The “Normal” Fallacy

Sometimes my ideas and behaviors don’t fall within the parameter range of what some people consider “normal”. Yet I consider them quite normal, though perhaps a bit uncommon.

When people don’t understand the nature of complex systems, they tend to make assumptions that don’t make sense from a complexity perspective. For example, people often assume that the variation in size of customer requests follows a normal distribution, or Bell curve. When plotted in a graph this distribution looks like my belly, when viewed from above.

The assumption people make is that, when considering change requests or feature requests from customers, they can identify the “average” size of such requests, and calculate “standard” deviations to either side. It is an assumption (and mistake) I noticed again in John Seddon’s book Freedom from Command & Control.

Uncommon but Normal

There is no “average” size of earthquakes. There is no “average” size of personal income. There is no “average” size of blog posts. There is no “average” size of organisms. And there is no “average” number of false assumptions in books by systems thinkers.

Events in complex systems tend to follow the exponential or Pareto distribution. Also known as Zipf’s law, the 80-20 rule, the power law, etc. It looks like my foot, when viewed from the side.


In complex systems there are many occurrences of small events. Like tiny earthquakes, low wages, small blog posts, microscopic organisms, and slightly erroneous books on systems thinking. But there are also few occurrences of big events. Like catastrophic earthquakes, excessive salaries, gigantic blog posts, huge organisms, and complete idiots among systems thinkers. In complex systems this is all normal. It is a pity that mathematicians named the Bell curve the “normal” distribution, because, in the real world, the Pareto distribution is more ubiquitous and normal than the normal distribution.

Customer Demand

I am convinced that the needs of your customers also follow the Pareto distribution. Most customers have only small needs. Few of them have big needs. Most of them have small budgets. Few of them are excessively rich. Most are quite reasonable. A few are minions from hell.

Of course, you can calculate the average of a number of specific occurrences that happened in the past. But your “average” has only little predictive value. With limited experience, your “average” is likely to include only the very common events, not the uncommon ones. Yet, in a complex environment, all events are normal. Both the common ones and the uncommon ones.

Customer demand is, by nature, an non-linear thing. If you assume that customer demand has an average, based on a limited sample of earlier events, you will inevitably be surprised that some future requests are outside of your expected range. You may call them “outliers” or “unexpected” or “black swans”. But fact is, you made the wrong assumption. You’re painting a distorted picture of customer demand. Like a picture of my face, when viewed from the rear.

The existence of rare events in complex systems is quite expected. Like me. Happily uncommon, but quite normal.

p.s. I do not mean there are no black swans, or unpredictable events. I just mean common thinking is no excuse for calling the uncommon events “unexpected” or “not normal”.

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  • Glen B. Alleman

    The customer demand arrivals are best modeled by a Poisson distribution. The “average” (mean) arrival rate must also have a variance (standard deviation) for the distribution to be useful. This is core queuing theory. You can monetize the arriving requests to create an assessment of the “value stream” of these requests.
    But in all cases there can be no “surprise” from a statistical point of view, if you have mean, variance, and the distirbution.

  • John Goodpasture

    What about the marching army? All those feet, thousands of feet representing thousands of low level requirements?
    For a work package or team leader concerned for the next requirement, your “foot” [exponential] is the likely distribution for all the reasons you give.
    But if you are the project manager or cost account manager responsible for an aggregate of requirements, then your “stomach” provides a more realistic planning scenario. As you’re no doubt familiar, the exponential distribution is in the same ‘family’ with the Normal [when I was in school, they called it the Gaussian distribution] and Poisson distributions.
    Consequently, the SUM of random variables from a population of independent exponential distributed entities will have central tendency that, in the limit, is Normal; so also will the expected value of the population.
    Your foot may be exponential, but to the project manager, it’s the army, not the foot soldier. And the army is Normal.
    PS: if you stomach really looks Normal, you should engage your feet more!

  • Leofdecarvalho

    The point here is that in a “belly curve” the probability of occurrence of small events is equal to the probability of occurrence of large events. But in a “feet curve” the probability of occurrence of small events is greater than that large events. I agree with you, Jurgen.

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