Community, Demography

Easy Math but Fake News

Yesterday, I read that US Life Expectancy had dropped by a full year due to Covid.  I didn’t really think about it – I had taught about the drop in life expectancy accompanying the Spanish Flu, and had invented hypothetical plagues for student exercises in demography class.  But when I had the full-year drop in life expectancy cited to me a second time, I realized that large numbers keep us from checking the math, even when the data is readily available.  Here’s the basic math for checking the assertion, worked as we would have in the slide rule era.

The US population is just a little under 330 million.  At present there are approximately 400,000 Covid deaths.  Using the Social Security life expectancy tables was a good decision – the data is readily available to check your work . . . but we don’t need complex math to check the claim that US life expectancy will drop 1 year due to covid.  It’s probably worth mentioning that life expectancy is a statistical thing, accurate for a large group but not particularly accurate for an individual.  I’ve known people who lived past 100 and others who died at 14.  At age 12, they had similar chances to live to old age.

To reduce US life expectancy by one year, Covid would have to take away 330 million years of life (remember, there are 330 million people. If each loses one year…)

This is possible, but to make the math easy, lets state the problem in millions to get away from the tyranny of large numbers. .  We’re left with 330 for population, and 0.40 for deaths.  To reduce US life expectancy by one year, we have to have 330 (million years of life) lost by 0.40 (million people).

US PopulationCovid Deaths
330,000,000400,000
330 million.4 million

Checking the math is nothing more than setting up a word problem: How many years of life are lost for each covid victim? Can there be 330 (million) total years of life lost with 0.40 (million) deaths due to covid?

Well, 330 years of life lost divided by .40 is: 825 years lost per covid death. That implies the average Covid death deprives its hypothetical victim of 825 years of life.  Since average life expectancy is now about 80 years, it looks like several orders of magnitude were lost in someone’s calculations.  The old slide rule techniques still have value in checking one’s work.

The same day, another stats guy ran numbers showing that the average Covid death was 13 years early.  That seems to have a bit more face validity – we can go to the charts that show death rates by age, develop percentages, and check his data against the tables – but I’m still making the math easy:

400,000 Covid deaths X 13 years = 5,200,000 lost years of life, or 5.2 million
5.2 million (lost years) divided by 330 million (population) = 0.0158 years of life expectancy per individual. 
0.0158 X 365 (days in a year) = 6 day drop in life expectancy.

The availability of data makes it possible for demography to be a science for everyone, and not confined to university campuses.