Return sequence

If you invested twenty dollars a week how much money would you have? 

Well, it depends. When did you start? 

The start is important because the sequence matters. Let’s follow the advice from Richard Zeckhauser and think in extremes. 

If things were ideal, an investor’s early years would have low (or even negative) rates of return and their later years would have high ones. Would you rather double your net worth at fifteen or fifty-one? 

The most favorable market returns transform 30,000 into 3,200,000 after thirty years. Wild. 

But the worst conditions cede only 300,000. Real-life, as often the case, is somewhere in the middle. 

$1,000 invested into the Wilshire 5000 each year.

Each of these graphs is the actual returns of the Wilshire 5000 (16%, -5%, .01%, etc.) but arranged in different sequence. A random ordering (yellow) offers an extra 40% over real life. It’s a luck of the draw as they say.

But this isn’t a what if you invested in ___ at ___ post. 

The point is to practice Maxims for Thinking Analytically. Extreme examples reframe how we understand and here we understand sequence matters. 

We touched on this idea in the Maximizing a 401k post and considered the tradeoffs between a 401k and a 15-year mortgage too. 

Dice tails

Maxim two, from Richard Zeckhauser, is “when you are having trouble getting your thinking straight, go to a simple case.” This maxim came to mind listening to Michael Mauboussin and the Acquired duo discuss business valuation and the difference between tangible and intangible assets.

“(Intangible assets like brand, code, etc.) also makes you vulnerable. If your product or service does not work there’s not much there left. If you think of pushing out the tails relative to traditional business, that’s the way I think about it. There are more extreme good things and more extreme bad things than we’ve witnessed in the past.” – Michael Mauboussin, Acquired, October 2021

We’ve thought about this idea before, in the complex world and in the increasing returns economy. But it’s a big idea and like the lead in a story, we need to fill out this character a bit more.

Here’s the distribution of results of one, two, three, and four dice rolls. For one, the results are equally likely. For two, as anyone who has played Catan knows, seven comes up the most.

one two three four dice distributions

Though it’s a basic Google chart, it is simple enough for Zeckhauser and satisfactory for Mauboussin. For a die, the chance of rolling the highest score is ~16%. In the case of two the chance is ~3%, for three it’s ~0.5% and for four it’s ~0.1%.

Different parts of life are more or less similar to different amounts of dice. Businesses with lots of intangible value are closer to the end of fewer dice, because those kinds of distributions have fatter tails. Business with more tangible capital are more like rolling many dice.

Now, dice distributions offer no mechanistic or explanatory approach about what kind of system a case may be. There’s nothing about “brand building” that makes it more like rolling two dice relative to something like pool construction. But the metaphoric fit is just fine.

Thanks to Michael Mauboussin for this post and all the others. He was one of the early podcast guests who was going around explaining things that seemed like really big ideas in a really basic way. He was so good at it I thought, hey, I should write some of this stuff down. Well, I’m still writing.

Fermi questions, answers, and landmarks

A Fermi question is something like, How many rolls of toilet paper do the residents of Columbus Ohio use in a week? Fermi questions are silly but embody some serious thought. Namely, how do we think about the world?

There’s some fun little math behind a Fermi question but the hardest part is often the start. For instance, how many people live in Columbus Ohio? Tim Harford knows. Rather, Tim Harford has a suggestion.

“Andrew Elliott—an entrepreneur who likes the question so much he published a book with the title Is That a Big Number?—suggests that we should all carry a few ‘landmark numbers’.”

Landmark numbers are figures we can use to guide our thoughts about the world. For instance, there are about four million Americans at any age under sixty. New York City has a population of about nine million. Columbus Ohio has a population of about one million. This is actually quite helpful just for a start.

Using a Zeckhauser maxim, “when you are having trouble getting your thinking straight, go to a simple case.” If every resident of Columbus Ohio used half a roll a week, how many rolls of toilet paper would they use? That’s easy! We have a million people, each uses half a roll, and that’s 500,000 rolls per week. No wonder we had a shortage.

Tsk tsk, Enrico Fermi would scold us. You can do better. And indeed we can. That is the point of thinking about Fermi questions. We can do better and even if we make a mistake, even if we make a few mistakes, we can still very likely be right. The reason is because of the random walk nature of our guesses. Some of our guesses will be too high (Columbus actually has 898,000 residents) and some will be too low, but overall these kinda-sorta balance out and that puts us in the right ballpark. Not only that, but making additional steps doesn’t necessarily mean additional steps in error. That, and more examples are here.

Good decision making takes nouns and verbs. We’ve got good verbs like inversion, mean reversion, extreme examples, and such. Landmark numbers give us a few nouns to work with too.

The very good Fermi book inspired this post: Fermi Knowledge.

Being better than Superman

Maxim four from Richard Zeckhauser is: “When trying to understand a complex real-world situation, think of an everyday analogue”.

Alex Tabarrok has been using this strategy to communicate about vaccines.

“To me the vaccines are like a superpower. Superman is immune to bullets and I tell people: ‘Wouldn’t you like to be immune to bullets? The virus has killed many more people this year than bullets have, and the vaccine makes you immune to the virus, it’s better than being immune to bullets!'” – Alex Tabarrok, July 2021

In Dan Levy’s book about Richard Zeckhauser he includes a section from Gary Orren who used the everyday analogy strategy to describe the AmeriCorps service program. AmeriCorps, Orren told legislators, is like a Swiss Army knife, it does many things well though it’s never the perfect tool. A few weeks after addressing the governmental staff Orren returned to their offices. “Oh yeah, I remember you. Swiss Army knife.”

This strategy helped, Orren explained, because it focused his thinking and the audience’s understanding. A lot of times our thinking is FAST and analogies shift complex concepts into simpler situations.

Simplification isn’t the end though. Extremes, like questioning the Ohio vaccine lotto, are not the final answers but a first foothold. If we can understand an issue’s basic components first, it can be easier to build up to the rubber-meets-the-road challenges of IRL.

My year of AmeriCorps was health based, and I remember many vision screenings .

Apples to apples in Iceland

The basic base rate question is: what should I expect in situations like this? Most often we have looked at base rates through the lens of projects. We have an optimistic tendency to think, “yeah but…”. Sometimes it is! Sometimes it’s not.

but it might work for us

The general advice for using base rates has been to start with them, rather than our impressions, and then adapt from there.

Another way to think about base rates is as sampling. It’s important to get the “situations like this” part right, right? This is tricky, and this came up during the summer of 2021 as more and more covid vaccinated people became infected with the covid virus. At one point 67% of Iceland’s cases were among the vaccinated.

“When you look at Iceland and graph out (cases) by who is vaccinated, who is not, and where the cases are, you can see that there are more cases in the vaccinated group than the unvaccinated group.” – Dr. Kat, NPR Planet Money, August 2021

That sounds like the vaccine doesn’t work, or doesn’t work as well, or never-worked?! Maybe, but maybe our conclusions are muddied by an initial assumption that’s wrong.

Rather than jump right to Iceland, let’s pull a Zeckhauser and simplify everything. Imagine in Indiana there is a group of 100 people, half are vaccinated and half are not. In the vaccinated group there are five infections and in the unvaccinated group there are five infections. Putting aside “long-infection”, hospitalization, and death, it-looks-like, in-this-case, that the vaccine is meh.

Okay, now in Nevada there is another group of 100 people. This time there are 90 which are vaccinated and 10 are not. In the vaccinated group there are five infections and in the unvaccinated group there are five infections. Putting aside the same other-factors, in this case the vaccine is doing a lot of work! This was the case in Iceland too. Six of every thousand vaccinated people caught covid while fifteen of every thousand unvaccinated people caught covid. And all of the other-factors were much worse for the unvaccinated group. Vaccination reduced someone’s risk by more than half.

This idea is known as the “base rate fallacy” but really it’s comparing apples to apples which will make the idea stick better anyway(another bit of Zeckhauser advice is to keep explanations simple). BRF is good for talking with economists and behavioral scientists but for implementing this idea it’s an apple-to-apples question a day that will keep the bad decisions at bay.

Free Meals

At the start of Dan Levy’s book Maxims for Thinking Analytically, a book about Richard Zeckhauser’s tools for thought, is this riddle: “Mary and Jim want to paint a room together. If Mary painted alone it would take her 2 hours, and if Jim painted alone it would take him 3 hours. How long would it take to paint the room if they paint together?”

It’s not 2.5 hours.

Zeckhauser’s first maxim is: “When you are having trouble getting your thinking straight, go to an extreme case”. We used this maxim to ask: was the Ohio vaccine lotto a good idea? And it probably was.

Danny Meyer uses a version of this maxim too. One of the most important factors for a restaurant’s success is the location. (Overall it’s a hard business). Meyer wants to avoid errors of commission. Even if a restaurant proves successful it is “stuck with” the location. So Danny explores many locations to find something that works and ask an extreme question:

“Sometimes a space says, don’t plant anything here, this place should not be a restaurant. The first question I ask myself when I look at a restaurant space is: would I want this even if it were free?” Danny Meyer, July 2021, The Knowledge Project

Another way to consider this kind of framing is the expression you couldn’t pay me to. One advantage to living in the south, where football rules the roost, is the access to football. If you like it that is. One friend uses you couldn’t pay me to to express her feeling about SEC football games, the same games where tickets can be hundreds of dollars.

Levy’s riddle is easy once we slow our thinking. Thinking fast we average the work, and get 2.5 hours. Thinking slow(er), like Zeckhauser, and we notice that Mary alone would take two hours. That’s the extreme.

Ohio’s Vaccine Lotto

On May 12, 2021 Governor Mike DeWine of Ohio announced a one million dollar vaccination lottery. Teens were eligible for a college scholarship. Two days after the announcement Ohio doubled its vaccinations-per-day figure to thirty-three thousand people. Success!

Maybe. “States with lottery programs,” noted the Boston Globe “are not doing any better compared to states without such initiatives.”


But, there are at least two reasons Ohio’s strategy was a good one. The first is the testing of new approaches. One of the beautiful things about the United States of America is the differences in states. When states do different things academics call this “heterogeneity” and “natural experiments”. While not perfect, these opportunities and observations lead to novel lessons. Part-of-the-reason there won’t be another 2020 are these learnings.

The second reason Ohio’s vaccine lottery was a good idea is an idea from Maxims for Analytical Thinking, a Michael Mauboussin recommendation:

MfAT is a book of thinking tools by Dan Levy who focuses on the ideas, information, and influence of Richard Zeckhauser. Maxim 1 is When you are having trouble getting your thinking straight, go to an extreme case. Using this lens, was the Ohio Lotto a good idea?

Imagine it this way. What if there were a Hypo-Ohio, where thanks to the industriousness, intelligence, and ingenuity of the individuals, a vaccine holiday was declared on February first. Employers gave employees the day off. Starbucks and Subway donated their stores for stick sites. Netflix was free for Ohio ISPs. Everyone that was willing and able to get a vaccine got vaccinated.

Ohio Vax

If that happened, like poker chips slid across a table, the May blip and March wave would be compressed into an early February explosion. This would have been awesome. We know from the vaccine friendship paradox that all social networks have a super-spreader. At the extreme, pulling the demand forward would be a good thing.

But what was the effect size? Here I’m over my skis. But that’s actually okay. The techniques I learned in my Ohio high school still work: remove the bad answers first. Like the 15y or 30y mortgage question, I’m looking for choosing from only the good options. At the extreme, pulling demand forward is a fantastic idea. How much effect, I don’t know, but I’m glad they tried.

Bias Warning: I thought the Ohio Lotto was a good idea from the start.