• riccardo

Managers are on AVERAGE wrong about AVERAGES

Updated: Dec 23, 2019



 

While many professionals often describe numbers like sales and costs through some Pareto characteristics – few customers or factors, say 20%, causing the majority of the results, say 80% – few realize what it really entails for effective decision making. Even worse, sometimes the correct takeaways may be opposite to common intuition and the results are potentially disastrous.


I have often been one of those working with the “big picture” – not really sure what it means – and I have often relied on few indicators like “the average value” in order to get to fast and high-level conclusions. Unfortunately, I was often proven wrong in that approach and I thank practice for those teachings that, in most recent years, have proven to be really useful and actionable. Moreover, I later realized that high-level pictures may be a good approach in engineering applications ruled by Gaussian phenomena – mechanical engineering in my case – while, they could be disastrous in business and financial domains where normal distributions are often just shortcuts.


Let’s discuss a common example: the first picture below shows the distribution of the worldwide net worth in 2018. That picture represents a kind of Pareto distribution and it considers something close to 5 Bil people as WW population associated to net worth and $320 Tri as WW total wealth – difficult to identify the correct numbers, however, our focus is on the distribution; moreover, this is net worth and not GDP. That picture implies a global wealth per capita of about $63.5k – similar results can be found at https://en.wikipedia.org/wiki/List_of_countries_by_wealth_per_adult.

Here is the first takeaway leading us to the core of this post: in the Pareto distribution below, the average value is not really the value verified most frequently; therefore, depending on the case, the mean could be considered a mathematical result rather than a “true” one. In that example, the majority of the values are to be found in the bucket related to a net worth below $10k, that is below the mean value – for the sake of discussion we are using the terms mean and average without distinction.



Wealth range in U.S dollars

Of course, the result can be highly dependent on how we group values and other things. However, even a slightly different distribution would be likely to have similar characteristics. It is possible to show that by running a quick simulation in Python: we can first draw 10,000 random samples from a similar Pareto distribution and then draw 10,000 random samples from a completely different one, the normal distribution. The resulting distributions with the corresponding means are shown below. The interesting fact is that, while the normal distribution verifies the mean about 50% of the times, making it the most verified value, the Pareto distribution verifies the mean only about 10% of the times. In reality, those numbers are not rigorous because the Pareto could verify the mean even more than the Gaussian for same deviations from the mean (let's say 0.5 or 1 StandardDeviation; both the distributions below can be considered having StDev = 1) and that would depend also on the specific Pareto. However, from a managerial point of view that would be probably non-actionable information because, we may prefer to focus on how possible values move around the mean and, in general, the Pareto would result in much higher surprises.


Pareto distribution with mean value at 0.66

Normal (Gaussian) distribution with mean value at 0.0

In management results do not depend only on decisions but, also on their timing and volatility (variation) of the involved parameters; there are important implications associated with that.


If a specific domain we were dealing with was normally distributed, we might be right in expecting a “reversion to the mean” or expecting that parameters would be likely to hover around the average value; that is where they like to be. However, if the domain was Pareto distributed – even different distributions – we could go bust by waiting for a reversion to the mean because values could stay below the average value for a long time. Moreover, since Pareto dynamics offset the majority of the values below the average with few values much above that, we would be in trouble if we were not prepared to handle large deviations rather than just reversions to average values.


Two domains characterized by the two distributions of the example above would require two very different approaches in order to apply effective decision making – mostly based on intuition rather than big data. As often mentioned, readers can find professionals discussing those arguments more rigorously, however, I think personal tinkering is crucial in order to understand how to leverage those situations and takeaways in our own specific practice.



 

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