My Uncle Joe is always fantasizing about ways to outsmart Father Time.
“Suppose you could reverse your aging process at some fixed point in your life,” he says to me, a crazed gleam in his eye.
“So you could pick any age to turn the clock backwards and start aging in reverse. What age would you pick to try to maximize your life span?”
In other words, suppose you pick age 75. That means you’d turn 75 and then start aging backwards another 75 years. So you could live up to 150 years.
Your risk of mortality increases with age, so picking a higher age doesn’t guarantee a longer life span. If you pick age 50, you’d live at most only 100 years, but your chances of dying before you hit the turnaround point are less than if you pick 75. So it’s a safer bet, for a slimmer payoff.
Uncle Joe posed the question because he knew the answer to this puzzle hinged on probability, the bedrock of inferential statistics.
What Are Your Chances of Kicking the Proverbial Bucket?
The Minitab time series plot below shows the probability of death at each age for U.S. males, based on a 2009 period life table by the U.S. Social Security Administration (SSA). (Gee Opie, I wonder why the SSA tracks our mortality risk by age?)
Looking at the graph, what age would you pick as your turnaround point?
The age you choose depends on how much of a gambler you are. Also, because these are average risk estimates, you'd need to consider how you stack up against the “average U.S. male” in terms of your health, lifestyle, genes, environment, and so on.
Let’s assume you’re an average American Joe. If you’re conservative, you might pick an age close to 60, just before the plotted points begin to show a perceptible increase. That, ideally, would give you 120 years on Planet Earth.
Or maybe you’d like do your chronological about-face before the odds of dying in a given year surpass 50%. If you hover your cursor over points on the graph in Minitab Statistical Software, you’ll discover that age 106 is the highest age that incurs less than a 50% chance of dying during that year.
That could give you a total lifespan of 212 years! (I can see my Uncle Joe turning cartwheels right now.) Sounds too good to be true, doesn’t it?
That’s because there’s a catch. (In statistics, you always have to read the fine print.)
The calculated mortality risk for each year is based on the assumption that you’ve already made it to that year. So it only reflects your risk of dying during that particular year, at that age. Not your cumulative risk of dying at some point on or before that year.
It’s always a good idea to examine data from different angles.
Who's Still at the Party?
The SSA period life table also tracks the number of males, from a starting cohort of 100,000 males at birth, expected to survive with each passing year. To help Uncle Joe visualize this data, I created a Minitab bar chart:
The ripe old age of 106 doesn’t seem a very wise choice now, does it? Not unless you’re a rootin’ tootin’ high-stakes gambler. Only 0.041% of U.S. men are expected to survive from birth to reach age 106.
I added a reference line to show the 50% breaking point (right-click a graph and choose Add > Reference Lines). More than 50% of American men are expected to survive to at least age 79. At 80, slightly less than half (49.42%) are expected to still be kicking up their heels.
So 80 might be a good age to turn around and hightail it back toward the womb.
But wait. There’s another catch.
This chart only shows the expected percentage of expected survivors from birth. In other words, it’s most useful for making your decision if you’re 0 years old right now. Somehow, I doubt that's the case.
Give Yourself Some Credit for Making It This Far
Once you’ve reached a certain age, you’ve already dodged some of life’s bullets. To make a more informed decision, Uncle Joe should examine the average life expectancy based on current age.
I created a Minitab area graph (Graph > Area Graph) to show the cumulative effect of adding the calculated life expectancy (the orange region) to each age (the yellow region).
The total expected life span at each age is indicated by the curved line at the top. If you right-click the graph in Minitab and choose Crosshairs, you can identify the expected life span (y) at each age (x).
For example, say you’re approximately 80 years old. By positioning the crosshairs on the x-value 80, you can see that your expected life span at that point is about 88 years old.
But don’t let that make you fear your 88th birthday, because the graph also shows that once you turn 88, you can plan on living to about 92. Even at 120, your life expectancy is more than 6 months!
It’s almost like Zeno’s paradox isn’t it? It seems you’ll never hit the finish line.
Which leads me to the profound conclusion of this post (drumroll, please):
The older you are, the longer you'll live. ;-)
A Better Way to Beat the Clock
I’ve got a better fantasy for Uncle Joe. One that doesn’t require analyzing mortality risk.
Your best bet is to be reborn as a hydra, jellyfish, or planarium flatworm. These creatures can perpetually regenerate all of the tissues in their bodies. So they're biologically immortal—they'll never die of old age.
And that, my fellow mortals, is the Social Security Administration’s worst nightmare.