## 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...

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