo nthly overa six-month period), although a per-son's buying rate can fluctuate duringthe period.

Although people buy according toa long-run rate, a person's purchaseintervals are irregular ("as if random")and are independent of the previousinterval.

People are heterogeneous in terms oftheir category-buying rates. A few buyheavily, but most b uy relatively lightly.

Although brand repertoires and brand-purchase probabilities vary from oneperson to the next, each person has asteady or fixed likelihood of buyingeach brand . Over time, brands are bough t by a per-son according to that person's fixed-purchase probabilities. What a personbuys, however, seems to be randomeach time.

There appears to be a good fit between thegamma distribution and the behavior ofindividual panelists in commercial pan-e l s . This leads to the observation (see the

foregoing): "Although people buy accing to a long-run rate, a person's purchintervals are irregular ('as if random')are independent of the previous intervIt implies th at it is impossible to use p rous purchases to judge w hen a personbuy something again, based on w hen boug ht last.

There also appears to be a goodbetween the zero-order Poisson distrtion and panelists' brand buying. leads to the assumption (see the fori n g ) , "Over time, brands are bought bperson according to that person's fipurchase probabilities. What a pebuys, however, seems to be random etime." It implies that we cannot tell wbrand people will buy next based on wthey bought last (although we can khow often they will buy each brand the specified period ). As an example, tof someone who uses each of two bra50 percent of the time. Their steady chase probabilities are 0.5 and 0 . 5 . Justroulette wheel spins in a random fashhowever, a previous purchase givesinformation about which brand somewill buy next.Psychologicai ExplanationsEhrenberg and his colleagues have been shy about making the theoreleap from the Dirichlet desc ription of ket behavior to a consumer psychothat might explain such behavior. Tsuggest, for example, that most peoplmature markets have learned all theygoing to about bran ds. As a result, pelearn nothing new from using a particbrand "yet again" or seeing "yet anoadvert" for it. To quote: "... the expenced consumers' steady purchase pensities can be thought of as the outcof years of past experience" (Ehrenand G ood hardt, 2004). Well-formed bropinionsrelatively impervious to ther marketinglead to steady purc

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probabilities that can be modeled by zero-order statistical distributions.

The "no-new-learning" theory gainssupp ort from the way people behave whenbrands are discounted. Although price-related promotions can lead to dramaticspikes in brand buying, analysis showsthat discounted brands mostly attract pre-vious users. To quote Ehrenberg: Before-to-after repeat buying doesn't change;no before-to-after market share changesoccur; and few new buyers are attracted.Indeed, the presence of any new buyersis all it takes for the possibility of market-share change. The entire body of evidencesuggests that discounting does not inducethe kind of use that leads people to chan getheir brand opinions.

In this view, there also is a "no-new-leaming" approach to advertising. Likediscounting, advertising m ay cause buying"spikes," but it works mostly by remind-ing experienced users of the brand's exist-ence. Mostly, therefore, it attracts peoplewh o have u sed the brand before. It does soby "publicizing" the brandor "nud ging"the brand closer to the front of a person'smental brand queue. By improving thebrand's psychological accessibility in thisway, it temporarily improves the chancesof the brand's being bought. Advertis-ing, from this perspective, does not "per-suade" or change minds.

In markets wherein repertoires arepossibleand most people do have arepertoire100-percent loyalty is rare. Ifloyalty, however, is a matter of degreefor example, varying from 0 to 100andif people buy the brands in their reper-toires according to fixed purchase prob-abilities, most people are what Ehrenbergcalls "typically polygamous." They areneither "monogamous"100 percentloyalnor "promiscuous"not attachedto anything. They buy according to "splitloyalties." This leads to more psychologyor, as Ehrenberg and Goodhardt observed

in the Journal of Business Research in 2004,"... staying with a repertoire requires lessmental effort than making new choices,but having a repertoire enables consumersto exercise some choice without having torvalua te all bra nd s.... "

In spite of the static psychology implicitin the Dirichlet, it is important to under-stand that DJ does not challenge the exist-ence of marke ting levers (e.g., discoun tingand advertising). What Ehrenberg et al.argue is that people's resulting behavioris "sufficiently idiosyncratic and irregularto be successfully modeled mathemati-cally as being quasi-random, especially c o l -lectively" (2004, author's italics). In otherwords, DJ is good at describing aggregatebehavior; that behavior is consistent withboth the Dirichlet assumptions aboutindividual behavior and a DJ-based cri-tique of marketing concepts such as brandstrength, differentiation, and persuasion.

Deviations From the ModelScholars have long noted that marketbehavior can deviate from DJmore spe-cifically, that DJ for big brands may beeven higher than predicted (Fader andSchm ittlein, 1993).

The most important deviation, how-ever, has to do with the model's descrip-tion of markets as "stationary." There aretwo obvious ways in which markets arenot stationary. First, market shares maychange as a function of the successfulintroduction of a new brand and, second,market shares may change over time.

Ehrenberg et al. acknowledge thatdynamic markets are as yet unexplained(Ehrenberg and Goodhardt, 2004). Theyargue, however, that the Dirichlet copesrather well with market share changes,because it continues to model fixed time-slices through the change. So, for examp le,between 1981 and 1992, the market shareof Folgers (a coffee brand), doubled in theUnited States. Dirichlet models fit at both

the beginning and the end of the period(Baldinger, Blair, and Echambadi, 2002).A CRITIQUE OF THE LAW ANDTHE IMPLICATIONS DERIVED FROM ITIn reality, the buying behavior of manindividual people in markets is dynami(DuWors and Haines, 1990). This sectiobegins with two examples of such behavior from panel data. The authors sho w th athese are not isolated instances and discuss the implications for the DJ approachto brand-performance estimation andconsequently, for the DJ understanding ohow advertising works.A Look at Two Examples of Real BuyingBehaviorIn an analysis of a purchase stream of thchocolate purchases of a person participating in a consumer panel (Table 1), thchanges in this person's purchase probabilities are clear: This panelist boughchocolate eight times in the first periodnine in the second, six in the third, andfive in the fourth. "Brand 1" is the firsbrand, but Brand 4 dominates for the firs6 months and then almost disappearsBrand 2 gets bought most in the second6 months but is hardly dominantanthen it, too, disappears. No brand dominates in the second and third periodsBrand 1 1 , however, dominates in the fina6 monthsand some might argue that oncan discern a developing preference for iin the third period.

For someone such as this, the only wato get "fixed p urcha se prob abilities" (as peDJ and the Dirichlet assumptions) is by thartifice of fixing them. So, in period onBrand 4 has a 50 percent share of walle(i.e., a 0.50 chance of being bought). Extenthe lens to 12 months and both Brands and 4 have a 0.29 chance of being b oughTogether, the two account for 59 percent owhat this person buys in year one. In yeat w o , they a r e not boug ht at all.

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TABLE 1A Two-Year Purchase Stream for a Panelist Buying Chocolate*

Brands1 2 3 4

TABLE 2A One-Year Purchase Streamfor a Panelist Buying Coffee

10 11 12 13Purchases 1

23456789

101112131415161718192021222324

25262728

11

1111

11

11

11

11

11

11

11

11

11

1111

Brand1 2 3 4

Purchases 123456789

1011121314151617

11

111

11

11 1

1

111111

*With thanks to the Aztec household panel in Australia for supplying all the panelist purchase histories used in this article.

In an analysis of a panelist's purchasesof coffee for a year (Table 2), once againbrand-purchase probabilities cannot easilybe "fixed." In the second six months, the

panelist switches main brand, increaseshis or her repertoire from three to fivebrands; and nearly doubles the rate of heror his coffee buying.

One cannot look at these panelbehavior without concluding that tpurchase probabilities are dynamic. only way to make them look "fixed" isthe artifice of taking their average behior for a specified time. Expandingcontracting the time at will may smoaway the dynamism and "fix" propsities by definition. Such "smoothihowever, does not do justice to the unlying behavior, nor do es it do justice toimplicit dynamism of the psychologpreferences revealed by the behavior.From Dynamic Individual Behavior to NStat ionary MarketsIf the behavior of the panelists shopreviously were exceptional, there m

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not be a problem. For each of four mar-ket-leading brands, the authors classi-fied chocolate lists' buying behavior over24 months and 12 months into one of sixmu tually exclusive group s as a function ofhow their purchase probabilities changefrom one six-month period to another.Using the typical Ehrenbergian definitionof a "user" in a period as someone whobuy s the brand at least once, there are four"user" and two "non-user" classifications:

- U p : significantly increase the share ofwallet that goes to the brand

- Static: share of wallet stays the same- Down: significantly decrease the share

of wallet for the bra nd- Defect: stop using the brand.

Nonusers- Adopt: start using the brand- Zero: remain non-users.

A difference in individu al behavior acrossa time period was defined to be statisti-ally significant if it exceeded the squareoot of the share of wallet in each of theuccessive periods.

As an example, consider someone whoives a brand 25-percent share of walletn the first time period and 36 percent in

e interval for thecent and 6 percent,

"Static." If, however, the shareis 49 percent

confidence interval + 7 percent), the per-ed as " U p " ; Table 3.

By this approach, very few users ' brand-

ion. This underlying dynamism

TABLE 3A Summary of Panelist Behaviors over Time (A: Chocolates,24 months; B: Coffee, 12 months)

B r a n d 1

B r a n d 2

B r a n d 3

B r a n d 4

UpStaticD o w nD e f e c tA d o p tZ e r oTotal




AP . - P 2 P 2 - P 3 P3-P.138 124 14183 63 60

122 145 11932 48 4937 37 5027 22 20

439 439 439100 78 10055 56 5483 94 7059 83 6473 60 7569 68 76

439 439 439

63 59 6642 45 3956 74 6870 67 7184 66 62124 128 133439 439 439

8 14 1211 9 1014 14 1256 29 6333 60 45

317 313 297439 439 439

Bi p _ p p _ p p _ p: 1 2 2 3 3 4: 31 28 3219 14 1428 33 277 11 118 8 116 5 5

100 100 10023 18 2313 13 1219 21 1613 19 1517 14 1716 15 17100 100 10014 13 1510 10 913 17 1516 15 1619 15 1428 29 30100 100 1002 3 33 2 23 3 313 7 148 14 1072 71 68100 100 100

AP - P1 22028293352

182344

913143532

241344

101141421

284344

06122513

288344

BP . - P ,

6881015 5 3 I

1 0 0 i3 I4 4

1 09 i

7 0 i1 0 0 i

3 i3 ^1 i4 i6

8 3 i1 0 0 I

02 i3 i7 i4 i

84 11 0 0 i

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behavior are offset by changes in others.In fact, market shares in the coffee marketwere stationary over the period, but thechocolate market was nonstationary.

The result is nonstationary behaviorunderpinning both a stationary and anonstationary market. In the chocolatemarket, the net effect of the behavior isthat the market shares of the four leadingbrands changed. Three of the four brandsexperienced large gains (from 32 percentto 39 percent; 11 percent to 14 percent; and1 0 percent to 12 percent, respectively). Thebig loser was the brand ranked second atthe start of the 18 months: Its share fellfrom 31 percent to 17 percenta statisti-cally significant change.

To follow up the original analysis, theauthors conducted additional studies infour markets: chocolate, cheese, laundrydetergents, and sweets (Table 4). Three ofthe four were stationary at an aggregatelevel. The authors focused on the pur-chase propensities associated with pan-elists' dominant brand s in two successive12-month periods. Panelists without adominant brand in either period becauseof ties were dropped. The reduction wasabout 14 percent leaving 86 percent of thepanelists with clear "winners" in bothperiods.

The question the authors sought toanswer: How man y panelists changed theirbuying behavior enough for that change tobe significant? In other words, how manypanelists do not have steady purchasepropensities? The binomial-distributionmethod was used to test for significant dif-ferences (Agresti and Cou ll, 1998).

The data showed that many panelists'purchase propensities change. The 24 per-cent whose brand preference for sweetschanged was not as revealing as the muchsmaller 7 percent who changed their pref-erence for laimdry detergents. The lownumber was not unexpected, given a cat-egory marketing history of high levels

TABLE 4Significant Changes in Purchase Propensities for a PanelistDominant Brand

Ciieese(Panelists: 555)(Brands: 163)

Chocoiate(Panelists: 542)(Brands: 53)

Laundry Detergents(Panelists: 466)(Brands: 55)

Sweets(Panelists: 499)(Brands: 222)

Main Brandy

Main Brandy

Main Brandy

Main Brandy

Main Brandy

Main Brand,

Main Brandy

Main Brandy

SignificantNot SignificantSignificantNot Significant




N6043 6

6 14 3 2

6637 9

8536 3

26386

33379

105317103324

Perc12881288

1585198 1

694

892

25752476

of brand commitment (a concept that DJtheorists do not seem to believe in). Sevenpercent, however, is enough to cause sig-nificant market share changes. It is alsoenough to refute the Dirichlet generaliza-tion about individual behavior.Reai Consumers and Dirichiet FictionsIn most stationary and nonstationarymarkets, there are many people whosepurchase probabilities are unsteady. Thisleads to the question: How can nonstation-ary individual behavior lead to stationarymarkets? The answer: It does so as long asthe changes in behavior of each person areoffset by changes in the behavior of others.

To illustrate the point, the authors sied three consumers buying three brathrough three time periods (Table 5a).three behaved more or less as manthe others had: They changed their bing rates and switched brands. In theperiod, the first consumer was a "heabuyer, and the other two bought at ahalf the rate. In the second period,second consumer became the "heabuyera change is offset by the fibuy ing less. In each period, each consuappeared to change his or her brand perences, but the changes were offsetchanges in the behavior of the others.three brands maintained market share

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WHY MODELING AVERAGES ISN'T GOOD ENOUG

TABLE 5Creating Fictitious Dirichlet Consumers (A: Typical Consumers;B: Dirichlet "Fictitious" Consumers, per Our Data)

Purchases 123

56789

1 01 11 21 31 41 5

111221

231

2311

A2

12

11211

1221

O

fi

1

2

2

11

11

1211121121111

B

322

23

3A

2

1

1

2

2

12

Noie; Ce//s /5fl shou) which of th e three brands was bought by each consumer at each purchase occasion. Cells in 5brearrange the purchases of th e first two consumers to create fictitious consumers whose behavior is "near steady state. " Th emarket is stationary: Brand 1 gets about 60 percent market share in each period, and brands 2 and 3 get about 30 percent and10 percent, respectively.

about 60 percent, 30 percent, and 10 per-cent, respectively.

It is a relatively simple matter to createconsumers whoconform to the Dirichletassumptionsin other words, consumerswhose buying behavior exhibits steadystate preferencesby rearranging pur-chase events (see Table 5). In this way, itis possible to make it look as if a marketis populated by consumers whose pref-erences do not change. And as long as amarket is stationary, brand purchases canbe assigned to"consum ers" in such a waythat it looks as if the market is populatedby consumers whose behavior is station-arya situafion that may be describedas "mutually compensating" changes in

behavior. The reconstruction, however,consists of fictitious characters whom theautho rs call "Dirichlet fictions." Addition -ally, DJ models are underpinned by ficti-tious consumers.In SummaryIf you fix things byartifact (i.e., by speci-fying a base time periodsix months or ayear), individual behavior c a n be made tolook static, and market shares can be mod-eled as if stationary. Moreover, as long asall panelists' changes in purchase prob-abilities are offset by changes in the pur-chase probabilities of others, aggregateBPMs based on the assumption of station-

ary individu al behavior will not need to re-estimated as time passes.

In the data analyzed by the authorhowever, the statistical assumpdons owhich DJ isbased are inaccurate descritions of individual purchase probabities. Nonstationary individual behaviis common enough tocause market shachanges. In four of the five markets, indvidual changes offset one another, anmarket shares were static. In the choclate market, however, market sharchanged. If the dynamic behavior did nlead to market share changes, one migstill argue that it does not matterthDJ is based on simplified descriptions oindividual behavior. BPMs in the markstill could be modeled and might havedegree of credibility, but accurate av eragproduced by a statistical method that donot describe individual behavior, is poscience.

When faced by nonstationary markethe typical DJ response is to argue thbrand performance can be remodeled ftime-slices of those markets. Each "slicehowever, would require new parametestimation; and the resulting BPMs woube particular to each "slice." The authobelieve this isnot an efficient approachbrand performance esdmation.THE LANGUAGE OF BRANDPERFORMANCEIn the authors' research, the statisticunderpinnings of DJ provided a podescription of the behavior of many paticipating panelists. How do these finings reconcile with the psychologicexplanadons that are derived from thidea that individual purchase probabilties are "fixed?" The autho rs explore threxplanations.

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A narrow focus on current customers will work only if italso leads, whether intentionally or not, to the creationof new customers." B i g " and "strong" (or "smail" and"weak") are not the same thingOver the years, DJ theorists have repeat-edly claimed that "there are no strongor weak brands, only big or small ones"(Ehrenberg and Goodhahrdt, 2004). Indynamic markets, how ever (e.g., the choc-olate market as measured in the authors'panel), most marketers would w^ant to beable to describe brands not only in termsof their size but in term s of the likely direc-tion of their market share changes.

During the two years covered by theauthors' chocolate data, the number-twobrand suffered a sustained fall in marketshare. If measures had been in place toforewarn of its impending losses, mar-keters might have described it as "big,"but they almost certainly would not havedescribed it as "strong." A more likelydescription would have been "big, butvulnerable." The same would be true forsmall brands about to get biggertheymight be described as "small," but theywould not be described as "weak." Indynamic markets, therefore, big and smallaren't synonyms for strong and weak.

The language of brand strength betterdescribes brands whose market sharesare changing. Perhaps one reason the DJposition on the language of brand strengthhas been relatively easy to defend is thatdramatic changes in market share are rela-tively rare. Perhaps another is that attitu-dinal BPMs do not have a good record ofpredicting such changes.

With respect to the second point:Progress is being made when in termsof attitudinal approaches that success-fully predict behavioral changes from

point-in-time surveys (Durbach, 2009).With respect to the first, the fact that dra-matic changes are relatively rare does notalter the need for a language that appro-priately encompasses the possibility ofchange . If there is a chance that a big brandmight be about to suffer a loss in marketshare, the language of "big but vulner-able" would better describe it than the lan-guage of "bigness " alone.A More Reaiistic PsychoiogyLike Ehrenberg, we adopt the idea that aperson brings a set of attitudinal brandpreferences to each purchase situation.One way to quantify this is in terms of aset of brand-purchase probabilities. Thereare at least two ways, however, to describethe position of brand s in the set.One uses the idea of "split loyalties"the idea tha t people are loyal to each of thebrands in the set because they continue tobuy each one according to its base prob-ability of being bought. The other is to usethe classic language of attitudinal brandattachment to signal differences in thestrength of attachment"strong" whenthe probability is high and "weak" whenit is low. Which you choose does not mat-ter, but we note that the latter is closer tothe language most people would use todescribe the way the mind works. Fromthis point of view, DJ argume nts that chal-lenge the idea of measuring attitudinalbrand attachment are mere semantics,nothing more.

The more serious DJ challenge comesfrom the idea of "no new learning" inmature markets where brands are wellknow n. This idea wo uld be easy to defend

if panel behavior were consistent wi"near-steady" purchase probabilities; bit isn't. Using the method of "revealpreferences"using actual behavior asguide to underlying psychological prefeencesour records suggest that individusets of attitudinal purchase probabilitare not stable.

And this leads to the question: Whatthe cause of the brand switching w e see

Obviously, a great many factors mplay a role in the drift of people from obrand to another. A brand may fall out operson's repertoire because it is no longwell distributed, because of pack and vaant cha nges, or because of pricing. All suchanges involve a consumer's "learningThere is one kind of "learning," howevthat DJ theorists argue does not occur: tkind that involves a consumer's changihis mind about a brand's characteristics

On the evidence of the dynamic behaior we show, there is no basis for the claithat "new learning" does not occur. Froa psychological point of view, dynambehavior may involve a person's chaning his or her taste rather than brand opions. If that were the only explanation, "new brand learning," in fact, would hataken place. The same scenario, howevcould result in a situation in which a pson's taste had not changed but his or hbrand opinions had. Both explanations aplausible, but which one is operativechanging tastes or changing brand opionscannot be answered by lookingbehavior alone.One final point: Support for the ideano new learning comes from the short-rbehavior that occurs when people swibrands for a promotion or in responto an advertisement. Some people talonger than this short time frame, hoever, to drift away from one brand anothera difference in panel behavthat needs to be analyzed in relationmarketing inp uts in greater detail and ov

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longer time periods. Just because peoplemight have bought a brand in responseto an ad does not necessarily mean thatthis new purchase is (or is not) the begin-ning of a long-term change in their brandpreferences.Can Individual Purchase Propensities BeMeasured by Observation Alone?In the second year of our analysis, thefirst panelist in our purchase-stream anal-ysis failed to buy either of the two brandsthat dominated his repertoire in the first(see Table 1 ) . In the second half of the firstyear, only on one occasion did he or shepurchase the brand that accounted for 50percent of his purchases in the first half.Such behavior could be expressed as afunction of the average propensity to buyeach brand during a specified period oftimethe "revealed preference" methodused as a way to quantify purchaseprobabilities.

The resulting averages however, wouldmask what we think is best described asthis person's dynamic drift from one pre-ferred brand to another. In fact, what thebehavior "reveals" is that brand prefer-ence has changed, and that leads to aquestion: Is it possible to establish a per-son's purchase probabilities at any pointin time? If so, is it at all possible to do soby observation?

When a buyer's behavior is dynamic,the problem with quantifying that indi-vidual's purchase probability is that pastpurchases no longer represent his or herongoing attitudes. Using past behavioronly produces accurate probabilities whenpeople's purchase propensities are station-ary. And if behavior is mostly dynamic,the method of "revealed preference" isirrevocably flawed .

The point is simple: If dynam ic behav ior

leaves only one alternative: the traditional

Is it possible to establish a person's purchaseprobabilities a t any point in time?method of attitudinal surveys. We con-jecture that only attitudinal surveys canprovid e a reliable method to establish howstrongly attached a person is to a set ofbrands at a point in time.

If marketers seek to understand whypeople have the preferences they do, atti-tudinal methods are essential becausebehavioral methods (revealed preference,for instance) cannot overcome the problemof out-of-date individual purchase infor-mation (Hofmeyr, Ho ltzman, Good all, andBongers, 2008).

People do have preferences, but thosepreferences change, and those changescannot be part of a "steady state."IMPLICATIONS FOR ADVERTISERSThe authors believe that consumer psy-chology built on the back of DJ is inad-equate. This premise has at least twoimportant implications for advertisers.What to Do if You Believe in a World of"Dirichlet Fictions"If you believe that consumers buy accord-ing to "near" steady-state purchase prob-abilities in stationary markets, your aimshould beas Ehrenberg and his col-leagues have often arguedto "publicize"the brand. Brand communications shouldbe about "nud ging" the brand to the frontof each perso n's m ental que ue. Your focusas an advertiser should be on maximizingboth the reach and the frequency of yourcommunication.

It is a world in which you would be"running hard to stay in the same place,"as DJ theorists sometimes say. You wou ldachieve very little, however, for yourbrand except by accidentor, more specif-ically, by accidentally "persuading," even

though you do not believe persuasion ipossible.What to Do if You Believe ThatConsumers' Brand Preferences ChangeBrand communication is not just abou"nudging" already well-known brandto the front of some "mental queue." Oudata show clearly that consumers' preerences, as expressed in their purchasstreams, change. Longitudinal survedata back this upmany people who arreinterviewed using attitudinal metricwill indicate that they no longer favor thsame bran ds as before (Hofmeyr and Rice2002).

The power that brand communicatioand other marketing levers have to shapwhat people think has been shown witincreasing clarity by new measurementools that allow us to study the brain (Montague et al., 2004). We also kn ow, througthe work of neuroscientists that the formation of brand associations involvechanges to the brain (Kandel, 2006). Stronbrands are built by linking the functionacharacteristics of the brand through thcontexts in which it is used and by the personal goals and values that are importanto people.

The message for advertisers and marketers: To truly understand the effecof any campaign, audit the consumerwhose behavior h a s changed in response the campaign. These include previouslrare but not new users; true "first-timeusers; and defecting heavy users. Understanding the impact of each marketininitiative at the marginsamong thoswho appear to be changingwill lead tunderstanding of the persuasive effects othat initiative.

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When it comes to advertising, the for-mula for success is relatively simple: Con-nect the brand to goals and values thatmatter to people.CONCLUDING COiVliVIENTSAt the turn of the century, the AmericanMarketing Association asked marketers tochoose the best advertising campaigns ofthe twen tieth century. The top five were asfollows: Volkswagen: "Think Small" Marlboro: "Cowboy" series Coca-Cola; "The Pause That Refreshes" Intel: "Intel Inside" Nike: "Just Do It"Although VW's "Think Small" campaignshows how an advertising campaignhelped to redefine what people wanted,the Marlboro "Cowboy" is a powerfulexample of a campaign that changed theway people thought about brands. Whenthe Marlboro campaign was devised in1952, the brand was seen to be a femininecigarette"as mild as May" accordingto the theme linewith only 0.5-percentmarket share. Leo Burnett put the brandin the hands of cowboys, and the rest ismarketing history: Without changing theproduct, M arlboro became a strong, mas-culine brand... and the market leader.

One might argue that neither VW orMarlboro is a good example of "newbrand learning" because both brands wererelatively unknown before the campaign.That would be to forget, however, thatthe campaigns changed the way peoplethought about other brands, not just VWand Marlboro. These anecdotes highlightthe importance of straightening brand lan-guage and fixing the mistaken accounts ofconsumer psychology that have been pro-posed by DJ theorists.

The authors' examination of the pur-chase streams of panelists in five markets

demonstrate that the assumptions aboutbehavior that underpin DJ models are notuniversally true. Many individual pur-chase propensities are not "near station-ary." Does it matter that the assumptionsabout ind ividual beh avior are false as longas the model produces accurate descrip-tions of brand performance in markets?In the authors' view, it would matter evenif the model accurately described marketsover time.

DJ theorists constantly use wordssuch as near or mostlyas in "behavioris near stationary" or marketing initia-tives "mostly attract people who've usedthe brand before." A close examination ofempirical information, however, confirmsthat behavior is dynamic and that it is thesmall incremental changesthe materialthat is excluded from the not-"mostly"in DJ generalizationsthat may be at theroot of long-term market share changes.They can be initiated by any of the market-ing levers available to a marketer, includ-ing brand com munications.

The authors, therefore, contend thatDJ theorists are inaccurate in the numer-ous conclusions they draw about people,brands, communications, and markets.More specifically, they argue as follows: It is an oversimplification to claim that

brands are only "big" or "small" andnot "strong" or "weak." Ind ependent ofa brand's size, it needs to be describedin terms of the likelihood th at its marketshare might change, and that conditiondeman ds a language of brand strength.

Individual behavior on panels supp ortsthe observation that people's prefer-ences change. Those changes couldcome from marketing communication.DJ theorists have not made the case forthe theory that "no new learning" takesplace in mature markets or that adver-tising does not "pe rsuade."

Using behavior to quantify individbrand-purchase probabilities is irrocably a wed . The only method measuring a person's brand-purchprobabilities at a point in time will found in attitudinal surveys.

DJ, in fact, has utility as a method describing market aggregates. It loses efficacy, however, when it is compromiby simplistic consumer psychology aa narrow view of the options availablemarketers.

Marketing scientists will surely get bter at predicting behavioral and psyclogical change. In this regard , we offer tfurther conjectures: Methods to understand changes in i

vidual behavior and market share wbest be found in attitudinal surv eys, as is the case with methods to estimindividual purchase propensities;

To the extent that covariates can hexplain nonstationary markets, thcovariates almost certainly will inclspending on brand image changmarketing initiatives, including advtising.

MARTIN BONGERS IS currently a business Intelligencespecialist for a leading mobile content provider. Mgraduated from the University of Cape Town BSc(Masters) in mathematical s tatistics while winningthe joint prize for the best statistical dissertationon muitivariate volatiiity modeiing in South Africa. I200 7. Martin joined Synovate as a statistician andstill maintains strong research ties with the SynovaLaboratories.

JAN HOFMEVR (P HD) is currently the international direof innovation at Synovate Laboratories. B efore joiniSynovate in 2 00 6, he spent 1 5 years marketing theConversion Modeltm internationaily, a marketingresearch tooi he deveioped in the 1980s. Since joi

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Synovate, Jan has developed numerous practicalmarket measures forSynovate, including the brandvalue creator (brand equity), connections (copy testing),and true customer view (customer experience). Janhas taught at universities and presented papers andseminars on matters of branding and commitment inmost countries of the world.

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EHRENBERG, A. S. C, and M. D. UNCLES. "Dirich-let - type Markets: AReview. Par t 1: Pat terns andTheory." Working paper . South Bank BusinessSchool andBradford M anagem ent Ce nt r e , 1995.

FADER, P. S., andD. C . ScHMriTLEiN. "Exc ess Be ha v-io r Al Loyal ty for High-Share Brands: Deviat ingfrom the Dir ichlet Mod el For Repeat Purchase."Journal of Marketing Research 30, N o v e m b e r(1993): 478-49 3.

HOFMEYR, J. H., and J. (BUTGH) RICE. Commit-ment-Led Marketing, Chichester, U.K.: Wiley andSons , 2000.

HOFMEYR, J. H., P. HOLTZMAN, V. GOODALL, andM . BONGERS. "A New M e a s u r e of Brand Att i tu-dinal Equi ty Based on the Zipf Dist r ibut ion."The International Journal of Marketing Research 50 ,2 (2008): 181-202.

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