Managing by the Numbers
One of the major problems with modern business (and science) is an over-reliance on mathematical models, coupled with an irrational belief that what has happened in the past can predictably be relied upon to continue indefinitely into the future.
In reality, any mathematical model is no more, and no less, than a whole bunch of assumptions flying in close formation. Models are useful for understanding how the world works today, and how it has evolved in the past, but they are a risky proposition when used to predict the future. If models were truly predictive, we would be able to avoid recessions!
Whether you can rely on mathematical models, as a decision-making tool, is a question of how much control you have; not over the model itself, but over the subject area being modeled.
There are three types of model:
Tactical models are used to understand how your business is working, and how it might work better. Tactical models use commercially available "business intelligence" products to analyze key indicators about your internal business systems. The type and quality of information collected is under the control of your information technology people, and if they are doing their job right, you can rely on what the model tells you is happening now, and likely to happen in the future. These are things you can manage.
Operational models start to explore the area of customer (and in some cases supplier) behavior. This is an area you can influence. These models look a little wider and include mathematical information from outside of your business - things like customer demographic information, market research results, etc. The type and quality of information collected is under the control of your sales and marketing functions, and is often derived from census information or surveys. Because you only have limited control over the quality and currency of the external data, you should be somewhat skeptical when using model predictions.
Strategic models are concerned with things that you cannot manage or influence, but things that you may need to, or may choose to, react to. They are qualitative, rather than quantitative. You cannot use commercial business intelligence systems to construct strategic models (at least, not at a level of complexity that is useful). These models require the analyst to have a particular approach to problem solving, good pattern matching skills, excellent general knowledge, and a wide range of interests.