Frequency vs. Magnitude: The Asymmetry of Outcomes
Taleb argues that the importance of an outlier depends on the question and the consequences of the observation. A rare event cannot be dismissed merely because it is infrequent when its impact dominates the total result.
THE IDEA
Symmetry and Science
In most disciplines, such asymmetry does not matter. In an academic pass/fail environment, where the cumulative grade does not matter, only frequency matters. Outside of that it is the magnitude that counts. Unfortunately, the techniques used in economics are often imported from other areas—financial economics is still a young discipline (it is certainly not yet a “science”). People in most fields outside of it do not have problems eliminating extreme values from their sample, when the difference in payoff between different outcomes is not significant, which is generally the case in education and medicine. A professor who computes the average of his students’ grades removes the highest and lowest observations, which he would call outliers, and takes the average of the remaining ones, without this being an unsound practice. A casual weather forecaster does the same with extreme temperatures—an unusual occurrence might be deemed to skew the overall result (though we will see that this may turn out to be a mistake when it comes to forecasting future properties of the ice cap). So people in finance borrow the technique and ignore infrequent events, not noticing that the effect of a rare event can bankrupt a company.
Many scientists in the physical world are also subject to such foolishness, misreading statistics. One flagrant example is in the global-warming debate. Many scientists failed to notice it in its early stages as they removed from their sample the spikes in temperature, under the belief that these were not likely to recur. It may be a good idea to take out the extremes when computing the average temperatures for vacation scheduling. But it does not work when we study the physical properties of the weather—particularly when one cares about a cumulative effect. These scientists initially ignored the fact that these spikes, although rare, had the effect of adding disproportionately to the cumulative melting of the ice cap. Just as in finance, an event, although rare, that brings large consequences cannot just be ignored.
When to use it
Risk management in finance: evaluating the impact of rare market crashes rather than just average returns.
Climate policy: incorporating extreme weather events into models for cumulative effects like sea level rise.
Insurance: pricing policies that account for low-probability, high-impact events (e.g., natural disasters).
Medical research: considering rare but severe side effects when assessing drug safety, rather than relying only on average outcomes.
FROM THEORY TO EVERYDAY LIFE
In practice
Education: Averaging Grades
Taleb uses a professor trimming extreme grades as a contrast with financial losses. Whether trimming is appropriate depends on the grading objective; the example does not justify discarding extreme scores in every pass/fail assessment.
Weather Forecasting: Removing Extreme Temperatures
Taleb contrasts a casual average for vacation planning with an analysis of cumulative ice melting. The second question requires attention to extreme temperatures that may have disproportionately large effects.
Climate Science: Ignoring Temperature Spikes
Taleb claims that early climate researchers overlooked temperature spikes and their contribution to cumulative melting. The excerpt uses that historical claim to illustrate his broader warning about ignoring large consequences.
A MOMENT TO REFLECT
Put it to work.
In what real-world decisions have you or your organization removed outliers? Could ignoring rare but impactful events have led to negative consequences?
How can you distinguish between situations where removing outliers is safe (frequency matters) and where it is dangerous (magnitude matters)?
Think of a case in finance or climate science where ignoring a rare event caused a major failure. What lessons can be applied to your field?
CONTINUE THE CONVERSATION
Source texts
- Fooled by Randomness The Hidden Role of Chance in the Markets and in Life (Nassim Nicholas Taleb)