Numeracy at Best Buy

We note that numeracy is important but it is hard to box in what numeracy is and how to use it well. Generally it is this idea that numbers explain some parts of the world well and we should use those numbers in a world full of people.

Yes?

Maybe an example will help:

“The Best Buy Geek Squad was reporting the mean (repair time) to their customers. A customer walks in to get their computer fixed, the part is on backorder, and the Geek Squad would quote the mean time to repair the computer. Of course, that means plenty of people’s repairs were not the average amount of time. So they changed and reported the 95th percentile time. They ranked the past times and now quote that to the customer – which is what people want!” – Elea Feit, March 2018

Like wet bias, maybe we can’t handle the truth. Or rather, maybe the way we see the world makes more sense one way rather than another.

One thing people are pretty bad at is randomness. We use stories to connect actions to events. Another thing we tend to miss is thinking that what did happen was the only thing that could have happened. It’s not.

We work around this through design. For instance, we know innovation is important but without separate metrics and incentives it’s less likely to happen. Put another way, it’s the framing stupid.

Wet bias makes sense. Being less honest than possible also makes sense. Quoting average waits may be more accurate but it’s less valuable.


Design and framing were two of my favorite ideas. For the ideas vitamin-style in a daily email drip, buy the email-drip on Gumroad. Find it on Amazon too.

A confusing life expectancy calculation

“Statisticians are sometimes dismissed as bean counters. The sneering term is misleading as well as unfair. Most of the concepts that matter in policy are not like beans; they are not merely difficult to count, but difficult to define…the truth is more subtle yet in some ways easier: our confusion often lies less in numbers than in words.” – Tim Harford, The Data Detective, 2021

One of Harford’s goals is to help people understand the world more as it is and less as they wish it. Harford kindly covers ideas like base rates, sampling bias, and algorithm associations.

That last one has some quite funny anecdotes. For instance, one AI system was trained to distinguish healthy skin from cancerous skin. Crunching and comparing over and over are two things computers do really well, so this seemed a good fit. And it was! The AI categorized correctly. But computer code is like a mango slicer – it has a singular use. In the case of the skin cancer, what the AI “learned” was that if a ruler was present it was cancer.

That’s funny.

But also not. One economic principle that’s going to affect (is affect_ing_) work is the idea that as something gets cheaper it’s used more. LEDs and cameras are two recent examples, name an electronic product that does not have one of those. Data too, is going to be part of our lives more, and Harford wants us to think about the numbers a bit more. For instance, what does “life expectancy” mean?

“They take the relative risk at every age and they integrate it. They ask, if the relative risk this year stayed constant forever, how long would someone born today live? That’s where we lost a year, but that’s assuming Covid stays and the year we just had gets repeated .” – Adi Wyner, Wharton Moneyball, July 2021

This isn’t the only way to calculate life expectancy, but it was the way that lead to headlines like, “US Life Expectancy in 2020 Saw Biggest Drop Since WWII, With Virus Mostly to Blame”. That’s true, but is that how most people understood it?

Most of what happens, and Harford starts his book on this idea, is that we think fast. “Biggest drop”, “WWII”, and “Virus” are all oh-boy-this-is-bad bits of information. But we dig in to what the words really mean and things look a little better.

Our tendency to think fast doesn’t have to be a hinderance. We can use this tendency to be more numerate. Books like Harford’s bump up (be Bayesian baby) these ideas. Riddles like: most British men live past the average age help too. A steady dose of numeracy uses the availability heuristic for our own good.


Not into the book thing? Harford has great podcast that cover these ideas. Wharton Moneyball is another with more of a sport’s bent. Gambling podcasts too cover these ideas. As Tyler Cowen said, it’s not that these things are VERY IMPORTANT but that if we see them more we update our mental toolboxes so they are marginally more important.

A confusing life expectancy calculation

“Statisticians are sometimes dismissed as bean counters. The sneering term is misleading as well as unfair. Most of the concepts that matter in policy are not like beans; they are not merely difficult to count, but difficult to define…the truth is more subtle yet in some ways easier: our confusion often lies less in numbers than in words.” – Tim Harford, The Data Detective, 2021

One of Harford’s goals is to help people understand the world more as it is and less as they wish it. Harford kindly covers ideas like base rates, sampling bias, and algorithm associations.

That last one has some quite funny anecdotes. For instance, one AI system was trained to distinguish healthy skin from cancerous skin. Crunching and comparing are two things computers do really well, so this seemed a good fit. And it was! The AI (read: computer code) categorized correctly. But computer code is like a mango slicer – it has a singular use. In the case of the skin cancer, what the AI “learned” was that if a ruler was present it was cancer.

That’s funny.

But also not. One economic principle that’s going to affect (is affect_ing_) work is the idea that as something gets cheaper it’s used more. LEDs and cameras are two recent examples. Data too, is going to be part of our lives more, and Harford wants us to think about the numbers a bit more. For instance, what does “life expectancy” mean?

“They take the relative risk at every age and they integrate it. They ask, if the relative risk this year stayed constant forever, how long would someone born today live? That’s where we lost a year, but that’s assuming Covid stays and the year we just had gets repeated .” – Adi Wyner, Wharton Moneyball, July 2021

This isn’t the only way to calculate life expectancy, but it was the way that lead to headlines like, “US Life Expectancy in 2020 Saw Biggest Drop Since WWII, With Virus Mostly to Blame”. That’s true, but is that how most people understood it? Does if this previous year repeated forever seem like a good conditional?

Most of what happens, and Harford starts his book on this idea, is that we think fast. But we can use this tendency to being more numerate. Books like Harford’s bump up (Bayesian baby) these ideas. Riddles like: most British men live past the average age help too. A steady dose of numeracy uses the availability heuristic for our own good.


Not into the book thing? Harford has great podcast that cover these ideas. Wharton Moneyball is another with more of a sport’s bent. Gambling podcasts too cover these ideas. As Tyler Cowen said, it’s not that these things are VERY IMPORTANT but that if we see them more we update our mental toolboxes so they are marginally more important.

Numeracy + Psychology

One of the consistent behavioral psychology findings is the framing effect. People judge what is pointed out and consider the number attached to it. Two out of every three dentists approve chewing no-sugar gum. Sure, but do they caveat that with increased flossing? Heck, no one cares. The thinking goes that if it was flossing that was important someone would have mentioned it.

This effect is most often seen in medical communication and Matt Yglesias captures it perfectly here:

But that headline is good. It’s salient – 4 people. It’s got friction. The real surprise is that they didn’t say ‘warn’ rather than ‘said’.

This kind of psycho-logic-magic needs countered with another kind of psycho-logic-magic.

We can assume two things work: (1) that people pay attention to and value what someone points out to them. This is normal, helpful, and completely understandable. It works. Most things that most people say are relevant to our lives. (2) that new news works. Different is interesting. This is also, normally helpful and understandable.

Here’s the pitch. This is the angle, the message. Here’s the psycho-logic-magic for vaccine interventions: opportunity cost.

If you’re pro-vaccine point out all the things that will be back to normal once people get it. Grandparents will visit grandchildren. Sports will resume. Christmas won’t be cancelled. Freedom and fellowship. Dining out and date nights. Cruise ships and college trips. Find whatever people value and point it out. People do not consider the opportunity cost unless it is explicit.

Closing note: if SkininTheGame is the ultimate signal, my wife had her second dose last weekend.

What the mean age means.

The Math of Life and Death is a good addition to the when are we ever going to use this collection of popular science books. With numeracy being so important in life, a regular diet of these ideas keeps someone mentally fit. Consider the story of student loans as one example.

Often the mathematical manuscripts show mean and median differing in network systems like in the case of income or the social graph. Or, how much Bill Gates skews average wealth but not legs.

Kip Yates reminds us of other instances.

“However, ecological fallacies can be more subtle than this. Perhaps it would surprise you to know that despite having a mean life expectancy of just 78.8 years, the majority of British males will live longer than the overall population life expectancy of eighty-one years. At first this statement seems contradictory, but it is due to a discrepancy in the statistics we use to summarize the data. The small, but significant, number of people who die young brings down the mean age of death (the typically quoted life expectancy in which everyone’s age at death is added together and then divided by the total number of people). Surprisingly, these early deaths take the mean well below the median (the age that falls exactly in the middle: as many people die before this age as after). The median age of death for UK males is eighty-two, meaning that half of them will be at least this age when they die.”

Kip Yates

Numeracy is becoming more important because we are generating more data. Luckily, we don’t have to become mathematicians but we do have to see if ideas pass the sniff test. We have to think about how survivor explains sampling, and consider gambling parlays. We have to be mathematically minded.

The Vaccine Friendship Paradox

One non-intuitive concept, at least in scale, is the network. Like average numbers, it takes some work to construct the correct conclusions. Graph, chart, and count the way that people interact, decide, and connect and there will be patterns. It’s network effects which fuel companies like Instagram and create the increasing returns economy.

Networks, as Nicholas Christakis notes, are agnostic. They spread whatever they are seeded with, whether real viruses like Ebola or WOW viruses like corrupted blood. The question then is; How and what to seed a network with?

Eric Bradlow wondered about Covid vaccines on Wharton Moneyball:

“We study diffusion of products all the time. In theory, you want to observe the social graph. In marketing the question is: Who do you give the free product to? This is standard network analysis and with that data you could do a smarter initial seeding (of a vaccine).”

Is there more bang for the buck if one person gets the vaccine rather than another?

Yes, though it’s not intuitive.

As the Friendship Paradox video shows, we aren’t all connected to the same number of friends. Some people have more, some have fewer friends and to wisely allocate a scare resource (like with marathon slots) it takes some small adjustments.

Christakis has spent a lot of time mapping networks and noted that across cultures, space, and time most human networks look the same. Some people are more connected than others. A few have hundred of connections and hundreds have a few.

It’s important for Christakis because like Bradlow, he works with a diffusion problem. Rather than marketing products though, it’s about sharing vaccines and vitamins. The thinking for both goes like this, if you can share something that works with the right person then they will share the benefits of that with the rest of their network.

But how do you pick the right person? Christakis shared this tip: “Go into a village and pick people at random. Have them suggest their friends and vaccinate their friends rather than the originals.”

Most networks are like the Curb Your Enthusiasm network (via Funkhauser).

curb_your_enthusiasm_-_season_9_-_network_graph

Randomly enter that network and you could get anyone but then ask for that person’s friend and more often than not you’ll get Larry. He’s the hub. He’s the super spreader. He’s who to vaccinate or market to.

It’s a neat bit of math. Rather than random choice, ask one question to improve the odds of an idea, movement, or effect catching on.

While there’s nothing on networks, my latests pay-what-you-want is on Tyler Cowen’s ideas about decision making. One idea is ‘meta-rationality’ or knowing when you don’t know AND knowing where or who to go to to find out. 

Large N Small p

Is it more likely for an infected football player to transmit a disease to their teammates or their competition? Adi Wyner:

"I would expect intrateam transmission by far. Not only huddle time, but the time on the bench, in the locker room, and while they travel. It’s a small chance of any given pairing but it’s lots of pairs. Anytime you multiply a large number by small odds you get a large number."

That’s via Wharton Moneyball and demonstrates the large N, small p principle. It’s the idea behind TikTok too. Ben Thompson said:

"What’s interesting thinking about Quibi and TikTok is that Quibi was such an arrogant idea, that professionally produced content is always going to be better. Are we sure about that? The vast majority of TikTok is garbage and that’s always the case with user generated content. But as it turns out, .1% of a massive, massive amount of content is super compelling. You find that one-percent not by being a picker, you find it by sourcing it."

Large N, small p is why something is always happening.

Survivor Explains Sampling

One of the nice parts of distance learning and social distancing has been extra family time. Without commutes, commitments, and the common-chaos, things are kinda quieter. So we’ve been watching Survivor.

I was a huge fan the first season. I was in college, online, and this was new. I kinda grew out of the show, losing touch with the premise, but now with kids that are twelve and ten we are ready.

We’ve watched as a family, working backwards from season thirty-four. Our favorite contestant of season thirty-three was Ken who played a straight version of the game; forming alliances, keeping his word, and winning challenges.

In this case it was the wrong way, as Adam took the final vote. Unanimously.

Ken was liked by all, played well, won challenges, and made it to the final three. What happened?

Two guesses.

Option 1: Survivor is a television show that’s edited a certain way. This is good. A time lapse or documentary or Instagram version of Survivor is worse. Television is a certain medium that excels with a certain message.

The producers know it’s sweeping panoramic of Bali islands, difficult-but-not-impossible challenges that make people at home say I-could-do-that, with some interpersonal drama mixed in. People are edited a certain way so there could have been a lot we didn’t see.

Maybe Ken wasn’t as sharp as he looked. Maybe Adam was even better.

Option 2: A sampling bias. The jury didn’t vote for Ken because they weren’t like him. They were there to play the game a certain way which is what Adam did. The people who want to go on Survivor want to play the game.

Sarah Tavel told Patrick O’Shaughnessy that in the early days of Pinterest there were a group of power users who wanted a specific feature to rearrange their pins. It would take a lot of work, but people really wanted it. So the engineering team built the feature and it largely went unused. What happened?

Sampling bias.

The power users weren’t a good sample.

The same thing was said by Ken Jennings about his run on Jeopardy. Everyone, Jennings said, that makes it to Jeopardy is really smart. That means they compete on something besides smarts. Competing against Ken was really about mastering the buzzer.

In his SSAC talk, Ken said that the producers didn’t know if his run was good or bad. Would this move Jeopardy to, “this is the spirit of the age” or repulse the loyal audience. After watching Ken rip off another week of winnings in a single day, the producers started to let the other contestants have longer buzzer practice. Jennings had mimed and timed the pattern and that was his key to winning.

Samples are fun to think about. With a good selection, a thousand people can explain the world. With a bad selection, and selection is often bad, we get things that may appear one way, but are not.

Want more? Check out this pay-what-you-want placebo prescription pdf.

Average Lies

“Often an average is such an oversimplification that it is worse than useless.” – Darrell Huff, How to Lie with Statistics.

We don’t really think about averages. The average hospital costs for hepatitis A was $16,000 in 2017. The average student loan debt for North Carolina residents is $36,000. The average American says they’ll spend $142 on Valentine’s gifts. Men, on average of course, say they’ll spend more than women.

For some things in life, average is fine. When my daughters were born, the hospital gave us a growth chart for their height and weight. It showed deciles and right in the middle was average. Growth charts are simple. Height. Weight. Plot. On chart meant on track, physically at least.

Now my daughters are twelve and ten and wow how things changed. New parents can track their child’s sleep, diet, movement—bowel or otherwise. And it’s not just parents. Everyone can track their taken steps, hours slept, and Spotify streams.

With technology, counting is easier.

With counts, averaging is easier.

Numbers are tools. Rather than bartering bananas for bread we have dollars and cents. With numbers, stores count their bananas bundles. With numbers, people have balanced budgets.

Numbers are tools. Like other tools, they take practice with feedback to build proficiency. I’m much more careful with the occasional use of power tools than the regular use of a chef’s knife. Numbers are like that. Well practiced and well used, numbers are a unique and powerful tool.

An example of numbers telling another story was the sabermetrics revolution in baseball. Smart teams realized that walks are better than hits, and that walks cost less to buy. Worth more, cost less. It’s like the successful Miller Lite advertising campaign: ‘tastes great, less filling’.

Decades later, sabermetrics happened in basketball with the insight that making one-third of three-point shots was the same as making one-half of two-point shots. Life, like sports, uses numbers more.

Numbers, though hidden in code, will become more prevalent in life and more important. 

Average, as numbers go, is often abused. This is due to many reasons, but just like technology has reduced the cost of tracking a baby’s bowel movements, average is used because the cost is low. It’s sixth-grade math. And it can hide important nuances.

For example, the average student loan borrower owed $28,000 in 2016. If we dig a bit deeper we find:

  • The median debt was $17,000.
  • The median for two-year degrees was $10,000.
  • The median for a four-year degree was $25,000.
  • One-in-four borrowers owed less than $7,000.
  • Only 7% of borrowers owed more than $100,000.

Those details are often omitted from the story. One poll showed that people viewed median debt of $17,000 as the “least bad figure about student loans”. Life is nuanced but numbers are not. Framed influences the way numbers are understood.

Thanks for reading.

Linda buys a bat and brand

There’s a quarrel in psychology research over Linda the banker. First some background. Most behavioral psychology is about crafting nearly identical situations with nearly identical composites of people who, despite the near identity, act in different ways.

One example is when employees are prompted with savings cues for their 401k. Imagine that with the annual corporate messaging about insurance, vacation adjustments, and outlook projections was a form that said “Did you know that your 401k contributions from October through December are eligible for a full employer match?” Employees who get the annual message with lines like that, raise their savings rates three percent. Employees who don’t get that message don’t change their rate.

What anyone saves is dependent on their own choices, right? However with the change in one line they aren’t.

Okay, now let’s talk about Linda.

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

  • Linda is a bank teller.
  • Linda is a bank teller and is active in the feminist movement.

When this original research was done, most people chose the second option.

And it’s wrong.

This ‘conjunction fallacy’ goes like this: there’s no way that there can be more bank tellers who are active in the feminist movement than there are all bank telllers.

This is mathematical logic. But it’s not how people think. When people hear Linda’s story they take the contextual clues that come along with it. If we could peak inside a participants mind we might see thoughts like this, ‘If you’re telling me all this stuff about Linda then it must be true that she is both a bank teller and active in the feminist movement.’

Any information that people get, people use and numbers are a special kind of information.

Numbers carry an authority.

Home values increased.

Home values increased by 8%.

And numbers lead to fast thinking. 

In his best-selling book, Daniel Kahneman framed this idea in terms of thinking fast or thinking slow. For some things in life, Kahneman wrote, we tend to think fast. Brands are fast thinking.

pasted image 0

There’s no interpretation here.

Numbers are like brands. Though an 8% increase in home values is a complex computation of home sales, realtor surveys, incomes, and so on, we see that and think it’s true without really thinking.

Joining Linda in the pantheon of psychology phrasing is the bat and ball problem. It looks like this:

A bat and a ball together cost $1.10. If the bat costs a dollar more than the ball, how much does the bat cost?

Ok, now try it this way.

Bat + Ball = $1.10, the bat costs a dollar more than the ball.

Or, the same idea in a different way.

A Ferrari and a Ford together cost $190,000. The Ferrari costs $100,000 more than the Ford. How much does the Ford cost?

Each step down slows thinking. People see the bat and ball problem the same way they see brands or 8% increases: fast.

Most of the numbers we encounter in life is like brands, the bat and ball problem or Linda the banker—our default is to move quickly past them. But to get all the details we’ll need to slow down.