A Time to Be Born

October 19, 2012
Posted by Jay Livingston

Muhammad Ali and Evander Holyfield, Ty Pennington and Chris Kattan, John Le Carre and Trey Parker. Give up? They all were born on October 19. Happy Birthday.

The birthday problem came up again on a New York Times blog earlier this month.

How many people do you need in a room to get 50-50 odds that at least two of them share a birthday?

The official answer is 23.  The blogger, Steven Strogatz, takes you through the math (without once using the word factorial!) and even embeds the video clip of Johnny Carson getting it wrong. 

But even 23 is too high.  It assumes that birthdays are randomly distributed throughout the year.  But they’re not.

(The lack of a zero-point exaggerates the differences.  Still, September babies outnumber January babies by nearly 10%.)

The first thing it called to mind was the hockey aperçu made by Paula Barnsley but made famous by Malcolm Gladwell in the first chapter of Outliers.  The revelation takes place at a junior championship hockey game in Canada.  One of the spectators was Canadian psychologist Roger Barnsley.

   He was there with his wife, Paula, and their two boys, and his wife was reading the program, when she ran across a roster [that listed the players’ vital statistics]
   “Roger,” she said, “do you know when these young men were born?”
Barnsley said yes. “They're all between sixteen and twenty, so they'd be born in the late sixties.”
   “No, no,” Paula went on. “What month.”
   “I thought she was crazy,” Barnsley remembers. “But I looked through it, and what she was saying just jumped out at me. For some reason, there were an incredible number
of January, February, and March birth dates.”

In Canadian age-graded sports, kids are grouped by the year of their birth.  A boy born on Jan. 1, 2000 and a boy born on Dec. 31, 2000 are both twelve years old, at least for purposes of hockey eligibility, even though one is a year older than the other.  The older 12-year old is likely to be bigger and to have whatever other physical advantages develop with age.

Horse racing uses the same rule. Officially, every thoroughbred has the same birthday – January 1.  So the breeding season peaks in the late spring.  Most Kentucky Derby winners are foaled in March, very few after May. 

Is anything similar going on among human breeders, usually called parents?  Apparently not. The numbers for the early months are low rather than high.  (In Canada too, births in the first quarter are lower than in the next seven months.) 

Some school systems use a cutoff date of September 1, so all those September babies have an edge, but if parents were breeding rationally, we’d expect lots of births in the following months as well rather than the dropoff shown in the graph.

It looks as though most parents are not breeding rationally, or if they are, other considerations are affecting their scheduling. 

Yes, you can find articles (this one, for example) about competitive parents redshirting their 5-year olds – delaying a child’s entry into kindergarten for a year so the little tyke will have an edge over his even littler classmates.  It would appear that there are too few of these to make a blip in the graph. Still, I wonder what the graph would look like if it were based only on upper middle-class births. 

In any case, births are not distributed randomly. Cue The Byrds, channeling Pete Seeger channeling Ecclesiastes: “To everything there is a season . . .  a time to be born . . ..”