Friday, December 31, 2021

COVID and the base rate fallacy

COVID and the base rate fallacy

Should we be concerned that vaccinated people are getting COVID?

I’ve spoken to people who’re worried that the COVID vaccines aren’t effective because some vaccinated people catch COVID and are hospitalized. Let’s look at the claim and see if it stands up to analysis.

Let's start with some facts:

Marc Rummy’s diagram

Marc Rummy created this diagram to explain what’s going on with COVID hospitalizations. He’s made it free to share, which is fantastic.

In this diagram, the majority of the population is vaccinated (91%). The hospitalization rate for the unvaccinated is 50% but for the vaccinated, it’s 10%. If the total population is 110, this leads to 5 unvaccinated people hospitalized and 10 vaccinated people hospitalized - in other words, 2/3 of those in hospital with COVID have been vaccinated. 

Explaining the result

Let’s imagine we just looked at hospitalizations: 5 unvaccinated and 10 vaccinated. This makes it look like vaccinations aren’t working – after all, the majority of people in hospital are vaccinated. You can almost hear ignorant journalists writing their headlines now (“Questions were raised about vaccine effectiveness when the health minister revealed the majority of patients hospitalized had been vaccinated.”). But you can also see anti-vaxxers seizing on these numbers to try and make a point about not getting vaccinated.

The reason why the numbers are the way they are is because the great majority of people are vaccinated

Let’s look at three different scenarios with the same population of 110 people and the same hospitalization rates for vaccinated and unvaccinated:

  • 0% vaccinated – 55 people hospitalized
  • 91% vaccinated – 15 people hospitalized
  • 100% vaccinated – 11 people hospitalized

Clearly, vaccinations reduce the number of hospitalizations. The anti-vaccine argument seems to be, if it doesn't reduce the risk to zero, it doesn't work - which is a strikingly weak and ignorant argument.

In this example, vaccination doesn’t reduce the risk of infection to zero, it reduces it by a factor of 5. In the real world, vaccination reduces the risk of infection by 5x and the risk of death due to COVID by 13x ( The majority of people hospitalized now appear to be unvaccinated even though vaccination rates are only just above 60% in most countries (,

The bottom line is very simple: if you want to reduce your risk of hospitalization and protect your family and community, get vaccinated.

The base rate fallacy

The mistake the anti-vaxxers and some journalists are making is a very common one, it’s called the base rate fallacy ( There are lots of definitions online, so I’ll just attempt a summary here: “the base rate fallacy is where someone draws an incorrect conclusion because they didn’t take into account the base rate in the general population. It’s especially a problem for conditional probability problems.”

Let’s use another example from a previous blog post:

“Imagine there's a town of 10,000 people. 1% of the town's population has a disease. Fortunately, there's a very good test for the disease:

  • If you have the disease, the test will give a positive result 99% of the time (sensitivity).
  • If you don't have the disease, the test will give a negative result 99% of the time (specificity).

You go into the clinic one day and take the test. You get a positive result. What's the probability you have the disease?” 

The answer is 50%.

The reason why the answer is 50% and not 99% is because 99% of the town’s population does not have the disease (the base rate), which means half of the positives will be false positives.

What’s to be done?

Conditional probability (for example, the COVID hospitalization data) is screwy and can sometimes seem counter to common sense. The general level of statistical (and probability) knowledge in the population is poor. This leaves people trying to make sense of the data around them but without the tools to do it, so no wonder they’re confused.

It’s probably time that all schoolchildren are taught some basic statistics. This should include some counter-intuitive results (for example, the disease example above). Even if very few schoolchildren grow up to analyze data, it would be beneficial for society if more people understood that interpreting data can be hard and that sometimes surprising results occur – but that doesn’t make them suspicious or wrong.

More importantly, journalists need to do a much better job of telling the truth and explaining the data instead of chasing cheap clicks.

Monday, November 29, 2021

What's a violin plot and how to make one?

What's a violin plot?

Over the last few years, violin plots and their derivatives have become a lot more common; they're a 'sort of' smoothed histogram. In this blog post, I'm going to explain what they are and why you might use them.

To give you an idea of what they look like, here's a violin plot of attendance at English Premier League (EPL) matches during the 2018-2019 season. The width of the plot indicates the relative proportion of matches with that attendance; we can see attendance peaks around 27,000, 55,000, and 75,000, but no matches had zero attendance. 

Violin plots get their name because they sort of resemble a violin (you'll have to allow some creative license here).

As we'll see, violin plots avoid the problems of box and whisker plots and the problems of histograms. The cost is greatly increased computation time, but for a modern computer system, violin plots are calculated and plotted in the blink of an eye. Despite their advantages, the computational cost is why these plots have only recently become popular.

Summary statistics - the mean etc.

We can use summary statistics to give a numerical summary of the data. The most obvious statistics are the mean and standard deviation, which are 38,181 and 16,709 respectively for the EPL 2018 attendance data. But the mean can be distorted by outliers and the standard deviation implies a symmetrical distribution. These statistics don't give us any insight into how attendance was distributed.

The median is a better measure of central tendency in the presence of outliers, and quartiles work fine for asymmetric distributions. For this data, the median is 31,948 and the upper and lower quartiles are 25,034 and 53,283. Note the median is a good deal lower than the mean and the upper and lower quartiles are not evenly spaced, suggesting a skewed distribution. The quartiles give us an indication of how skewed the data is.

So we should be just fine with median and quartiles - or are there problems with these numbers too?

Box and whisker plots

Box and whisker plots were introduced by Tukey in the early 1970s and evolved since then, currently, there are several slight variations. Here's a box and whisker plot for the EPL data for four seasons in the most common format; the median, upper and lower quartiles, and the lowest and highest values are all indicated. We have a nice visual representation of our distribution.

The box and whisker plot encodes a lot of data and strongly indicates if the distribution is skewed. Surely this is good enough?

The problem with boxplots

Unfortunately, box and whisker plots can hide important features of the data. This article from Autodesk Research gives a great example of the problems. I've copied one of their key figures here.

("Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated Annealing", Justin Matejka, George Fitzmaurice, ACM SIGCHI Conference on Human Factors in Computing Systems, 2017)

The animation shows the problem nicely; different distributions can give the same box and whisker plots. This doesn't matter most of the time, but when it does matter, it can matter a lot, and of course, the problem is hidden.

Histograms and distributions

If boxplots don't work, what about histograms? Surely they won't suffer from the same problem? It's true they don't, but they suffer from another problem; bin count, meaning the number of bins.

Let's look at the EPL data again, this time as a histogram.

Here's the histogram with a bin count of 9.

Here it is with a bin count of 37.

And finally, with a bin count of 80.

Which of these bin counts is better? The answer is, it depends on what you want to show. In some cases, you want a large number of bins, in other cases, a small number of bins. As you can appreciate, this isn't helpful, especially if you're at the start of your career and you don't have a lot of experience to call on. Even later in your career, it's not helpful when you need to move quickly.

An evolution of the standard histogram is using unequal bin sizes. Under some circumstances, this gives a better representation of the distribution, but it adds another layer of complexity; what should the bin sizes be? The answer again is, it depends on what you want to do and your experience.

Can we do better?

Enter the violin plot

The violin plot does away with bin counts by using probability density instead. It's a plot of the probability density function (pdf) that could have given rise to the measured data. 

In a handful of cases, we could estimate the pdf using parametric means when the underlying data follows a well-known distribution. Unfortunately, in most real-world cases, we don't know what distribution the data follows, so we have to use a non-parametric method, the most popular being kernel density estimation (kde). This is almost always done using a Gaussian estimator, though other estimators are possible (in my experience, the Gaussian calculation gives the best result anyway, but see this discussion on StackOverflow). The key parameter is the bandwidth, though most kde algorithms attempt to size their bandwidth automatically. From the kde, the probability density is calculated (a trivial calculation).

Here's the violin plot for the EPL 2018 data.

It turns out, violin plots don't have the problems of box plots as you can see from this animation from Autodesk Research. The raw data changes, the box plot doesn't, but the violin plot changes dramatically. This is because all of the data is represented in the violin plot.

("Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated Annealing", Justin Matejka, George Fitzmaurice, ACM SIGCHI Conference on Human Factors in Computing Systems, 2017)

Variations on a theme, types of violin plot, ridgeline plots, and mirror density plots

The original form of the violin plot included median and quartile data and you often see violin plots presented like this - a kind of hybrid of violin and box and whisker. This is how the Seaborn plotting package draws Violin plots (though this chart isn't a Seaborn visualization).

Now, let's say we want to compare the EPL attendance data over several years. One way of doing it is to show violin plots next to each other, like this.

Another way is to show two plots back-to-back, like this. This presentation is often called a mirror density plot.

We can show the results from multiple seasons with another form of violin plot called the ridgeline plot. In this form of plot, the charts are deliberately overlapped, letting you compare the shape of the distributions better. They're called ridgeline plots because they sort of look like a mountain ridgeline.

This plot shows the most obvious feature of the data, the 2019-2020 season was very different from the seasons that went before; a substantial number of matches were held with zero attendees.

When should you use violin plots?

If you need to summarize a distribution and represent all of the data, a violin plot is a good choice. Depending on what you're trying to do, it may be a better choice than a histogram and it's always a better choice than box and whisker plots.

Aesthetically, a violin plot or one of its variations is very appealing. You shouldn't underestimate the importance of clear communication and visual appeal. If you think your results are important, surely you should present them in the best way possible - and that may well be a violin plot.

Reading more

"Statistical computing and graphics, violin plots: a box plot-density trace synergism", Jerry Hintze, Ray Nelson, American Statistical Association, 1998. This paper from Hintze and Nelson is one of the earlier papers to describe violin plots and how they're defined, it goes into some detail on the process for creating them. 

"Violin plots explained" is a great blog post that provides a nice explanation of how violin plots work.

"Violin Plots 101: Visualizing Distribution and Probability Density" is another good blog post proving some explanation on how to build violin plots.

Monday, November 22, 2021

Mouse jiggling: the good, the bad, and the ugly

What's a mouse jiggler?

Recently, I was reading Hacker News and one of the contributors mentioned a mouse jiggler. I'd never heard of one before, so I searched around. I was both horrified and fascinated by what I discovered.

A mouse jiggler is a device that randomly 'jiggles' your mouse so it appears that you're at your computer. It prevents the screen saver from kicking in and it keeps your status as active in Slack and Zoom. Here's a picture of one type of mouse jiggler.

(Jamsim1975, CC BY-SA 4.0, via Wikimedia Commons)

The good

As it turns out, mouse jigglers are used by law enforcement during raids. One of the agents is tasked with getting to the suspect's computer quickly and setting up the mouse jiggler. The goal is to stop the computer from locking up; if that happens the suspect has to provide their password or a court has to order them to do so. Far better to stop the computer from locking up in the first place.

In the old days, the FBI and other agencies used software mouse jigglers; the mouse motion was set by software installed on a USB stick. Mechanical mouse jigglers are better because they don't rely on the availability of USB ports and they don't rely on security settings on the suspect's computer (not all systems will allow software to be installed via USB).

This blog post has some interesting things to say about mouse jigglers and other software/hardware used during raids.

The bad

There's a reason why security teams have computers lock themselves after a few minutes of user inactivity and the reason is security. Leaving a computer unattended and unlocked is bad, leaving a computer unattended and unlocked with a mouse jiggler over extended periods is even worse. If I were a CISO, I would ban mouse jigglers - or better still, make sure that no one feels the need to use one.

The ugly

For everyone who's not law enforcement, why would you want a jiggler? The sad answer seems to be fooling employee surveillance software. Instead of trusting their employees or measuring by results, some companies have installed surveillance software that tracks mouse usage (mouse use = work). Jigglers are an attempt to circumvent these kinds of trackers.

Jigglers have been around for a while and now there's software to detect them; you too can detect if your employees are jiggling. In response, some of the newer jigglers offer random and subtle jiggles that are harder to detect. I can see a jiggling arms race coming.

The reviews for this jiggler on Amazon are enlightening; there are 2,612 of them, an astonishing number, and the product has a 5-star rating overall. Many of the reviews mention fooling IT surveillance software. If you don't like this one, there are plenty of other models to choose from, many with over 1,000 reviews. 

Think about what this says. There are enough people who're concerned about surveillance to spawn a mini-industry for $30 devices. These devices add no value - it's not like a mouse or a keyboard or a camera. As one of the reviewers said, the jiggler lets them go to the bathroom without feeling like it's being noted. It's all about trust, or the lack of it.

If people are using mouse jigglers at your company, it's an indication that something has gone quite wrong.

Wednesday, November 17, 2021

Ice ice baby

Is this the coolest/most Canadian data set ever?

Late last year, I was studying for a machine learning course and I was looking for a data set I could use for the course capstone project. I settled on English Premier League data, but not before I had a serious look at what's probably the coolest (and most Canadian) dataset I've ever seen.

(cogdogblog, CC BY 2.0, via Wikimedia Commons)

The icicle atlas

The University of Toronto Physics Department has a large dataset on icicles created as part of a research project to understand the factors important for icicle formation, size, and shape. Under laboratory conditions, they grew 237 icicles, capturing movies and images of their growth. 

As part of the growth process, they varied speed, salinity, and water source, obviously having a little fun with their choice of water sources as you'll see in the atlas. As it turns out, the ridges that sometimes form in icicles are due to impurities in the water (maybe all of us need impurities to be interesting😉).

All the images, movies, and data are covered by a creative commons license. You can see all their icicle data on their icicle atlas page - the related links at the bottom of the page are fantastic.

Icicle pictures

You can view the rogues' gallery of icicle pictures here. Here are some pictures of my favorite icicles from the gallery.

(University of Toronto Physics Department, Icicle Atlas, Creative Commons License.)

Icicle movies

You can see videos of how most of the icicles formed. It's kind of interesting and restful to watch - the opposite of watching a fire burning, but still hypnotic and engaging. Here's a video that I found restful.

(University of Toronto Phyics Department, Icicle AtlasCreative Commons License.)

If you want more, there's a YouTube channel of the movies from the atlas.

Ice Ice baby

This winter, I'm going to see icicles form on my gutters. I've seen some weird formations over the years, and now I know that temperature, wind, and water purity govern the size and shape of icicles. It's nice to know that we can still take time to understand the processes that form the world around us.

Even though I better understand how icicles form, I know they can damage my gutters and house. Pretty as they are, I'm still going to smash them away.

Monday, November 8, 2021

Football crazy: predicting Premier League football match results

I can get a qualification and be rich!

A long time ago, I was part of a gambling syndicate. A friend of mine had some software that predicted the results of English football (soccer) matches and at the time, betting companies offered fixed-price odds for certain types of bets. My friend noticed his software predicted 3-2 away wins more often than the betting company's odds would suggest. Over the course of a season, we had a 20% return on our gambling investment. 

During the COVID lockdown, I took the opportunity to learn R and did a long course that included a capstone project. I decided to see if I could forecast English Premier League (EPL) matches. If I succeeded, I could get a qualification and get rich too! What's not to like? Here's the story of what I did and what happened.

Premier League data

There's an eighteenth-century recipe for a hare dish that supposedly includes the instructions "First, catch your hare." The first step in any project like this is getting your data.

I got match results going back to the start of the league (1993) from football-data. The early data is only match results, but later data includes red cards and some other measurements.

TransferMarkt has data on transfer fees, foreign-born players, and team age, but the data's only available from 2011.

At the time of the project, I couldn't find any other free data sources. There were and are paid-for sources, but they were way beyond what I was willing to pay.

I knew going into the next phase of the project that this wasn't a very big data set with not that many fields. As it turned out, data was a severely limiting factor.

What factors are important?

I had a set of initial hypotheses for factors that might be important for final match scores, here are most of them:

  • team cost - more expensive teams should win more games
  • team age - younger teams perform better
  • prior points - teams with more points win against teams with fewer points
  • foreign-born players - the more non-English players on the team, the more the team will win
  • previous match results - successful (winning) teams win more matches
  • home-field advantage
  • disciplinary record - red and yellow card history might be an indicator of risk-taking
  • season effects - as the season wears on, teams take more risks to win matches

I found evidence that most of these did in fact have an impact.

Here's strong evidence of home-field advantage. Note how it goes away during the 2020-2021 season when matches were played without fans.

Here's goal difference vs. team cost difference. The more expensive team tends to win.

Here's goal difference vs. mean prior goal difference. Teams that scored more goals before tend to score more goals in their current match.

I found more relationships you can read about if you're interested.

Machine learning

Thinking back to my gambling syndicate, I decided to forecast the score of each match rather than just win/lose/draw. My loss function was the RMSE of the goal difference between the predicted score and the actual score. To avoid COVID oddities, I removed the 2020-2021 season (the price being a smaller data set). Of course, I used a training and holdout dataset and cross-validation. 

The obvious question is, which model machine learning models work? I decided to try a whole bunch of them:

  • Naive mean score model. A simple model that’s just the mean scores of the (training) data set.
  • Generalized Linear Model. A form of ordinary linear regression.
  • Glmnet. Fits lasso and elastic-net regularized generalized linear models.
  • SVM. Support Vector Machines - boundary-based regression. After some experimentation, I selected the svmRadial form of SVM, which uses a non-linear kernel function.
  • KNN. K-nearest neighbors. Given that EPL scores are all in close proximity to one another, we might expect this model to return good results.
  • Neural nets.
  • XGB Linear. This is linear modeling with extreme gradient boosting. Extreme gradient boosting has gathered a lot of attention over the last few years and may be one of the most used machine learning models today.
  • XGB Tree. This is a decision tree model with extreme gradient boosting.
  • Random Forest.

The model results weren't great. For the KNN model, here's how the RMSE for full-time away goals varied with n.

Note the RMSE scale - the lowest it goes to is 1.1 goals and it's plain that adding more n will only take us a little closer to 1.1. Bear in mind, football is a low-scoring game, and being off by 1 goal is a big miss.

It was the same story for random forest.

In fact, it was the same story for all of the models. Here are my final results. My model forecast home goals and away goals.

The naive means model is the simplest and all my sophisticated models could do is give me a few percentage points improvement.

Improving the results

Perhaps the most obvious way forward is combining models to improve RMSE. I'm reluctant to do that until I can get better individual model results. There's a philosophical issue at play; for me, the ensemble approach feels a bit "spray and pray".

In my view, data shortage is the main problem:

  • My data set was only in the low thousands of matches. 
  • Some teams join the Premier League for just a season and then get relegated - I don't model their history prior to joining the league. 
  • I removed the COVID season of 2020-2021. 
  • I only had team value and disciplinary data for ten or so seasons. 
  • Of course, I only modeled the Premier League.

Football is a low-scoring game, famous for its upsets. It may well be that it's just too random underneath to make useful predictions at the individual match level. 

What's next?

I wasn't able to predict EPL results with any great accuracy, but I submitted my report and got my grade. If you want to read my report, you can read it here.

At the end of the 2021 season, I saw some papers published on the COVID effect on match results. I had similar results months before. Perhaps I should have submitted a paper myself.

At some point, I might revive this project if I can get new data. I still occasionally hunt for new data sources, but sadly, I haven't found any. My dreams of retiring to a yacht on the Mediterranean will have to wait.

Monday, November 1, 2021

Why conditional probability screwiness matters for business

Things are not what they seem

Many business decisions come down to common sense or relatively simple math. But applying common sense to conditional probability problems can lead to very wrong results as we'll see. As data science becomes more and more important for business, decisions involving conditional probability will arise more often. In this blog post, I'm going to talk through some counter-intuitive conditional probability examples and where I can, I'll tell you how they arise in a business context.

(These two pieces of track are the same size. Ag2gaeh, CC BY-SA 4.0, via Wikimedia Commons.)

Testing for diseases

This is the problem with the clearest links to business. I'll explain the classical form of the problem and show you how it can come up in a business context.

Imagine there's some disease affecting a small fraction of the population, say 1%. A university develops a great test for the disease:

  • If you have the disease, the test will give you a positive result 99% of the time. 
  • If you don't have the disease, the test will give you a negative result 99% of the time.

You take the test and it comes back positive. What's the probability you have the disease? 

(COVID test kit. Centers for Disease Control and Prevention, Public domain, via Wikimedia Commons)

The answer is 50%.

If you want an explanation of the 50% number, read the section "The math", if you want to know how it comes up in business, skip to the section "How it comes up in business".

The math

What's driving the result is the low prevalence of the disease (1%). 99% of the people who take the test will be uninfected and it's this that pushes down the probability of having the disease if you test positive. 

There are at least two ways of analyzing this problem, one is using a tree diagram and one is using Bayes' Theorem. In a previous blog post, I went through the math in detail, so I'll just summarize the simpler explanation using a tree diagram. To make it easier to understand, I'll assume a population of 10,000.

Of the 10,000 people, 100 have the disease, and 9,900 do not. Of the 100, 99 will test positive for the disease. Of the 9,900, 99 will test positive for the disease. In total 99 + 99 will test positive, of which only 99 will have the disease. So 50% of those who test positive will have the disease.

How it comes up in business

Instead of disease tests, let's think of websites and algorithms. Imagine you're the CEO of a web-based business. 1% of the visitors to your website become customers. You want to identify who'll become a customer, so you task your data science team with developing an algorithm based on users' web behavior. You tell them the test is to distinguish customers from non-customers.

They come back with a complex test for customers that's 99% true for existing customers and 99% false for non-customers. Do you have a test that can predict who will become a customer and who won't?

This is the same problem as before, if the test is positive for a user, there's only a 50% chance they'll become a customer.

How many daughters?

This is a classic problem and shows the importance of describing a problem exactly. Exactly, in this case, means using very very precise English.

Here's the problem in its original form from Martin Gardner:

  1. Mr. Jones has two children. The older child is a girl. What is the probability that both children are girls?
  2. Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?
(What's the probability of two girls? Circle of Robert Peake the elder, Public domain, via Wikimedia Commons)

The solution to the first problem is simple. Assuming boys or girls are equally likely, then it's 50%.

The second problem isn't simple and has generated a great deal of debate, even 60 years after Martin Gardner published the puzzle. Depending on how you read the question, the answer is either 50% or 33%. Here's Khovanova's explanation:

"(i) Pick all the families with two children, one of which is a boy. If Mr. Smith is chosen randomly from this list, then the answer is 1/3.

(ii) Pick a random family with two children; suppose the father is Mr. Smith. Then if the family has two boys, Mr. Smith says, “At least one of them is a boy.” If he has two girls, he says, “At least one of them is a girl.” If he has a boy and a girl he flips a coin to say one or another of those two sentences. In this case, the probability that both children are the same sex is 1/2."

In fact, there are several other possible interpretations.

What does this mean for business? Some things that sound simple aren't and differences in the precise way a problem is formulated can give wildly different answers.

Airline seating

Here's the problem stated from an MIT handout:

"There are 100 passengers about to board a plane with 100 seats. Each passenger is assigned a distinct seat on the plane. The first passenger who boards has forgotten his seat number and sits in a randomly selected seat on the plane. Each passenger who boards after him either sits in his or her assigned seat if it is empty or sits in a randomly selected seat from the unoccupied seats. What is the probability that the last passenger to board the plane sits in her assigned seat?"

You can imagine a lot of seat confusion, so it seems natural to assume that the probability of the final passenger sitting in her assigned seat is tiny. 

(Ken Iwelumo (GFDL 1.2, GFDL 1.2 or GFDL 1.2), via Wikimedia Commons)

Actually, the probability of her sitting in her assigned seat is 50%.

StackOverflow has a long discussion on the solution to the problem that I won't repeat here.

What does this mean for business? It's yet another example of our intuition letting us down.

The Monty Hall problem 

This is the most famous of all conditional probability problems and I've written about it before. Here's the problem as posed by Vos Savant:

"A quiz show host shows a contestant three doors. Behind two of them is a goat and behind one of them is a car. The goal is to win the car.

The host asked the contestant to choose a door, but not open it.

Once the contestant has chosen a door, the host opens one of the other doors and shows the contestant a goat. The contestant now knows that there’s a goat behind that door, but he or she doesn’t know which of the other two doors the car’s behind.

Here’s the key question: the host asks the contestant "do you want to change doors?".

Once the contestant decided whether to switch or not, the host opens the contestant's chosen door and the contestant wins the car or a goat.

Should the contestant change doors when asked by the host? Why?"

Here are the results.

  • If the contestant sticks with their initial choice, they have a ⅓ chance of winning.
  • If the contestant changes doors, they have a ⅔ chance of winning.
I go through the math in these two previous blog posts "The Monty Hall Problem" and "Am I diseased? An introduction to Bayes theorem".

Once again, this shows how counter-intuitive probability questions can be.

What should your takeaway be, what can you do?

Probability is a complex area and common sense can lead you wildly astray. Even problems that sound simple can be very hard. Things are made worse by ambiguity; what seems a reasonable problem description in English might actually be open to several possible interpretations which give very different answers.

(Sound judgment is needed when dealing with probability. You need to think like a judge, but you don't have to dress like one. InfoGibraltar, CC BY 2.0, via Wikimedia Commons)

If you do have a background in probability theory, it doesn't hurt to remind yourself occasionally of its weirder aspects. Recreational puzzles like the daughters' problem are a good refresher.

If you don't have a background in probability theory, you need to realize you're liable to make errors of judgment with potentially serious business consequences. It's important to listen to technical advice. If you don't understand the advice, you have three choices: get other advisors, get someone who can translate, or hand the decision to someone who does understand. 

Sunday, October 3, 2021

Battle leadership: some lessons for managers from World War I

Battle leadership

Books on military leadership and management have been popular in the business world for a long time. "The art of war" is a best-seller 2,500 or so years after it was written and books authored by US military leaders have consistently sold well. To state the obvious, business is not war and companies are not armies, but given this, there are still lessons military leaders have to offer; the art is picking out what applies and what doesn't.

I recently stumbled across an old military leadership book dating back to World War I. Although the world has changed greatly since then, I found some of the ideas and discussions still relevant to today's business environments. Read on to find out more.

(The book and a German soldier in World War I. Internet Archive Book Images, No restrictions, via Wikimedia Commons.)

The book and its history

The book is "Battlefield Leadership" and was first published in 1933 in the US. The author was Adolph von Schell (1893-1967), an officer in the German army in the First World War. He led troops in the European theater during the war, winning a number of medals and commendations [,_1893)]. After the war, he trained at the US Army's Fort Benning where he was asked to speak about his experiences leading men in combat. His talks became the book, "Battlefield Leadership" which was published in English (strangely, the German translation was published much later).

The book is an odd mix of psychology, management, and battlefield stories, not all of which are relevant to the world of business. Plainly, warfare has moved on a lot since the First World War; tactics and strategy have changed greatly, but what hasn't changed are some of the core ideas of people management, as we shall see.

Core ideas

Battlefield psychology

Schell states that in "modern" warfare, people fight in small groups, often as individuals, against an enemy they can't see. Therefore, commanders need to know how individuals are likely to react and how they can be influenced. A unit may well have soldiers from diverse backgrounds, so the commander has to have an appreciation of their culture. Similar lessons apply further up the command hierarchy; a general must know his subordinates and how to motivate them: "Furthermore, each one reacts differently at different times, and must be handled each time according to his particular reaction", Schell gives a crude example in the book, but despite the crudity, the underlying lesson is clear.

He has some valid points to make about the need for individuals to exert some measure of control over their situation. Soldiers that wait under hostile fire have time to think and become stressed because they can't change their situation; they lie waiting for bullets to hit them. Soldiers on patrol are more at risk, but their destiny is in their hands so they're willing to go out and take control of their situation. He talks about soldiers under fire moving their position to be more secure: "it makes no difference whether or not the security is real; it is simply a question of feeling that it is".

Men under fire need some measure of security. Schell gives examples of a commander who ordered his men to have haircuts while their position was being shelled. The point isn't the haircuts, the point is the sense of normality the haircutting process gave. Even though men died during the shelling, morale stayed high because the team had a sense of security.

Experience matters in many ways

In several places throughout the book, Schell gives examples of how experienced troops behave compared to troops that had not seen combat. He gives an example from the early days of the war when his company of inexperienced troops first crossed into Belgium; despite meeting no resistance, they shot at shadows in the forest and spent a restless first night afraid of an attack that never came. By contrast, later in the war, he led battle-hardened troops in Russia. Despite similar circumstances, they didn't shoot at shadows in the forest, instead, they posted two sentries and the rest of the company slept soundly, even though they were in enemy territory.

As a practical matter, he recommends mixing inexperienced and battle-hardened troops. He comments that even on a day-to-day basis, and away from battle, seasoned troops coach the inexperienced troops on what to do and how to behave. He similarly cautions against changing commanders, a commander has to get to know his troops, and wartime is not an ideal time to do it:
"If we give these inexperienced troops a backbone of experienced soldiers and experienced commanders their efficiency will be tremendously increased and they will be spared heavy losses."

False data and preparation

I'm going to quote two of his lessons verbatim:
"(1) At the commencement of war, soldiers of all grades are subject to a terrific nervous strain. Dangers are seen on every hand. Imagination runs riot. Therefore, teach your soldiers in peace what they may expect in war, for an event foreseen and prepared for will have little if any harmful effect.
(2) As leaders be careful both in sending and in receiving reports. At the commencement of a war, ninety percent of all reports are false or exaggerated."

Change the word "war" for "competitive situation" and you get something obviously relevant for business.

Orders based on incomplete information

Quite correctly, Schell points out that leaders have to make decisions based on partial information, and on information which is doubtful at best: 
"In open warfare a leader will have to give his orders without having complete information. At times only his own will is clear. If he waits for complete information before acting he will never make a decision."

Orders, improvisation, and maps

This is my favorite part of the book. It recalls an action where the Germans and Russians faced off against one another in Russian territory. The German commander received continual updates on the Russians' position and he changed his tactics in response to the new information. His commands to his men were clear, simple, and to the point. Here's his summary:
"This example shows clearly that difficult situations can be solved only by simple decisions and simple orders. The more difficult the situation the less time there will be to issue a long order, and the less time your men will have to understand it. Moreover, the men will be high-strung and tense. Only the simplest order can be executed under such conditions."

In the same action, the Germans were facing a larger Russian opponent. They needed to watch a Russian position but didn't have the troops to. A corporal solved the problem. There was a large herd of cows in a nearby village, so the Germans moved the cows to a field between them and the Russians. Whenever the Russians tried to advance across the field, they disturbed the cows, so alerting the Germans.

(Cows are free watchdogs. Jonas Eppler, CC BY-SA 4.0, via Wikimedia Commons)

Eventually, of course, superior numbers prevailed and the Germans had to retreat. The commander knew where to retreat to, but didn't have a map. Waiting for a map would have meant defeat, so based only on a rough knowledge of geography, they retreated, eventually joining up with other companies. The commander had to take a risk by retreating into unknown territory, but not retreating would have been more dangerous.

Mission orders

Notably, Schell discusses 'mission tactics' which are better known as 'mission orders' today. The idea is simple, commanders will achieve more if they can exert some control, so orders should focus on the mission and not on how it's to be executed. There's a sound operational reason too: "This is done because the commander on the ground is the only one who can correctly judge existing conditions and take the proper action if a change occurs in the situation". The relations to modern business are obvious: give senior people goals to achieve and give them the freedom to do it in whatever way they can. 

Some miscellaneous quotes

I found little nuggets of wisdom throughout the book, here are some I want to share:

  • "To leave the bulk of the artillery behind may strike the reader as dangerous but I believe the decision to do so was correct. The Germans were pursuing and almost anything can be dared where opposed to a beaten opponent. Everything had to be sacrificed to speed if the Russians were to be overtaken. In this situation legs were the important thing, not cannon."
  • "The importance of surprise in war cannot be overestimated. As it becomes increasingly difficult to obtain so does it become increasingly effective when it is obtained. No effort should be spared to make the decisive element of surprise work for us in war."
  • "There is only one opportunity to issue detailed orders and that is before battle. When the action has actually begun, orders must be short and simple."
  • "Every fight develops differently than is expected. Officers and troops must realize this in peace, in order that they will not lose courage when the unexpected occurs in war."

There's very little new in management

This book was first published in 1933 based on Schell's experience in war over the period 1915-1918.  There's more in this short book than I've seen in some much longer and more recent management books, and frankly, there's more of substance in this book than some highly-paid consultants I've worked with. Is this the only management book you should read? Absolutely not. Does it contain some interesting insights? Yes it does. 

The book was published in 1933 and the author died in 1967. It's not clear to me what the copyright situation is. You can buy a copy cheaply on Amazon, but you can also find free PDFs available online from legitimate sources.

Monday, August 16, 2021

The seven dysfunctionalities of management books

The problems with popular management books

Over the years, I've read many management books ranging from the excellent to the terrible. I've noticed several dysfunctionalities that creep into even some of the best books. I'm going to list them out in what I think is their order of importance. See what you think.

The seven dysfunctionalities

My idea is worth 30 pages, I'll write 300

With few exceptions, most books fall into this trap. The author could express their ideas in a few pages and provide supporting evidence that would fill a few pages more. Of course, the economics of books means they can't. There's no market and no money in a 30-page pamphlet (when was the last time you paid $20 for 30 pages?) but there's a huge market for books. The logic is clear: spin out your idea to book-length and make some money.

This is a little odd for two reasons:

  • Business writing emphasizes brevity and getting to the point quickly - neither of which management books usually do.
  • No one has disrupted the market. Maybe our business culture and market economics mean disruption is impossible?

What I say is important, I worked with important people at important companies

This is a relatively new dysfunction. The author claims their work is important, not because of its widespread adoption, or because many people had success with it, but because they held senior positions at well-known companies in Silicon Valley. Usually, these books have lots of stories of famous people, some of which offer insight and some of which don't. In a few cases, the storytelling degenerates into name-dropping.

My evidence will be stories or bad data

The plural of anecdote is not data. Why should I believe your experience generalizes to me? Storytelling is important, but it doesn't amount to a coherent management framework. According to the esteemed Karl Popper, science is about making falsifiable statements - what falsifiable statements do stories make?

The other form of dysfunctional evidence is bad data. The problems here are usually regression to the mean, small sample sizes, or a misunderstanding of statistics. There are examples of management gurus developing theories of winning companies but whose theories were proved wrong almost as soon as the ink was dry on their books. This might be why newer books focus on storytelling instead.

I'll write a worse sequel and then an even worse sequel to that

Even the best authors fall prey to this trap. They publish a best-selling book and the temptation is there to write a sequel. The second book is usually so-so, but might sell well. So they write a third book which is even worse, and so on.

I'll create new words for old ideas

Here the author rediscovers psychology or sociology that's been known for decades. Sometimes, they'll admit it and provide a new twist on old ideas; but sometimes it's just known ideas repackaged. In any case, the author usually creates a trendy buzzy phrase for their idea, preferably one they can trademark for their consultancy practice.

I'll talk about my time in the military

The military does have some very interesting things to teach managers. Unfortunately, most of the military books for business management focus on events without providing much in the way of context for what happened and why. When they explain how it can be used in a civilian setting, it feels clunky and unconvincing. These military books also tend to focus on successes and brush over failures (if they mention any at all). This is sad because I've read some really great older military management books that have something to offer today's managers.

I'll push my consulting company

This is the original sin and the cause of many of the other sins. After the success of their book, the author forms a consultancy company. They create a 2nd edition that includes cherry-picked success stories from their consulting company, or maybe they write a second book with anecdotes from their consulting work. The book then becomes a 'subtle' promo for their consulting work.

Don't throw the baby out with the bathwater

I'm not saying that popular business management books have no value, I'm saying very few of them will have value in ten years' time when the hype has passed. Think back to the business books published ten or twenty years ago. How many stand up now? 

Despite the faddish nature of the genre, most business management books have the core of some good ideas, you just have to wade through the nonsense to get there.

What should you do?

Every manager needs a framework for decision-making. My suggestion is to get that framework from training and courses and not popular business books. Use quotes to get some extra insight. Management business books are useful for a refresher of core ideas, even if you have to wade through 300 pages instead of 30. If nothing else, the popular books are a handy guide to what your peers are reading now.

Monday, August 9, 2021

Criminal innovations: narco-subs

How do you transport lots of drugs internationally without getting caught?

The United States is one of the world's largest consumers of illegal drugs but the majority of the illegal drugs it consumes are manufactured in South America. Illegal drug producers need to transport their product northwards at the lowest price while evading detection. They've tried flying, but radar and aircraft have proved effective at stopping them, and they've tried boats, but coastguard patrols and radar have again stopped them. If you can't go over the water, and you can't go on the water, then how about going under the water? Drug cartels have turned to submarines and their variants for stealthy transportation. These submarines go by the generic name of narco-subs. As we'll see, it's not just the South Americans who are building submarines for illegal activities.

South American narco-subs

The experts on transporting drugs long distances by sea are the South American drug cartels; they've shown an amazing amount of innovative thinking over the years. Currently, they're using three main types of craft: low-profile vessels, submarines, and torpedoes. Low-profile vessels and submarines typically have small crews of 2-4 people, while torpedoes are uncrewed.

Low-profile vessels (LPVs)

To avoid radar and spotter planes, the cartels have turned to stealth technology; they've designed boats that have a very low radar cross-section with the smallest possible above-the-sea structures. 

(A low-profile vessel that was intercepted. Image source: US Customs and Border Protection.)
(Another low-profile vessel. Image source: US Customs and Border Protection.)

These vessels originally started as variations on existing commercial speedboats, with modifications to make them run lower in the water. Now, they're custom designs, typically long and thin, designed to pierce waves rather than ride over them. A typical newer LPV might be 3m wide by 30m long - quite a long vessel, but very narrow. H.I. Sutton describes several types of LPV in his Forbes article.


There are various types of narco-subs, ranging from semi-submersibles to full-on submarines.

Semi-submersibles ride just below the surface, typically at snorkel depth. This image of a 2019 semi-submersible captured off Peru gives you the general idea.

(Semi-submersible narco-sub, Peru, 2019. Image source: Wikimedia Commons.)

The vessel is plainly based on a 'standard' boat and is designed to run just under the water. The very few above-surface structures make the vessel hard to spot with radar, or even from the air.

The Peruvian vessel is plainly a modified boat, but custom-built vessels exist, here's an image of one custom semi-submersible used by Columbian drug smugglers just before its capture in 2007. The blue paint job is camouflage.

(Semi-submersible narco-sub caught in 2007. Image source: Wikimedia Commons.)

This September 2019 image shows USCG boarding a 12m semi-submersible in the eastern Pacific. It had a crew of 4 and was carrying $165mn in cocaine.

(Source: Navy Times)

The drug cartels have created true submarines capable of traveling under the water to depths of a few hundred feet. Some of these submarines have even reached the astonishing length of 22m, making them comparable to midget submarines used by the world's navies (see Covert Shores comparison). 

In 2010, this 22 m-long monster was discovered in the Ecuadorian jungle. NPR has a long segment on how it was found and what happened next. The sub is estimated to have a range of 6,800 nautical miles and a dive depth of 62 feet. These numbers aren't impressive by military standards but bear in mind, this sub is designed for stealth, not warfare.

(22m long, fully submersible narco-sub. Image source: Wikimedia Commons.)

This isn't even the largest sub found, Hannah Stone reports on one narco-sub with a length of 30m, a crew of 4, air conditioning, and a small kitchen!

In November 2019, a narco-sub was caught in Galicia in Spain. Although the design was nothing new, its origin was. Authorities believe it started its journey in Brazil, crossing the Atlantic ocean to get to Spain (Covert Shores). This vessel was a semi-submersible design.

Bear in mind, all these submarines were built surreptitiously, often far away from population centers, which means no cutting-edge machine tools or precision parts and limited material supply. The subs are often constructed using wood and fiberglass - not special-purpose alloys.


This is a relatively new innovation. Torpedoes are submersible vessels typically towed behind fishing vessels or other ships. If the ship is intercepted, the torpedo is cut loose, and after a period of time, it surfaces a camouflaged marker, allowing it to be retrieved after the authorities have gone.

This article on Insight Crime describes how torpedoes work in practice.

European narco-subs

It's not just the South Americans who are creating narco-subs, the Europeans are at it too. In February 2020, Spanish police raided a warehouse in Málaga where they found a very sophisticated narco-sub under construction. This is a well-constructed vessel, using hi-tech parts imported from countries around Europe. The paint job isn't accidental either - it's all about stealth.

(Image source: Europol)

Covert Shores reports that this is the fourth narco-sub caught in Spain.

Transporting cars illegally

So far, I've focused on narco-subs and drug trafficking, but similar technology has been used for other criminal activities. In China, Armored Stealth Boats have been used to traffic stolen luxury cars. The whole thing seems to be so James Bond, it can't be true, but it is. Covert Shores has an amazing article and images on the whole thing.

Some disturbing thoughts

There's a tremendous amount of risk-taking going on here; how many of these subs end up at the bottom of the sea? On the flip side, how many are getting through undetected? Of course, if large amounts of drugs can be transported this way, what about other contraband? Many of these subs are constructed with relatively primitive equipment and materials. What could a rogue nation-state do with up-to-date machine tools and modern materials?

Innovation - but for the wrong ends

All this innovation is amazing. The idea of constructing a submarine in the jungles of South America with limited materials and piloting it across the Atlantic is incredible. The sad thing is, all this creative effort is in support of criminal activity. It would be great if this get-up-and-go could be directed at something that benefits people instead. It seems to me that the fundamental problem is the economic incentive system - drugs pay well and there are few alternatives in the jungle. 

Reading more

The expert on narco-subs, and indeed on many OSINT aspects of naval warfare, is H.I. Sutton, who produces the website Covert Shores. If you want to read more details about narco-subs, check out his great website, Covert Shores.

USNI covers stories on narco-subs and other naval topics.

"Narco-Submarines: Specially Fabricated Vessels Used for Drug Smuggling Purposes" is a little old, but it's still good background reading.