Saturday, September 12, 2009

The Flaw of Averages

Everyone in your company who makes decisions or supports decision-making needs to read
by Sam Savage. Why? Because together you are likely committing the flaw of averages, wasting time and exposing yourself to unnecessary risk. Savage shows you how to avoid this pitfall in a cleverly written, enlightening, and fun to read guide to making better decisions.

Most likely you have never heard of Jensen's Inequality, and most likely you don't care. However, you should care, and The Flaw of Averages introduces why this concept poses profound implications to the way we tend to think about making decisions. The problem is that in thinking about the issues or opportunities we face and the decisions we exercise to address them, we often go through a kind of accounting process in which we consider the best case, most likely case, and worst case scenarios (or any number of scenarios) and the corresponding conditions that have to exist for each scenario to be realized. We let ourselves believe that those assumed conditions are averages that we can use as proxies for the full range of uncertainty we face. Our final conclusion is that the outcome of our analysis closely corresponds to the average real-world outcome and the extent of possible variation (if we get that far). Understanding that, we commit to action, often disastrously so.

Savage reveals the flaw in the traditional way of thinking by explaining the implications of Jensen's Inequality. In short, Jensen's Inequality says that in situations where the output we care about varies in a non-linear way to inputs (which is much of life), the outcome as a function of average inputs (the flawed traditional analytic approach) is NOT equal to the average outcome as a function of the inputs treated as they naturally vary. [For those mathematically inclined, if E() is an operator that determines the average of a sample, and f(Xi) is a function of inputs, then E( f(Xi ) ) does not equal f( E(Xi) ). For those not so mathematically inclined, don't worry. The Flaw of Averages is not a math book; rather, it is a book about making decisions and how math can be used constructively to support that process.]

The way around this failure is to use Monte Carlo simulation to consider simultaneously the effects of the range of the assumptions as they naturally vary on the outcome we care about. Instead of thinking about the outcome as a single point or a constellation of points representing exhaustive guesses about the future, we see the full range of potential outcomes and their likelihood as a distribution. We see the implications of our decisions and corresponding uncertainties as a picture and not a point. As a result, not only do we avoid never ending analysis paralysis, we gain a deeper appreciation for the effect of typically unconsidered outcomes, both good and bad, and are able to plan accordingly with contingencies and options.

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