Some Bob Runs the Numbers episodes have been published. Some are in the pipeline. And some are yet to be written. Many of these analyses rely on making actuarial assumptions. This appendix will explain some of those assumptions... and, if I’m not too forgetful, I will link to this appendix from Bob Runs the Numbers episodes that rely on these assumptions.
I’m not aiming for five significant digits of precision here. These exercises are back-of-the-envelope calculations that will hopefully end up with conclusions that are in the ballpark of reality. (Plus, if I am relying on these assumptions to buttress an argument, then I want the argument to be strong enough that minor precision simplifications won’t invalidate the conclusions.)
American Population Assumptions
Most analyses will assume an American population. Unless otherwise specified, I’m not running the numbers on global populations or anything other than the United States. This will typically be because other countries won’t be apples-to-apples comparisons.
I will generally round the U.S. population to 300 million. I won’t be a stickler about this, but I may need to keep the math easy, and nothin’s easier than one significant digit!
Assumptions About Economics
The Federal Reserve Bank of St. Louis maintains one of the most useful economics websites around. FRED includes graphs of just about every economic index you can think of.
A minute or two of fiddling with graph parameters gives you, for example, American Gross Domestic Product for Obama’s tenure and the first year or so of Trump’s.
Lifespan Assumptions
I will assume that expected lifespan is eighty years. This is a teensy bit optimistic, but holy moly are the numbers easier to work with when I do math with an 80-year life expectancy instead of a 78.74-year life expectancy. (Again, if I can choose to do math with one significant digit then sign me up!)
I will assume that “surprising” (typically accidental or violent) deaths occur, on average, mid-way through a lifespan. Therefore I will count an individual accidental death as costing 40 years (i.e. half of 80) of lifespan. Some accidental deaths happen later in life, “costing” less; other accidental deaths happen, tragically, earlier in life, “costing” more lifespan. But overall I’ll make the assumption that an accidental or violent death costs 40 years.
I will assume that health-related deaths (cancer, heart disease, etc.) occur closer to the end of a lifespan and, to pluck a number from ... let’s say thin air ... I’ll assume that a health-related death costs 20 years. (That’s half of the second half of one’s life.)
These assumptions will allow us to convert a number of deaths to a corresponding actuarial equivalent of average lifespan impacts. It’s the flip side of the delightful Steve Jobs anecdote about how reducing Macintosh startup times saves lives.
Health Cost/Benefit Assumptions
Some “nuggets” that may be dropped in are these calculations that follow the form “every cigarette you smoke reduces your lifespan by ...” Sourcing these examples can be tough and in a vacuum I’d prefer to derive stuff like this from the lifespan assumptions, but I’m all about shortcuts so here are some examples of nuggets that may inform other articles or arguments:
A cigarette reduces expected lifespan by eleven minutes
Briskly walking for one minute adds three minutes of lifespan
Bicycling for one minute adds five minutes of lifespan
Skipping rope for one minute adds eleven minutes of lifespan
Obviously these nuggets must be applied judiciously. If someone bicycles twelve hours a day, common sense suggests that they don’t have an expected infinite lifespan. Most of these nuggets assume a generally sedentary lifestyle, where marginal time spent exercising “pays off” by increasing lifespan.
Averaging out typical calories per minute for walking/bicycling/skipping rope, we get a range of results, but we could do worse than to assume one calorie’s worth of exercise pays off as thirty seconds of additional lifespan.
Let me give some concrete examples.
Example: Actuarial Cost of Motor Vehicles
In 2010, the U.S. had about 10 motor vehicle fatalities per 100,000 inhabitants. What’s the motor vehicle fatality “tax” for each of us?
10 / 100,000 * 80 * 40 * 365
(annual fatality rate) * (number of years) * (cost, in years, per death) * (days per year)
... and we end up running the numbers to reach the conclusion ...
Motor vehicle deaths cost each of us, actuarially speaking, 117 days or about four months of our lifespan.
(What we do with this information is a separate question. A cost/benefit analysis of motor vehicle usage would have to take into consideration the ability to live more than, say, a mile from work, for example, or acknowledge the cost of alternatives. But starting out with a clear-eyed acknowledgement of the cost – four months of my life! – is necessary for an honest look at the cost side of the equation.)
Example: Actuarial Cost of Lightning
Now the lightning round! Lightning kills 40-50 Americans per year. Call it
40 / 300,000,000 * 80 * 40 * 365
to end up with 0.16 days. Lightning strike fatalities, actuarially speaking, cost each of us about four hours of lifespan.
(We spend a lot of effort to minimize lightning fatalities. Building codes, aircraft regulations, public service announcements especially when bad weather is approaching – all of those contribute to the current low actuarial cost of lightning fatalities. Early in the twentieth century we lost ten times as many Americans annually, even though the U.S. had a smaller population ... call it
400 / 130,000,000 * 80 * 40 * 365
or three and a half days! of lifespan lost for each American. The actuarial cost of lightning has dropped 95% over the last 80 years; how much marginal effort is useful to reduce the actuarial cost further? That’s the kind of question worth grappling with.)
Silly Example: “Paying” for a Smoke
Another kind of silly example illustrates doing a balancing act with different actuarial assumptions.
If you want to grab a smoke but don’t want to sacrifice that eleven-minute lifespan reduction, pair it with a one-minute jump-rope session and voilà! you’re coming out even-stephen, actuarially speaking.
(This editorial board specifically does not recommend this.)