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.

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