IMO

…or so says the “news” ticker in my office building’s elevator. I found myself very intrigued by this statistic. Let’s break it down a bit here. I saw this less than 2 min ago and I am going to compose at the keyboard so this could be sloppy but bear with me.

First let’s recognize that the probably of being born on any given day is the same across all days. I understand this may not be the case. But I would be stunned if it was wildly wrong, so I’m fine operating under that assumption. However, notice I said days not dates. And that is an important distinction, especially today. That is of course because today’s date only occurs every 4 years and a day, or 1461 days, which is nearly 1/4th as often as any other date on the calendar.

So now we know that about 1 out of every 1460 births occur on February 29th. Well with an global population of roughly 7 billion people, that would predict that about 4791000 of them were born on February 29th. I assume my elevator got to this point, decided to round up, and reported 5 million people celebrating birthdays today. Not a bad estimate. Seems to check out. 

But can we do better? Absolutely.

The biggest problem I see with our 4.80 million number is this: it assumes that there are an equal number of living 1,5,9,13,17,21,… year olds as there are 4,8,12,16,20,24,… year olds. Do you see what I am getting at? All of our leap day babies were born in 2008, 2004, 2000, … You know, leap years. This means that as of today (or even better, as of yesterday) people born on leap day are, on average, older than people not born on leap days.

This in its self would not be a problem. After all, take any 4 year bucket of consecutive birth years and you will still find roughly an equal number of birthdays on any given day. But here is the kicker, not all of those people are equally likely to be alive, specifically when you look at those born 1,2,3, and 4 years ago. 

The sad truth is that infant death is a huge threat, especially when we extend our scope beyond the United States, to developing countries without adequate healthcare. A quick Google search yielded a world wide population pyramid for every 5 years since 1950 (as well as projections out to 2050). The pyramid shape itself illustrates exactly my point. Death rate decreases as age increases and this trend is especially evident among the youngest population groups.

As a quick side note: It is interesting to note that this trend has grown less severe over the last 6 decades. No doubt a tribute to the technological progress we have seen in the medical field.

So finally we can get a sense for how to better calculate the number of people who are celebrating their birthday today. The figure we are looking for is the number of people who are precisely 1461, 2922, 4383, 5844, … days old. This numbers can be pulled from our population pyramid. At the moment all I have is the plot. Actually finding those numbers and adding them up would take some significant work and my lunch break is over. Suffice it to say that our new number would be south of 4.8 million, already a good 100K people short of the 5 million presented by the news ticker. But we will excuse the small margin of error.

As we just learned, the number of people alive born on February 29th should boom today, and then “erode” at a high but decreasing rate for the next four years, and then boom again.

A depressing thought for sure. Probably good of them to not include that on the monitor in the elevator.

What do you think? Can we do even better?