Life expectancies and tennis racquets
6 min read 20 May 2022, 02:12 AM ISTIn all the countries, India among them, the actual count of deaths is significantly less than the expected count that we calculate from population and life expectancy
PremiumWhen I was so much younger than today, I played tennis more regularly than I do today. And we amateur players heard of a simple formula that seemed very reasonable. Re-string your tennis racquet, it went, as many times in a year as you play in a week.
It made sense and was easy to remember. Those days, I played at least four times a week, so I’d restring four times a year, or about every three months. If I played more often, the restringing happened more often. When my playing slacked off - as it has in recent years - so did the restringing. It wasn’t that I kept trackcolu of these things. I didn’t need to. The more often I played, the quicker the strings got noticeably less taut.
Sometime then, while a bunch of friends and I were playing and enjoying the game, we heard of a new formula - “the current wisdom", said the guy who regularly strung my racquet. I don’t now recall the new formula, though it wasn’t as easy and intuitive as the old one.
But whatever it was and however often you played, it suggested more frequent stringing than the old one did. Which figured, because the new formula was concocted by the Professional Racquet Stringers’ Association or some such. Naturally, it was in such an Association’s interest that we string our racquets more often.
Now I’m not fully sure why an email message after my last column here got me thinking about tennis and restringing. Maybe it will be clearer by the time I finish writing this column. Or maybe not. Who knows.
You will remember that my last column was about questions that India’s announced covid death toll raises. I started it by stating that about 10 million Indians die every year: a number, I wrote, that nobody really contests. Except ... the next day, there was a message in my Inbox. “I don’t understand your figure of 10 million Indians dying per year", wrote an alert reader (you know who you are). “An average human lifetime is maybe about 70 years, and so, very roughly, about 1 person in 70 should die each year. If you divide 1.4 billion by 70, you get about 20 million."
The alert reader raises a good point. If this reasoning is not immediately clear, though, approach it this way.
Consider the fictional country Freedonia. It is populated by a million people who sport large moustaches and their life expectancy is just one year. This makes them grouchy, because as a little reflection will tell you, all Freedonians alive today will be dead within a year. i.e. Divide Freedonia’s population - one million - by the Freedonian life expectancy - one year - to get the number of deaths in a year there - one million. You’d be grouchy too.
Ah, but one day, Freedonia totally revamps its healthcare system and mandates a better diet for all its people. It takes a while, but eventually, these measures bear fruit: life expectancy in Freedonia doubles to two years. Some more reflection will tell you that everyone in Freedonia will be dead in two years. Half - the ones born a year ago - will die this year. The other half, the ones born this year - will die next year. Again, divide the country’s population by life expectancy, two years, to get the annual death toll: 500,000 this year, 500,000 the next.
Freedonia keeps at it, and its life expectancy keeps rising. Gets up to four, and only 250,000 die each year. Reaches 20, and the country sees about 50,000 deaths annually. By the time Freedonia has pushed its life expectancy all the way to 70 years, its population has also exploded to about 1.4 billion and maybe it’s not so fictional any more. It’s now renamed India. Still, the same general rule applies. Divide 1.4 billion by 70 to get the yearly expected death count: 20 million.
Why then is India’s announced annual death toll half of that?
Faced with this question, you wonder: is there something wrong with this rule? It’s hard to imagine, though, because on the face of it, it is so simple and intuitive. Well, do other countries’ figures follow the rule? Take a look at a few at random. Remember that these are pre-pandemic figures; covid death counts skew these in different ways.
Consider Australia: population 26 million, life expectancy 83 years. The expected annual count of deaths is thus 26 million/83, or about 313,000. Actual count: 161,000, or about half the expected number.
What about Brazil? Population: 213 million, life expectancy 76 years. Divide 213 million by 76 and we expect 2.8 million deaths per year. Instead, the number is 1.66 million deaths. Just over half, again.
The US? Population 330 million, life expectancy 77 years. The annual death count should be 4.29 million. Instead, it is about 2.85 million.
Or take China, with its population of about 1.41 billion and life expectancy of 76.91 years. The expected annual death count: 18.33 million. But the actual number is about 10.24 million.
In all these countries, India among them, the actual count of deaths is significantly less than the expected count that we calculate from population and life expectancy. So did I, just by chance, pick the only five countries in which this is the case? Or is this just normal?
Well, here are the numbers from five more countries at random:
Madagascar: population 27.7 million, life expectancy 67.04 years, expected annual deaths 413,000 - but actual annual deaths are only 160,000.
Iceland: 366,000, 82.56 years, 4433 - but actually 2275.
Nigeria: 206 million, 54.69 years, 3.77 million - but 2.4 million.
Ecuador: 17.6 million, 77 years, 229,000 - but 90,000.
Laos: 7.3 million, 67.92 years, 107,000 - but 46,000.
Believe me, this applies across the board. In fact, for the world as a whole, these are the numbers:
World: 7.6733 billion, 72.74 years, 105.5 million - but 57.3 million.
All of which leaves two broad questions. This is in some ways an unusual column for me, because instead of trying to answer them myself, I want to leave you with those questions too. So here they are:
First, what’s going on with all these figures? Is there an explanation for why annual deaths across the world are much lower than life expectancy numbers would suggest?
I don’t know the answer. Perhaps there is another way to consider this data, and statisticians or demographers can explain it. Maybe it is an obvious explanation. Still, for the time being, I’m deliberately not searching for it because I’m trying to explain and understand it myself. For example, are there reasons for the decline of death rates that are separate from the increase in life expectancies? Hypothetically, if a country has a very low life expectancy - if not quite as low as Freedonia’s one year - would this difference be smaller? If a country has a very small population, would that have any bearing on the difference?
Second, what’s the connection, if any, to my experience with my tennis racquets? For example, is there an analogy between longer life expectancies and longer intervals between restringing a racquet? Something strikes me as similar in both situations, but I can’t put my finger on exactly what.
Still, it always seems to me that that is the great appeal of mathematics, whether you’re serious about it or just a dabbler. There’s charm in those connections.
Can you help with answering either question, or both? Please get in touch - via my Twitter handle, or email to dilip.fbk@gmail.com.
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun
