Applied Probability Models in Marketing

To understand, explain, and predict the behavior of businesses and consumers in the workplace, marketing departments frequently apply probability theory to model the reality of the marketplace. These models allow marketing managers and analysts to run "what if" scenarios and manipulate variables in order to better utilize marketing resources to influence consumer behavior. Marketing models fall into three categories: Explanatory models that attempt to explain how some part of the marketing process works, predictive models that help the marketer forecast buyer behavior, and decision support models that help managers make decisions about various marketing problems. Many marketing models are based on behavioral economics, taking into account insights from both psychology and economics, and use the principles of statistics and probability to model the real world situation.

Keywords Artificial Intelligence (AI); Consumer; Customer Lifetime Value; Customer Relationship Management; Expert System; Forecasting; Market Share; Marketing; Model; Probability; Variable

Marketing > Applied Probability Models in Marketing

Overview

It is the responsibility of the marketing function within an organization to create, communicate and deliver value to customers and to manage customer relationships in ways that benefit the organization and its stakeholders. This means that the marketing department is concerned with two constituencies: Customers — who want value for their money — and the organization — which wants to increase its profitability. In some ways, the two constituencies are in conflict. As long as the value is high, most customers would be perfectly happy to have the lowest price possible. Most organizations, on the other hand, would be perfectly happy to charge as much as possible in order to reach their goal. In the tension between these two disparate sets of needs and desires, there is a middle ground where both the customer and the organization win. Part of the task of the marketing function is to determine where this middle ground lies and how to best attract more customers for the organization's products or services.

To this end, many marketing departments rely on the use of mathematical models to help them forecast consumer buying behavior under various sets of variables and "what if" scenarios. Marketing is concerned with both the description of actual behavior (e.g., when we marketed the widget as a home tool, more people bought it than when we marketed it as a business tool) and the prediction of behavior (e.g., if we price the widget at $X, will more people buy it than if we price it at $Y?). A mathematical model is a mathematical representation of the system or situation being studied.

Marketing Models

There are three basic types of models used in marketing: Explanatory models, predictive models, and decision support models.

Explanatory Models

This model attempts to explain how some aspect of a marketing process works. For example, a model could be developed to explain how various factors such as product features, packaging, or perceived benefits affect consumers' perceptions of the product and their likelihood of purchasing it. This information can help marketers better understand how to best position a product or brand to gain a larger market share. Marketers use the results observed in the model to explain such factors as customer perceptions and to develop marketing strategies for the brand or product.

Predictive Models

Predictive models are designed to help the marketer forecast buyer behavior, future marketplace trends, or other factors of interest. For example, a simulation model could be developed to predict sales for a new product for the first six months. This information could be used to support the marketing department and the supply chain in estimating how many units to produce, warehouse, etc.

Decision Support Models

Decision support models are computer based information systems that help managers make decisions about semi-structured and unstructured problems. For example, a decision support model could be developed to investigate a series of "what if" scenarios to determine the optimal marketing mix for the introduction of a new product in the marketplace. Decision support systems can be used by individuals or groups and can be stand-alone or integrated systems or web-based.

Application of Marketing Models

Marketing models are firmly based on the contributions of two disciplines. The applied psychology of consumer behavior helps marketers better understand how businesses and customers behave within the marketplace and to better know how to influence them as a result. In addition, most marketing models are applications of economic theory. Both of these disciples use mathematical modeling tools that take advantage of probability theory to explain and predict behavior in the marketplace. Many marketing models use the approach of behavioral economics, which integrates the insights from both of these disciplines. This approach allows marketers to link the psychology of consumer behavior to the economics of consumer choice and activities.

Ideally, a marketing model should be able to explain, predict, and support decision making. In reality, however, this is not always the case. Models — particularly comprehensive ones — are frequently expensive to develop. Many organizations find that it is better to develop a model that will meet its primary objectives well and cost-effectively rather than trying to develop a more comprehensive model that will do multiple things. In addition, some marketing problems are more difficult to model than others (e.g., isolation of the long-term effects of advertising or measurement of factors that currently do not exist in the marketplace). Such factors set a limit to how much one can do with one model as well as detract from the development of a sharply focused model. Further, measurement of variables can limit the validity of a model. Not only are some variables difficult to measure, but various measurement errors can affect the validity of the data. For example, the collection of subjective data (e.g., answers to questionnaires) is liable to contain several types of errors that can skew the results and negatively impact the effectiveness of the resultant model.

The Mathematical Models

No matter their application, the mathematical models used in marketing attempt to succinctly describe reality and clarify important relationships between variables. To do this, models simplify the relationships observed in the real world. For example, if one wanted to find out whether a proposed new logo projected a more positive image than the current logo, marketing research might be done to collect consumers' opinions on the two logos. Some people would say that they liked the new logo more than the current logo, and others would not. However, there could be a number of reasons that the ones who disliked the new logo did so that were extraneous to the logos themselves. Such extraneous variables affect the outcome of research but are not related to the independent variable. For example, one consumer might not like the proposed new logo because it was red and she had had a fight with her husband that morning and he had been wearing a red tie. Another consumer might prefer the current logo because it is blue and blue is his favorite color. Neither of these reasons has anything to do with the research question: Whether or not the new logo projects a more positive image than the current logo. However, these extraneous variables — reactions for or against a particular color — affect the outcome of the research.

Impact of Variables on Marketing Models

The number of extraneous variables that can affect the outcome and effectiveness of a model are legion. Although it is important to control as many of these variables as possible, it is not possible to control them all. The design of a comprehensive model that takes into account all possible extraneous variables is not only a virtual impossibility, but not feasible from a practical standpoint, either. Even if a model complex enough to take into account all the variables could be designed, sufficient detailed data could be operationally defined and collected, and the research subjects willing and able to discriminate on such minutia, the cost of developing such a model would be prohibitive and the model probably could not be designed until after the research question had become moot. Therefore, one of the goals of mathematical modeling is to be able to explain the relationship between variables elegantly; that is simply and parsimoniously expressing the relationship between the important variables rather than trying to explain all possible permutations of the problem in all possible conditions.

The question, of course, is how to best choose which variables need to be included in the model and which can be excluded without negatively affecting the validity of the model. The best models hit the right note between being able to predict in all circumstances and predicting accurately. A model that leans too far to one side or the other will not have much applicability. A model that fits the real world situation with its multitude of extraneous variables would more than likely be too general to be of much practical use. For example, to know that women 35 years of age who are currently dating but are not engaged and who prefer to eat a hot breakfast like the new logo design may be an accurate picture of reality, but unless the marketer is trying specifically to reach that target demographic, the observation is not of much help. A model with these parameters might be a better predictor, but too narrow to be helpful.

In part, choosing which variables to include or exclude in the model building process should be done based on the relevant literature. In most situations, the theorists and researchers will have given serious thought to the relationship between variables and corresponding literature will express the state-of-the-art thinking about various aspects of the universe of data at which one is looking. Similarly, observations of trends and relationships by the marketing personnel or management in the organization can lead to other strong assumptions that are good points of departure for building a model of consumer behavior. However, strong assumptions alone are insufficient. A useful model also needs to be testable. No matter how good the assumptions seem in theory or the relationships look on paper, it is important that marketers or analysts be able to actually collect data to test the validity and reliability of the model. Model building is an iterative process. Based on empirical observation, one posits a theory and develops a model based on its assumptions. The model is then tested with real world data and modified to better reflect the real world experience. This process is repeated as necessary to refine the model and improve its accuracy.

Factors Influencing Customer Behavior

It is also important to remember that models are not set in stone: The factors influencing customer behavior change over time and the marketing model needs to be flexible to reflect those changes. For example, fifty years ago the concept of a store-bought frozen dinner that one could eat in front of the television was a novel concept. Not only was the television a relatively new technology in most households, but most women did not work outside the home and cooked from scratch. A few decades later, however, the opposite situation is true in many households. As a result, the frozen food aisles in grocery stores today offer an amazing array of frozen dinners and even the fresh food departments offer conveniences such as pre-sliced onions to cook with one's liver, marinated meat that only needs to be thrown on the grill, or bags of pre-washed and chopped lettuce that were unheard of in the mid-twentieth century. The important assumptions and variables for grocery store marketing of fifty years ago (e.g., fresh food; full-time homemaker) are no longer appropriate today (e.g., convenience foods; bi-vocational or single parents).

Applications

Mathematical models can be used for many applications in marketing. Generic models to forecast customer lifetime value can help marketers better understand how to spend their budgets to both acquire and retain customers. In addition, expert systems utilize the power of artificial intelligence to develop models that are more flexible and integrate numerous sources of data.

Customer Lifetime Value

To improve the cost-effectiveness of their efforts, the objective of many marketing departments is not just to win the customer for a one-time purchase, but to gain customer loyalty to the business or brand and thereby win continuing sales over the long term. This approach to marketing is called customer relationship management. In this process, the business identifies prospective customers, acquires data concerning prospective and current customers, builds relationships with customers, and attempts to influence their perceptions of the organization and its products or services. One statistic that is helpful in this endeavor is customer lifetime value. This is an estimate of how much a customer will spend with a business or brand over his or her lifetime. This information is of interest because it theoretically allows a business to know how much each customer is worth in terms of dollars of income which, in turn, allows businesses to better know how to spend their marketing budget. For example, if the 20-35 year old demographic will potentially spend ten times as much money on widgets during their lifetime than the 60-75 year old demographic, then the business is well advised to focus their efforts on the younger demographic (although not necessarily excluding the older demographic). This approach to weighting marketing emphases, however, is not without its drawbacks. Calculating customer lifetime value tends to be complex (e.g., the customer's need or desire for the product may change, the competition may bring out a product that better fits the customer's needs), and reliable data to build a usable model and net cash flow from the customer are difficult to gather.

Particularly where markets are mature and there is significant competition, it would be helpful to be able to forecast the lifetime value of a customer to a business or brand. This is a good example where mathematical marketing models can be of use. Berger and Nasr review five general marketing models of customer lifetime value. The simplest case assumed one sale per customer a year with both the cost of marketing efforts to retain customers and their actual retention rate remaining constant over time. The second approach removed the assumption of once-yearly sales and allowed examination of time periods both longer and shorter than one year. The third and fourth cases examined the effects of gross contribution margin and promotion costs that vary over time. Case 4 examined a model that takes into account the added complexity of continuous rather than discrete cash flows. The final model assumed a shrinking customer base in which customers are lost over time and treated as new customers when they return. These models can be used by marketers for a variety of purposes including decisions concerning the allocation of marketing dollars for advertising campaigns and forecasting the effect of a marketing strategy particularly vis a vis acquisition and retention of customers and the associated costs and tradeoffs.

Expert Systems

Mathematical models today can do more than mere number crunching. Expert systems — decision support systems that utilize artificial intelligence technology to evaluate a situation and suggest an appropriate course of action — can help marketers better understand the marketplace and forecast consumer behavior. The use of expert systems in modeling in support of marketing processes can consider both qualitative (judgmental) and quantitative data. These hybrid models (sometimes referred to as knowledge-based systems) can utilize multiple sources of data. As opposed to standard mathematical models that rely solely on the inputs of quantitative data, knowledge-based systems allow the user to specify the constraints and objectives under which the model should process the data. The model then synthesizes both quantitative and qualitative data to develop a potential solution. The major difference between standard mathematical models and knowledge-based models is that in the former, the marketing environment needs to be represented mathematically. The model also needs to be complex enough to represent the real world situation accurately but simple enough to be solvable. A knowledge-based system, on the other hand, relies not just on mathematical rules but on heuristics — rules based on empirical relationships — generated from non-quantifiable sources such as experience or insight.

There are several steps to building a knowledge-based model. First, the decision needs to be made when to develop a model. Some of the situations in which it may be of use to develop a knowledge-based model include when the organization has a recurring problem, experts are retiring or leaving the organization and their replacements do not have the same skill based on long experience, or decision making processes could be aided by the consideration of qualitative data. Once it is determined that a model needs to be built, the next step is to decide who needs to be involved in the model building process. The individuals involved should understand the discipline of marketing, have experience building models, understand probability and statistics, and be familiar with expert systems. After the model building team has been developed, the shell for the model needs to be chosen. There are a number of readily available shells for model building on the market. First time users are well advised to select a shell that is easy to learn at the cost of sacrificing some flexibility rather than a very flexible shell that is difficult to learn. Once the shell has been selected, the next step is to structure the problem domain. This involves defining the variables that need to be considered and anticipating the relationship that will be impacted by the analysis. This will allow one to establish a framework within which to work. The next steps are to gather and process the data. To maintain the usefulness of the model, it also needs to be updated on a regular basis.

Terms & Concepts

Artificial Intelligence (AI): The branch of computer science concerned with development of software that allows computers to perform activities normally considered to require human intelligence. Artificial intelligence applications include developing expert systems that allow computers to make complex, real world decisions; programming computers to understand natural human languages; developing neural networks that reproduce the physical connections occurring in animal brains; and developing computers that react to visual, auditory, and other sensory stimuli (i.e., robotics).

Consumer: A person or organization that acquires goods or services for direct use rather than for resale or use in a manufacturing process.

Customer Lifetime Value: An estimate of how much a customer will spend with a business or brand during the period when s/he purchases from that business or brand. Analysis of customer value should include consideration of the depth, breadth, and duration of the customer's relationship with the business or brand as well as the cost to acquire, serve, and retain each customer.

Customer Relationship Management: The process of identifying prospective customers, acquiring data concerning these prospective and current customers, building relationships with customers, and influencing their perceptions of the organization and its products or services.

Expert System: A decision support system that utilizes artificial intelligence technology to evaluate a situation and suggest an appropriate course of action.

Forecasting: In business, forecasting is the science of estimating or predicting future trends. Forecasts are used to support managers in making decisions about many aspects of the business including buying, selling, production, and hiring.

Market Share: The proportion of total sales of a given type of product or service that are earned by a particular business or organization.

Marketing: According to the American Marketing Association, marketing is "an organizational function and a set of processes for creating, communicating and delivering value to customers and for managing customer relationships in ways that benefit the organization and its stakeholders" (http://www.marketingpower.com/content24159.php).

Model: A representation of a situation, system, or subsystem. Conceptual models are mental images that describe the situation or system. Mathematical or computer models are mathematical representations of the system or situation being studied.

Probability: A branch of mathematics that deals with estimating the likelihood of an event occurring. Probability is expressed as a value between 0 and 1.0, which is the mathematical expression of the number of actual occurrences to the number of possible occurrences of the event. A probability of 0 signifies that there is no chance that the event will occur and 1.0 signifies that the event is certain to occur.

Variable: An object in a research study that can have more than one value. Independent variables are stimuli that are manipulated in order to determine their effect on the dependent variables (response). Extraneous variables are variables that affect the response but that are not related to the question under investigation in the study.

Bibliography

Berger, P. D. & Nasr, N. I. (1998). Customer lifetime value: Marketing models and applications. Journal of Interactive Marketing, 12, 17-30. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=348356&site=ehost-live

Coussement, K., & Buckinx, W. (2011). A probability-mapping algorithm for calibrating the posterior probabilities: A direct marketing application. European Journal of Operational Research, 214, 732-738. Retrieved November 15, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=62844526&site=ehost-live

Ho, T. H., Lim, N., & Camerer, C. F. (2006). Modeling the psychology of consumer and firm behavior with behavioral economics. Journal of Marketing Research, 43, 307-331. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=21945242&site=ehost-live

Keon, J. W. (1991). Point of view: Understanding the power of expert systems in marketing — when and how to build them. Journal of Advertising Research, 31, 64-71. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=9202171002&site=ehost-live

Shugan, S. M. (2002). Marketing science, models, monopoly models, and why we need them. Marketing Science, 21, 223-228. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=17463152&site=ehost-live

Wyner, G. A. (2006). Why model? Marketing Research, 18, 6-7. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=20577118&site=ehost-live

Yi, Q., & Hui, X. (2011). No customer left behind: a distribution-free bayesian approach to accounting for missing xs in marketing models. Marketing Science, 30, 717-736. Retrieved November 15, 2013, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=65097007&site=ehost-live

Suggested Reading

Barns, D. M. (2005). Comment on the value of simple models in new product forecasting and customer-base analysis. Applied Stochastic Models in Business & Industry, 21(4/5), 475-476. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=18071419&a,p;site=ehost-live

Fader, P. S. & Hardie, B. G. S. (2005). The value of simple models in new product forecasting and customer-base analysis. Applied Stochastic Models in Business & Industry, 21(4/5), 461-473. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=18071420&site=ehost-live

Hanssens, D. M., Leeflang, P. S. H., & Wittink, D. R. (2005). Market response models and marketing practice. Applied Stochastic Models in Business & Industry, 21(4/5), 423-434. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=18071428&site=ehost-live

Ho, T. H., Lim, N., & Camerer, C. F. (2006). How "psychological" should economic and marketing models be? Journal of Marketing Research, 43, 341-344. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=21945228&site=ehost-live

Jones, S. & Eden, C. (1981). Modelling in marketing: Explicating subjective knowledge. EuropeanJournal of Marketing, 15, 3-11. Retrieved June 12, 2007, from EBSCO Online Database Business Source Complete. http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=5117933&site=ehost-live