The following is a guest post by Louise Firth Campbell and Amram Shapiro, the authors (with Rosalind Wright) of The Book of Odds: From Lightning Strikes to Love at First Sight, the Odds of Everyday Life.
Rare news stories recur with surprising regularity — one of these annual stories is the birth of twins in two different years.
You can see the appeal to editors. Babies are photogenic, especially twins. The symbolism of the New Year as a baby which ages to dotage by year end is an old one, a staple of thousands of New Year’s cards. There is an interesting apparent time tension in the story. Twins share a womb and genomes. Yet a few seconds separation in time of birth makes an apparent year’s worth of difference. This event is considered a rarity and only a handful of cases are reported in the press each year. This rarity makes it news, but is the event really as rare as it seems?
Let’s start with the news in 2013/2014. If the cases reported in the North American media, two in the U.S. and one in Canada, are the only cases, these events are rare indeed. There are about 4 million births a year in the U.S. That would suggest these events are as rare as 1 in 2 million. Someone visiting the Grand Canyon is more likely to die by falling off the edge (1 in 1.5 million). That doesn’t feel right to us.
Not all cases of twins born a year apart are reported. One or two are all the media need for their annual story. Given that such births add complications — two birthdays, separate parties, bragging rights issues, and who knows what tax consequences –people can be forgiven for fudging or ignoring the hours. Moreover, a birth is an intense event, especially twin births. More attention will be paid to the procedure than the clock. And some parents may wish to guard their privacy and pass on Warhol’s “fifteen minutes of fame.”
Dr. Michelle Silba, who delivered Lorraine (11:58) and Brandon (12:01) to Yaleni Tohalino in Washington, D.C., told ABC News that “none of us were looking at the clock.”
It is plausible then that there are more cases than make the papers. But how can we demonstrate that? And how many more?
We thought to put it to a test by doing a rough speculative and assumption-based estimate of the likelihood. We’ll be interested to see whether Freakonomics’ creative readership has suggestions for refining the estimate.
Book of Odds used a thread, or linked chain of independent probabilities, to get an estimate. Where there are hard numbers, we used those. Where there aren’t good data, we made as reasonable an assumption as we could.
Let’s start with all U.S. live births since we assume that C-sections are more likely to be scheduled for a more convenient time than midnight, and emergency ones tend to have a short interval between first and second twin’s birth — this leaves almost 4 million in a year. An emergency C-section hitting just on New Year’s Eve might be overlooked by this assumption, but it will apply far more often than not.
Of these, the odds are 1 in 30.1 the birth with be of twins, or about 131,000 births. We don’t know exactly how many of these are vaginal births, but the CDC tells us it is more than half. Using 51 percent we get to a rough estimate of 66,896 vaginal twin births. Obviously it could be higher than that, but we erred on the low side.
Now it gets interesting. We know the births by month and the odds a birth will be in December or January, and we also know the average interval between first and second birth — 17 minutes. By taking the twin births in those two months and assuming they are evenly distributed, we can take all the variations of 17 minutes which work and add them up. So first twin born at 11: 44 PM in December, and the second at one minute into January would count, and so on.*
Run the numbers and we get an expected number of twins born a year apart as 67, a good deal more than 2 or 3. If our reasoning is good enough for a rough swag, the odds a live birth will be of twins born in different years are 1 in 59,200.*
We don’t often make predictions, but we think it is a safe bet that no matter how many cases there are next year the media will report on only a handful of cases of twins born a year apart.
*CORRECTION: Thanks for the comment, Abe, and the same to the others who found our error. Actually there are two errors. First, having determined the number of intervals which span the year, we counted each in terms of its minutes not as a single instance, ending up with an overstatement of 17 times. If you take the final number of 67 and divide it by this overstatement you get an expected number of spanning twin births of 3.9 The second error was to apply the odds to the sum of December and January births. If only December births were used, 3.94 would be approximately halved to 2 , which is what is reported by the press.
Only December’s possible intervals matter since the January ones are simply 17 – December minutes. There are 16 of these combinations which span the year from 1 minute in Dec + 16 minutes in January to 16 minutes in Dec + 1 minute in January. Out of the total December minutes, or 44,640, only 16 will span the year. This means the odds a 17 minute interval spans December and January are 16/44,640 or 1 in 2,790. Apply this to number of births in December alone, which is 5,590, and you get 2.
Could it be that our expectation that there was understatement in the press blinded us to the errors we made? We think it is possible, since just like those we were implicitly critiquing, we were attracted to our narrative: the news that the news isn’t always news.
 As a management consultant, I encountered a witty play on this issue of time at the boundaries, this time the International Date Line. A scientist at Motorola stood on one side of the date line and filled out a patent filing. He then stepped back across, going into the day after, and filled out a memorandum of invention. This dance allowed him to brag that he filed a patent the day before he made the invention. What the Patent & Trademark Office made of this anomaly, I never learned.
 Books of Odds estimates based on data in MP Ghiglieri, TM Meyers, Over the Edge: Death in Grand Canyon, 1st ed., 13th rev., Flagstaff, AZ: Puma Press, 2006.
 REWeiss, Pregnancy & Childbirth, Labor and Birth with Twins: “more than half of twins will be born vaginally.”