§ Improving the Vidale/Wolfe Advertising Optimization Model        Butterfly Dynamics for Internet Marketing and Video-Driven Sales



        I.    The Problem (§ represents a Gordon knot for a Bridges "Cutting Edge Paper.")

        II.   The Challenge

        III.  The Butterfly Effect - Internet Marketing

        IV.   Background 

        V.    The Fatal Flaw

        VI.  The On-line Video Impetus


        VII. The Original Model

        VIII. The Update Draft


I. The Problem

     In "An Operations Research Study of Sales Response to Advertising" M.L. Vidale and H.B. Wolfe devised in 1957 a model that has stood the test of time. They sought to answer three specific questions, quoted below from the first page of the article:

    1. How does one evaluate the effectiveness of an advertising campaign?

    2. How should the advertising budget be allocated among different products and media?

    3. What criteria determine the size of the advertising budget?


II. The Challenge

    An updated version of Vidale/Wolfe seems well suited to optimize on-line marketing expenditure. Specifically, it could be used to determine a budget for the production and dissemination of video sales drivers, from product description and landing page website videos to fully automated webinars.


How should the Vidale/Wolfe model be adapted for On-line analysis and usage?


    This question is "des Pudels Kern," the heart of the matter. The Bridges challenge is for you to co-author a sound answer with supporting empirical evidence and ANOVA.1

    Vidale and Wolfe used three key parameters to describe the relation between sales response and advertising:

    1. The Sales Decay Constant

    2. The Saturation Level 

    3.The Response Constant (sales generated per advertising dollar when S = 0)

Based on these parameters, they developed a simple, powerful optimization model. The Internet, with its high transaction speeds and low transaction costs, has made the application of quantitative models to business decisions practical. For example, Google Analytics split testing tools include multivariate analysis. Therefore taking a similar step with Vidale/Wolfe seems feasible.

    Before considering the Vidale Model, let us establish a marketing frame of reference for the Internet. One may do this in terms of the Butterfly Effect and Dragonfly Dynamics.


III. The Butterfly Effect1 - Internet Marketing

    In 1952 Ray Bradbury (best known for Farenheit 451) postulated in "A Sound of Thunder," a short story about time travel, that a single butterfly could have a ripple effect on far distant events. Science fiction became science fact when Edward Lorenz (1917 - 2009), a mathematician and meteorologist who was a professor at M.I.T., ran a computer forecasting model for the weather. He truncated an input variable from .506127 to .506. To his astonishment, an entirely different weather scenario was generated. Further studies in this area led to his becoming the founding father of chaos theory.

    Lorenz used the butterfly analogy often. In 1973 a colleague of his suggested the title for a paper he was presenting at a conference:"Does the flap of a butterfly's wing in Brazil cause a tornado in Texas?" Variations of that phrase have entered the common language.

    The Internet in general and social media in particular have lent remarkable power to concatenative ripple effects -- by "butterfly consumers." By way of example, bumbling airline baggage handlers break a musician's guitar. Stonewalled by customer service, the frustrated musician "flaps his scintillating wings," i.e. sings an engaging song about his woes. He posts the video of it (and two sequels) on YouTube: "United Breaks Guitars." Ten million views later United is facing a relentless public relations nightmare. Some observors attribute $180 million of losses to that negative publicity. Even if that observation is only 1% true, the butterfly effect of that lone musician still cost United close to two million dollars.

    On the Internet you are not usually dealing with the isolated flap of an individual butterfly's wings, the single distraught customer -- or raving fan. For instance the Monarch butterflies depicted below do not travel alone. Think of the immediate links of a member of a Google + group, or one at Facebook, LinkedIn or Twitter. The groups interlink over large regions.

Monarch butterflies*


You are dealing with veritable information migration. This phenonom is not entirely understood on the Internet, or in nature either.

    The Monarch butterfly, one of the few insects capable of trans-Atlantic flight, makes for an interesting example of the "natural" case. Monarchs have a wide range, appearing in Western Europe, including Greece, and in Bermuda, Australia, India, and Ceylon. However they are most common in North America. The image below is not an example of information flow on the Internet. Rather it is depicting migration routes of the Monarch butterfly.




  Monarch butterfly migration (Wanderung des Monarchfalters) Harald Süpfle, 2008*


The Monarch is the only butterfly which, like birds, has a two direction (depart and return) migration. The massive southward migration shown above starts in August. It continues until the first frost, when the butterflies stop for the winter. The butterflies generally live two months (some, born in the winter, for as long as seven). No individual butterfly lives long enough to make the complete south-north and return migration, which takes place over three to four generations. How the flight patterns are determined and passed on from one generation to the next is not entirely understood.2


    Bricks and mortar with ivy-covered walls - one thinks of lush green lawns and fluttering butterflies. Clicks and Flicks with sparkling LED screens - one thinks of silicon and steel and robotic butterflies.


  Robot butterflies*


Pursuing Aristotle's doctrine of the mean -- bricks and clicks -- seems reasonable. However this position has been attacked as "osciallating between an unhelpful analytical model . . . and a substantively depressing doctrine in favor of moderation."3  The philosophical objection was from the point of view of ethics, not of corporate strategy. Still, there are certainly plenty of unhelpful analytical strategy models on the one hand, accompanied by an equal amount of amorphous "muddling though" strategies of moderation on the other. 

    Focus and intensity are more likely to lead to success. They need to brought to bear on real customers, real people, not on some computer-generated butterfly customer avatar. This generalization is true enough, but not too helpful to plan specific actions. Can a quantitative approach to butterfly dynamics lead to more practical insights? This question brings us back to the Vidale-Wolfe model.

IV. Background

    As a graduate student at M.I.T. I noticed a model for optimizing an advertising budget in a footnote in Kotler's standard textbook on marketing.4 I was interested in applying the model in direct mail. There you have precise, accurate data about cost per lead and cost per close. However cycle times in the days of snail mail were slow. One would not be able to build a large database and thoroughly test hypotheses by running iterations in the course of a few months.

    With the advent of the Internet, optimizing advertising became more interesting for three reasons. First, cycle times were exponentially reduced. Campaign response times could be measured in hours and days instead of weeks and months. Second, transmission costs were a tiny fraction of what direct mail postal costs were. Third, as a result, split testing with different E-Mails and websites had become practical. This combination of factors led me to consider updating the Vidale/Wolfe model for the Internet.5

    To my considerable dismay I soon realized that my math skills had not just become rusty since graduate school days, they had disappeared entirely! Therefore I enlisted the cooperation of a co-author, a Russian theorectical physicist at the Max Planck Institute in Munich. I asked him to solve the question I posed about applying the model in the Internet world.



V. The Fatal Flaw


    A first draft of the paper was finished fairly quickly in 1991. With a preliminary computation completed, the physicist returned to his scientific research. My task was to formulate the next question. A question-answer iteration would be followed until we had a "unified theory" of advertising optimization - or at least had taken some steps in that direction. 

     However the more I looked at the preliminary work, our point of departure, the less confident I became. After about six weeks of off and on deliberation, I reached the unhappy conclusion that I had posed the wrong question. Therefore the wrong equation set had been solved, which made moot the correctness and elegance of the calculations. Frustrated, I set the draft aside.

    Some months later I showed it to an English friend who had received a double first in engineering and economics before effortlessly obtaining an MBA from London Business School. (In fact, he had graduated number one of several hundred engineering students at his previous university.) He read the draft over supper and frowned. A good six minutes later he told me the initial equation was not asking the right question. He had reached a conclusion in six minutes that had taken me six weeks to figure out! (That roughly corresponds to the difference in our levels of intelligence.)

     I therefore decided to return Vidale/Wolfe to the dormant file, until an occasion surfaced for me to take another look at it.

VI. The On-line Video Impetus

    The strategic alliance with Aladin Video is that occasion. The financial cost (as opposed to the cost of management time) for most Internet advertising is easy to control. Sending out an E-Mail and following the chain from open rates to credit card purchase is fairly straightforward. Cost per click and cost per action campaigns provide immediate feedback in accordance with the billing cycle. Here, sophisticated models are unwarranted both for the small company and the multinational.

    However producing a video for a website can be another matter entirely. A do-it-yourself or budget priced video will be the solution of choice for most small companies. However a Fortune 500 company and the demanding (premium brand) medium sized company may well decide on a full blown professional shooting.

    The cost of the video production is essentially the cost of the advertising campaign because the video distribution costs are minimal. Depending on the length of the video and features such as professional voice-over or a brief celebrity appearance, prices can vary from a few thousand Euro to 50,000 € or more. At this level of expenditure, taking a more sophisticated approach to determine an advertising (video production and dissemination) budget is indeed warranted. 


VII. The Original Model

    Below is a link to a PDF of the orginal Operations Research paper published in 1957 by M.L. Vidale and H.B.Wolfe of the consulting firm Arthur D. Little. Should the link not work, cut and paste it into Google. The title should re-appear at the top of page one. Clicking on it there will bring you to it. The 12 page article needs to be read to understand the basic flaw in the first attempt at an updated draft, which is presented below.





File Format: PDF/Adobe Acrobat - View as HTML


VIII. The Draft

1) Major Correction

    Understanding the basic flaw is the key to realizing the correct question to pose. Hint, read Section I, pp. 1-2, carefully, then skip forward to the concluding equations accounting for the effect of competition. The logic is not consistent with the actual dynamics of the system being described. The correct question to pose is (relatively) straightforward. However the solution of that equation is a little more demanding than the work presented below.


N.B. The "initiation rite of passage" to be a co-author for the revised article is to submit the equation for the question I should have asked!


2) Minor Corrections 

    The correct spelling is Vidale (not Vidal). The model was first introduced in 1957 (not 1961). The correct abbreviation for dollar is $ (not D).


Note: Footnotes for the above text appear after the model. They range from a brief explanation of ANOVA in the first to some personal comments about Tom Peters and his McKinsey cohort Robert Waterman Jr. in the last. 



1 ANOVA refers to Analysis of Variance. Basic ANOVA tests whether the means of different groups are equal. Note that the chance of Type I error* increases as one does more two-sample t-tests,** which makes running ANOVA desirable. There two main kinds of ANOVA models: (1) fixed effects and (2) random effects.

    1) In fixed effects one applies different approaches to a sample to see how the response variables change. Then one draws conclusions about the effect those approaches would have if used on the entire population.

    2) Random effects models are used when the approaches themselves are not fixed.  

The Vidale-Wolfe is describing a non-linear system. Can be it back-checked with a linear model for which ANOVA is appropriate?


* Type I error, designated by the Greek letter Alpha, is a false positive. In other words, a statistical test rejects a true null hypothesis H0). It equates to the significance level of the test.

   Type II error, designated by the Greek letter Beta, is a false negative. A statistical test fails to reject a false null hypothesis. It is related to the power of a test (1 - Beta).


** T-tests were devised in 1908 by William Sealy Gosset as a quality control measure for Guiness beer (Wikipedia, 2011). They are used in regression analysis and entail the sample size, degrees of freedom, the mean, the standard deviation and an assumption of a normally distributed population. 


2 The  source for the lepidopteran and ondonate information was Wikipedia (2011). (The unusual words refer to the insect classes to which butterflies and dragonflies belong.)


3 Monarch butterflies two generations later fly to the same winter quarters as their ancestors, an inherited destination. Their navigation is a subject of on-going research. It is based on a "time-compensated sun compass depending upon a circadian clock that is in their antennae." They appear also to make use of the earth's magnetic field. (Wikpedia, 2011)


4 Bernard Williams, Ethics and the Limits of Philosophy, 1985, p. 36.


5 Philip Kotler, with a Masters from the University of Chicago and PhD from M.I.T., both in economics, is a professor of marketing at the Kellog School of Management at Northwestern University, a top ten program (often top five, depending on who is doing the rating) MBA program. He is the author of the most widely used graduate school marketing textbook, Marketing Management, among other books and numerous journal articles, including several award winning ones. The classic textbook has been updated 14 or 15 times since its first publication in 1971 (or possibly earlier).


6 There was also a personal motive based not so much on academic snobbery, but rather a certain peculiar academic jealousy. Tom Peters and his fellow McKinsey consultant Robert H. Waterman, Jr. wrote  In Search of Excellence in 1982. They both left McKinsey soon after the book became a bestseller.

    The book gives the impression that the companies discussed were selected on the basis of rigourous research and financial screens. Actually the two authors asked people they knew, mostly McKinsey colleagues, for companies doing "cool work." From that list of 62 companies, they eliminated 19 because of their 20 year performance on the stock market. Then they attributed some common denominators to the remaining, wrote in an entertaining style, and, voila, one of the bestselling business books of all time.

    I had found the research in the book suspect upon reading it at publication. I was astonished that at first so few reviewers raised questions. Over the years the companies flaunted in the book as excellent fell one by one to the wayside. And "ex post facto" negative reviews did indeed surface. Meanwhile the book had launched Tom Peters to management guru status. He continued to ascend from one high (pun intended) to the next.

    For some reason this scenario of dubious research leading to spectacular success made me want to publish, if not a book, at least an article of substance. At universities "substance" means theory building empirical research. I was not quite that ambitious, but did want to write something quantitative to reflect my education.

    Tom Peters went on to write a number of popular business books such as Thriving on Chaos, 1987, The Pursuit of WOW! 1994 and most recently The Little Big Things, 2010. The latter has been heavily criticized as a poorly done rehash of his previous writings.  To give him his due, he is more than a flamboyant showman brillanting packaging basic common sense, blessed with the "luck of the media," as some detractors would have it.

     What many people do not realize is that the charismatic (or shameless publicity hound, depending on one's viewpoint) Tom Peters has a PhD from Stanford Business School. Besides his popular books, he has published scholarly articles in academic journals. He has kept this accomplishment surprisingly low profile, in contrast to his self-promoting guru activities.

    To conclude with a personal postscript: In 1987/88 Robert Waterman was launching his own consulting firm after having left McKinsey. I attended a seminar he held in San Francisco to promote it. The subject was empowerment. I enthusiastically asked him the very first question at the seminar's conclusion. "How did Mckinsey, his old firm, use empowerment, and how did he use it in his own firm now?"

    He responded that neither McKinsey nor he needed empowerment. The concept was rather for clients. This reply did not sit well with the audience at all, who pursued the issue with vigor. Somewhat to my embarrasment, my question had wrong-footed him. The seminar did not finish with a whimper, but, no thanks to me, certainly not with a bang either. For some reason his star never did ascend as rapidly or as high as Tom Peters' did.


*© Monarch butterflies - Father of JGKlein, Iowa, USA, 2001 released to public domain; Monarch migration - Wanderung und Verbreitung des Monarchfalters (Danous plexippus) in Nordamerika (Animation) Harald Süpfle,  CCAS 3.0, 29.09.2008; Robot butterflies, onarch motodisc, Getty Images; Gyan Web Design 2010