How a Statistician Helped Save People from Floods and Stood Up to the Nazis


To help propagandize the usefulness of statistics for the regular public, I would like to dedicate some time every week to telling the stories of various people who made large impacts on our everyday lives through the use of statistics. I believe that common knowledge of these methods could enrich or empower citizens to be more active in their communities and also reason more rationally about the notion of risk. This post is going to be about E.J. Gumbel, who was an important figure in the formation of statistics.

Elias Julius (E.J.) Gumbel began his career as a mathematical statistician shortly before World War I. Statistics at that time was roughly 20 years old and was still taking hold of the scientific community. During the Weimar era, many political, industrial and judicial figures were in the pocket of the nazi party, which at this point was still pretty much just a violent street gang that marauded the homes of political opposition and minorities. The old-guard was angry at the amount of power and prestige they had lost after the kaizer was removed, and thus wanted to use the militaristic, right wing doctrines of the nazis for their own gain.

E.J. Gumbel witnessed the cold-blooded murder of a close friend by a gang of nazis in broad daylight and attended a trial in which the judge did not even consider any evidence against the brownshirts who committed the murder and set them free. In response to this Gumbel used his skills as a statistician to begin an investigation into the wider judicial system and the political murders of the nazis, which led to the publication of Four Years of Political Murder in 1922. After releasing more anti-nazi publications and evidence, he quickly became one of the most hated german intellectuals among the nazi party and their sympathizers.

Bookshops would refuse to put Gumbel’s books on their shelves for fear of being targeted by the brownshirts. Gumbel was finally forced out of his university by nazi sympathizers in 1932 and went on to teach in France and then in the United States. It was in the United States where he would embark on furthering a vital and underappreciated topic in statistics: extreme value theory.

The Problem of Floods

The origin of extreme value theory comes from the study of floods. Flood control is interested in protection against inundations. An inundation happens when water flows where it shouldn’t. Consider a water station along a river that computes the mean daily discharge through a given area, measured in cubic feet per second. Out of the 365 days of measurement per year, the day with the greatest discharge is called the annual flood (and it may occur across multiple days as well). Every waterway has an annual flood, but these floods need not lead to inundations, which is what people really care about. The purely empirical hydrological analyses of the engineers simply didn’t work well because the engineers of the time didn’t realize that they shouldn’t be analyzing the discharges themselves, but instead the distribution of discharges. We need to scientifically model what could happen and measure that risk, not what has already happened. The historical data is simply used as a means to determine the character of the distribution and the relevant statistics. However big floods get, there will always be a bigger one coming. Engineers need to be able to think about the flood situation decades in advance.

E.J. Gumbel derived what is now known as the Gumbel Distribution, which is a cornerstone of flood frequency analysis that helps us better model the maxima and minima of a number of samples from many distributions.

Here is a basic introduction to flood frequency analysis to explain the core concepts.

Here is an approachable Microsoft Excel tutorial on flood frequency analysis using the Gumbel distribution for those who are curious to learn more.

Extreme value theory can be applied across any discipline you can imagine in several use cases, so it is worth checking to see if you yourself can apply this idea to an extreme value problem in your own life.


Kevin, thanks for this, but now I have another book on my reading list. Along with to 100’s of others.

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Nice post and I hope you keep it up. Oh my, the “could” word is huge in the quoted segment. I fear it is more wishful thinking than reality that very many “citizens” care two hoots about much that goes against their opinion.

All this brings to mind the time a BOD member commented on being surprised by some DMS data and proceeded to ask if “anecdotal evidence” could be found to counter it. SMH.


Yeah. “Could” is big. I mean – I’m smart and I read. However, I’m more into “feel good” fiction. It’s a big effort to research my votes, much less do any research-style reading.

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Great post. If I could put in a vote on the next one, I’d request Hedy Lamarr or Philo Farnsworth. Even though they’re not statisticians they both made huge contributions to our modern day lives.

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I think this cynicism is typical, but unjustified.

I’d like to argue two points:

  1. Everything is simply a matter of good salesmanship and patience.
  2. The goal should be to propagate methods and habits rather than relaying facts.

For the first point, I’d like to call attention to @dryad2b’s statement that she is more into “feel good” fiction. While this is true, it is important to remember that this is because “feel good” fiction has a target audience and a set of goals related to that target audience which, in the case of a sound story, guides the design process when it comes to world-building, character development and so forth. For example, it makes no sense for there to be humans in star wars, yet they exist precisely so the audience can relate to the characters.

Math, math education, scientific research and so forth are no different from this in principle. Those works have target audiences and goals related to that target audience that guides their design process and writing style. @bertberaht I would ask you to consider who truly does not give two hoots. Is it really the many citizens or is it the few citizens, the scholars and policymakers, who mostly only write for each other? They care about the discipline and furthering their field, but most have absolutely no incentive or desire to make their field accessible to the public by simplifying concepts, definitions, examples and so forth. As jobs start to become more cerebral and manual labor is being increasingly automated, we are seeing more and more attempts to create tutorials and simpler online courses for harder material, but they rarely address the more fundamental issue of whether the very conceptual structure of their discipline is needlessly complex and abstract in a manner that is hostile to outsiders.

@bertberaht 600 years ago the royalty would’ve said about teaching the peasantry to read what you are saying about the “many” citizens. I think it far bolder to place a cynical limitation on humanity’s capability than it is to excite them and incentivize them to go further. It is my belief that statistics and scientific methodology, like reading, can enrich all parts of our life, not merely the academic and the political.

Now I am not chiefly interested in promoting the facts of statistics or the facts of physics or the facts of this or that science. What I am interested in promoting is the method of statistics, the method of physics and the methods of many sciences since they can usually be generalized to problems all around us in our personal and professional lives. The pranks of Los Alamos by the physicists there who used their method of thinking about mechanisms and probability to, say, figure out how to pick-lock every top secret cabinet in the building to fuck with the head of the laboratory are a testament to the playfulness and enriched experience that knowledge of method can bring.

No one taught Feynman the fact of how to pick those cabinets; it was his mindset and his desire to engage with the world in his immediate proximity that led him to methodically experiment and discover how to mess with his boss.

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You obviously don’t know me to leap to the conclusions you drew from my post. I have been a life-long advocate for valid data, properly analyzed as well as a proponent of the scientific method of investigating all manners of things. I assume you are a few decades younger than I am and I vaguely recall having similar optimism that when nudged properly, people would strive to objectively look at their prior conclusions and revise as necessary. You probably are comfortable changing your mind about something when presented with new data or perspective and see it not as a prior failure, but a lesson learned.

All I can say is good luck on your mission. I have been beaten down by the realization that pundits of old nailed it when they concluded that it is easier to fool an entire crowd than it is to get an individual to admit they were fooled. If the “QAnon”, “Covid is a hoax”, “Italian satellites changed votes on the air gapped voting machine” crowds haven’t given you data about the enormity of the challenge … you might want to come up for air. As for a parallel between royalty not teaching peasants … that’s the opposite of me. I suggest you would find a more likely parallel looking at the “news” opinion hosts who want listeners to accept their BS without question.

All that to say I hope you and others like you will take up the yoke and continue the war on illiteracy on many fronts. I suspect there will be many lost battles along the way, but also hope there is a point somewhere, sometime when the pendulum stops and begins to head back toward a more sane place.