# On the likelihood of having all three of your kids share a birthday

In his Guardian column yesterday, Dr Ben "Bad Science" Goldacre schooled us (and the Daily Express) on some basic statistical numeracy:

Often one data point isn't enough to spot a pattern, or even to say that an event is interesting and exceptional, because numbers are all about context and constraints. At one end there are the simple examples. "Mum beats odds of 50 million-to-one to have 3 babies on same date" is the headline for the Daily Express on Thursday. If that phenomenon was really so unlikely, then since there are less than a million births a year in the UK, this would genuinely be a very rare event.

Their number is calculated as 365 x 365 x 365 = 48,627,125. But in reality, of course, it's out by an order of magnitude: one in 50 million are the odds of someone having 3 siblings sharing one particular prespecified birth date that the editors of the Daily Express sealed in an envelope and gave to a lawyer 50 years ago. In reality there is no constraint on which day the first baby gets born on, so after that, the odds of two more babies sharing that birthday are 365×365=133,225. And they might even be a bit lower, if you two feel friskier in winter and have more babies in the autumn, for example.

Then there is the context. Living on your street, hanging out with the people from work, it's easy to miss the sheer scale of humanity on the planet. In England and Wales there were 725,440 births last year. From the ONS Statistical Bulletin "Who is having babies" 14% were third births, and another 9% were fourth or subsequent births. So there are 102,000 third children born a year, 167,000 third or more-th children, and if we include the rest of the Kingdom there are even more, so on average, three shared birthdays will happen once or twice a year in the UK (although to be written about in the Express it would need to be a birth within a marriage, making 55,000 chances a year, or once every two years)

Guns don't kill people, puppies do

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1. rebdav says:

or cheat and have triplets

2. Anonymous says:

My mom had both of my brothers on the same day, but not me. In both cases she started labouring the day prior, which is my grandfather’s birthday. I was born on a cousin’s birthday, which is also our great-grandfather’s birthday. Needless to say, there’s a lot of weird birthday sharing in our family.

3. Michael_GR says:

Since there is quite a gap between their kids’ birth years, and assuming they did not abstain from sex in the intervening years, it’s safe to say they were using contraceptives. Although they claim to not intentionally set out to have all their kids’ births at the same date, they must have planned for about the same season, at least. This brings the chances down even further.

4. morcheeba says:

I think “seasonal friskiness” could be narrowed down even further… my sister and I shared the same due date, which was 9 months after a certain major holiday. Biology conspired to put 2 weeks between us, which is a tighter distribution than the norm of 13 weeks.

5. Anonymous says:

Ah, Bull. You can elect to have a child born just about any date you want. Doctors induce labor all the time, and if it’s going to be a C-section there is even less of an issue. It’s not too hard to arrange for full term to be about the date you want. That being said, you’d have to be a pretty sick bastard to want to do that.

6. Wirelizard says:

“although to be written about in the Express it would need to be a birth within a marriage”

Excellent subtle snark, and an interesting stats lesson. Hey, I was both amused and educated! Excellent!

7. Anonymous says:

And what’s the likelihood of this being posted on my birthday?

8. Nylund says:

Entirely agree. Before I got too far in the post, I was already thinking, “but the first date doesn’t matter!” which already makes it 365×365 AS AN UPPER BOUND (or should that be lower bound?). All sorts of behavioral and seasonal effects should be taken into account as well that could significantly change the probability.

Plus, there is the story of my great aunt. Her first two children were both born on Christmas day. For her third child, she did everything she could regarding every scientific, pseudo-scientific, and folkish thing she could think of…have sex, run up and down stairs, etc. to have that third baby on Christmas as well! (and it worked).

And, as you point out, when events happen in very large numbers, rare events will happen. Maybe winning the lottery is a 1 in a million chance, but get 10’s of millions of people together and its going to happen to some of them (and it does!).

9. markaa says:

I have 2 daughters born on the same day 7 years apart. The 2nd, our 7th born on the 7th of the 7th on our other daughter’s 7th birthday. Also 2 sons born within a few hours of being exactly 14 year apart.

10. Marchhare says:

So, then what is the probability of two people being born on the same day? It’s not 1/365*365. This model suggests that the probability of having three people born on the same day isn’t 1/3(365).

1. japroach says:

huh, two would be 1/365.

2. sapere_aude says:

The probability that two randomly selected people will share the same birthday is approximately 1/365.25 (the .25 is due to Leap Year, and the “approximately” is due to the possibility that birthdays may not be randomly distributed across the population). The probability that three randomly selected people will share the same birthday is approximately (1/365.25)*(1/365.25).

But the probability that, in a group of size n, at least two people in that group will share the same birthday is 1-((365!)/((365^n)*(356-n))). Yeah, that’s a bit hard to follow; but what it basically means is that in a group of at least 23 people, there is a 50% chance that at least two of them will share the same birthday; and in a group of at least 57 people, there is more than a 99% chance that at least two of them will share the same birthday.

11. Anonymous says:

The other commentators are correct, biology has made women tend to get pregnant the same time of year and be due the same time of year (for themselves, not necessarily in correlation to other women). In a woman’s set of progeny most of her offspring will be born around the same time of year. Some women are better timed, like caribou.

12. Anonymous says:

Good remark from Nylund; actually 365×365 is not an upper bound, but an uninformative prior. The true probability distribution should take account of strong biases (such as, here, the mother aiming at a specific date after the birth of her first child). Which makes the true probability sharply peaked around the “target” date. And subsequently makes the odds much less impressive :)

13. Anonymous says:

1 in 8000 births result in triplets. Higher if you factor in fertility treatments. So this should happen at least 30 times a year.

14. oschene says:
15. lewis stoole says:

what are the odds of one of the kids being the anti-christ?
now, what if the anti-christ is female?

16. Michael_GR says:

Nylund @6 – Did your great aunt’s kids get both a Christmas present and a birthday present on their (and Jesus’) birthday? Or did she go through all that just so she could skimp on buying presents?

17. kristofer says:

we came really close with two of our kids… Their birthdays are 1-22-01 and 1-21-02

18. Anonymous says:

A friend of mine was complaining about a novel that was so filled with unlikely coincidences that his credulity was shot. He said that you can have ONE amazingly unlikely coincidence in a book because THEY HAPPEN and after all, that’s what the book is about.

19. Anonymous says:

Also, the odds depend on how many kids she has. If she has six kids (assuming no twins,) the odds are about one out of 6661 that three will have the same birthday.

20. Marshall says:

My roommate, her mother and her grandmother all share the same birthday. I’ve always thought that was somehow amazing and as a perpetual birthday forgetter, convenient.

21. Clemoh says:

In our family, my two cousins, who are ten years apart(And the eldest and youngest siblings), share the same birthday. This is also the same birthday as their father. Another has the same birthday as her mother, and still another shares her birthday with me: same month, day and year!

22. Bryan Price says:

I’ve got four (step, not that it matters really) kids with their birthdays one week apart.

Two sets of twins, 5 years apart.

The funny(?) thing about it is that the conception date for both sets is their father’s birthday! The ONLY two times that those two had unprotected sex. Go figure.

23. aixwiz says:

Here’s a good one:
My brother, my father and my father’s father were all:
1. Born on October 14th
2. Born on a Monday
3. And were the first son in their family

Don’t believe me; check out “Ripley’s Believe It Or Not” 19th edition, page 109.

24. ericreiss says:

I have 3 cousins, all siblings, no twins who all have a birthday today. They are their only three kids, and oddly enough, their anniversary is 9 1/2 months ago. All natural births also, no cheating c-sections.

25. Anonymous says:

Your statistics seem to assume that a woman can get pregnant any day of the month, which is incorrect. If she’s on a regular cycle, she’s only ovulating a short time during every 28 day increment. That window of fertility, not your intentions at romantic babymaking, is what really decides if the pregnancy starts or not.

26. Anonymous says:

My uncle is born on December 8. My aunt (his sister), Jan 8. My boyfriend, Feb 8. My grandfather’s companion, March 8. My cousin, April 8. My sister, May 8. My childhood best friend, June 8. Another close friend: September 8. I’m looking for ways to complete the set :)

27. klossner says:

“Please don’t let them have my birthday” pleaded my eight-year-old as I rushed my wife to the hospital. But the twins were born that day, three months early.

So that each might have a special day all to herself, we celebrated on the anniversary of the day each twin came home from the hospital. That spread the days out to one per month.

28. Anonymous says:

This is the crummiest statistical analysis I’ve ever read. In order for it to be truly probabilistic, you have to eliminate confounding personal variables such as menstrual cycle and frequency of intercourse.

The original calculation would be sound if an opportunity for conception occurred every day of every year, but it simply doesn’t. First of all, because a woman cannot conceive a child on everyday of every year. Secondly, because couples aren’t having sex everyday of every year.

The date of conception often seems random, but it’s not and often has more to do with personal choices and circumstances.

29. Scary_UK says:

Me and my sister have the same birthdate 2 years apart.

As kids we always thought this was an odd co-incidence but then it occurred to us that our birthday was at the end of June and our parents anniversary was at the end of October!

My son was born on my birthday last year. 9 days early. I have friends who are 5 years and 5 hours apart and a student whose brother is 2 year and 1 hour younger.

The birthday problem says chances are 99% that if 57 or more people are together 2 of them will share a birthday. When I started my job there were 45 people working there. 6 of us shared birthdays with one other person (6 people = 3 birthdays). Also, we had a disproportionate number of birthdays in Sept., Mar., and May. Even through changes in staffing those are our 3 biggest months.

31. Shelby Davis says:

My second sister’s (early September) due date was the same as my first sister’s birthday, but she ended up four days late. And yep, I never thought about it before reading this post, but my parents’ anniv is indeed at the very end of December. (and come to think of it, my brother’s bday is the start of October. Early-to-bed winters, indeed. And I, as the sole Spring birth, could be explained by being my parents’ first, and therefore originating when they were newlyweds and more frisk–gah, statistics giving me more inferences on parents’ sex lives than I ever wanted!! Make it stop!

32. Anonymous says:

couldn’t the odds be tipped in their favor if they consciously became pregnant on the same night as the previous one, making the likelihood of the next baby being born on the same day drastically higher?

33. Anonymous says:

I share a birthday with my two-year-younger sister, and that’s considered surprising to most people, even though the odds really aren’t all that bad.

34. takeshi says:

The odds of a person being born on any given day is approximately 1 in 365.25. It doesn’t matter how many siblings you have who share the same birthday.

When we’re talking about one sexually active couple, it’s never going to be completely up to chance. It’s not the same as asking, “what are the odds of 3 siblings being picked by a blindfolded stranger from a group of 1095.75 people?”

The couple’s sexual activity (or lack thereof) is obviously a factor. The probability of three siblings being born on the same date is not the same as that of three randomly selected people. If a couple only has sex once a year, in February, the odds of three children being born in February are infinitesimal. However, the odds of their three children being born on the same day in November increase significantly.

35. Aurini says:

Something that should be pointed out to more people is that winning the lottery (at 1 in 14 million odds) is an event so improbable that it effectively *never* happens.

Compare, say, to your probability assessment of aliens blowing up the sun (I take a rather cynical view of the Drake Equation, so personally I’d probably rate this one lower than winning the lottery)? What about the probability of the LHC destroying the earth? I’m sure that’s higher than 0.0000000714.

When I point this out to people they always insist that “Well, derp, my coworker’s cousin once won the lottery…” Selection Bias! Of course you’ll ‘know’ somebody who already won, but out of the two- or three-hundred people you’re actually aquainted with already, none of them are ever going to win.

I trust my life to worse odds every time I drive on the freeway.

36. Anonymous says:

My parents have children born in every month. Two were born in the same year- one in January the next in December. Two share a birthday. Two were born a year and a day apart. My 7th sister was born on my dad’s birthday- a nice gift- and he was born on his aunt’s. That aunt considered my Dad a gift to her and my sister a gift from him.
We have several birthdays on holidays and now with spouses and grandkids the doubled and tripled up birthdays are growing every year.

37. Anonymous says:

I have a friend who had her two children, on her birthday, and my daughter, niece, friend, and cousin’s adopted daughter all share the same b-day.

38. Miss Cellania says:

My former boss had four children, each several years apart, and three had the same birthday. We all joked that the date must be nine months after their wedding anniversary.

39. Anonymous says:

I am not a mathematician, but it seems that (a) you cannot apply 365x365x365 to this ‘coincidence’, since the parents conceived on a certain date and that would place the normal birth approximately 270 days away. It’s feasible that birth may happen the day after conception(not resultant in a healthy baby, obviously, nor a date that the parents might celebrate year after year) but could it also happen 365 days from conception? Unless there is absolutely no control over the results, pure math doesn’t work here; and (b), labor can always be induced.

40. Courtney says:

My Nana and her brother (fraternal twins) and her older (fraternal) twin sisters were born on the same day, 5 years apart.

41. theturtle says:

Dear humans:

just please stop making more humans, we have far more than we need already. When we need more, we’ll let you know.

Thanks…

Earth

42. Anonymous says:

Also, consider that the female reproductive cycle is in fact, cyclical – therefore one would naturally expect a higher degree of periodicity within births. Of course, most armchair statisticians ignore these things.

1. Anonymous says:

Well, over a sufficiently large population (of women), I guess “fertility days” shall be uniformly distributed (law of large numbers, or something like that)

For only one woman, I’m not sure that the fertility is predictible one year after. I heard menstruations may often be irregular.

43. trevoranderson says:

@30 True enough that there are other factors that could be taken into account to get more accurate chances, but that doesn’t make the figure totally invalid.

Suppose we have a bag with two red balls and two white balls in it, and my friend and I each draw one without looking and keep it closed in our hand. Without knowing what my friend pulled, I say my chance of drawing red are 2/4=50%. But if my friend shows me he pulled red, then I now know my chances of having a red in my hand are only 1/3=33%. I open my hand and there’s a red and now I know it was actually 100% all along.

In general, you can think of “randomness” in everyday life as an expression of our level of knowledge in a given situation. Is there a certain minimum level of knowledge where it’s fair to make a probability statement? I don’t think so. How would you even judge that? All you can say is “based on this and this, I estimate X probability”. That’s what the original poster did, nothing wrong with that.

44. Samantha says:

Obviously this post is about having birthdays on the same days, but I want to put my late grandmother up for honorable mention. With two different fathers and a 20 year span amongst them, my grandma managed to have my mom and her two sisters on consecutive days. The oldest was born Feb 1, the middle child was born 7 years later on Jan 31, and 13 years after that (by my grandfather), my mom was born on Jan 30. I think this definitely speaks to the fact that people have tendencies to do things at the same time!

45. Anonymous says:

Lets talk statistics.

Your basic assumption (as you even point out yourself) is wrong. You assume that having a baby born on any given day is equally likely. That’s like saying that winning the lotterey carries a 50% chance, since you can either win or lose.

If you consider the odds of a woman trying to have three children in a row (Her trying means that she’s doing everything possible each day, then we can actually make the rough assumption that the propability is the same each day), then the propability comes out much higher simply due to the fact that the pregnancy period takes away a large amount of the year from consideration.
A woman i typically pregnant for 38 weeks, or 266 days.

If we define n as the number of days one has to try to get pregnant before success, then the probability is 0 if n < 99 (which is 365-266 ) but when n is above or equal to 99, the probability is just 1/n^2 which has the upper bound of just 1 in 9801. The lower bound for n is ofcause pushed lower for every day the womans waits before trying to get pregnent, so if she waits four and a half weeks the upper bound could be as much as 1 in 1000. Ofcause then you have to figure out what the propability is that a woman fits this pattern of having three children "in a row". Anyways, the point is that the statistics are much more influenced by the individual person and their patterns, which lead to the propability of having a child on any given day, which for most people will be anything but 1/365 for each day. Don't spend your money on that 50% chance of wining the lottery, as we know tough there are only two options, they carry wieldly different propabilities.

46. Anonymous says:

Well. I had both of my daughters on MY birthday. It was never planned and I actually unfortunately had a few miscarriages in the mix. 28 hour labour with my first which lead to an emergency cesarean and my second decided to come 10 days early NATURALLY. Still blows me away and I have to say after just sharing OUR birthdays a month or so ago… it’s goin g to be interesting in our household in a few years.

47. Anonymous says:

My sisters and I wasn’t born on the same day, but we all were born on the 23rd of the month we were born, my sister had her son on her birthday so another 23rd, my maternal Grandmother was also 23rd and I have a second cousing born on the 23rd of a month too…

48. Anonymous says:

The majority of women in any one populated area ovulate around the same time. This is much more noticeable if you break it down to social groups. A woman and her girl friends who spend a lot of time together likely all ovulate within a week of each other. Research suggests this is due to a primal instinct to compete for mates and produce viable offspring. Someone on birth control who’s “spotting” or “bleeding through” is probably experiencing this adjustment where their body is trying to match the reproductive cycle of another female they spend a lot of time with.

Funny, but unfortunately very true. It’s also a factor and probability reducer in the equation.

49. Anonymous says:

My birthday is August 18, my sisters is August 20th, and my brothers is August 22. What are the coincidences of that? haha

50. Anonymous says:

My parents had three of us on the same day but different years. My older sister and younger brother and I were all born November 10. I asked my dad once how they managed to have three of us on the same day and he quipped “I don’t know, but every February your mother would send me away for a month”. We may have fought against it when we were younger, not wanting to share anything, but as we’ve learned, it is a terrific story to share whenever our birthday comes around.

51. Anonymous says:

My husband and his first wife had their first child, a boy, who was born on my husband’s birthday. Two and a half years later, their baby girl was born on her mother’s birthday. (No planning, no C-section, etc.) They divorced 6 years later, he was granted custody of both kids, we met and married, raised his children, and had one child together………no, not on anybody else’s birthday!

52. Anonymous says:

hi, i gave birth 2 my little boy nov 12 2008 he was 2 weeks overdue! My little girl was born nov 12 2010 10 weeks early! Me and my husband moved in 2gether nov 12 2005 and got engaged nov 12 2006 my dear grandfather died nov 12 1990 WIERD!

53. Anonymous says:

My birthdy is 8 20, my sisters is 8 18, and my brothers is 8 22

54. Anonymous says:

My son was born naturally on my birthday, which was also his due date. I cannot find any statistics on a child being born on its due date which is also the birthdate of the mother. Has anyone ever heard of this or am I the first??

55. Anonymous says:

I have 3 kids in all My youngest and oldes are both girls and share the same B-Day may 28th and were both born on a Thursday, were 11 years apart and if my youngest would have been born 11 minutes later it would have been exactly 11 years apart. My son who is the middle child shares my cousins B-day September 10th and my 2 girls also share their Great Great Grandmother’s B-Day.

My youngest was May 28th 2009- hers sister’s B-day
Borna at 2:24 Pm(I was born 2-24-1976)
and she weighed 6 lbs 7 oz- the same as her great uncle.

56. Sally says:

Well, if you or ANYONE could figure THIS amazing coincidence of same birthday’s I would be thankful, and pass this statistical chance fact to my little ones. We have 5 children. One was biological now age 16. Born August 2nd. Our next child is adopted through Foster care (reminding that we have no control over a baby being placed to us by the Agency and cleared for adoption) She is now 3 and her birthday is August 25th. Our next child also adopted through Foster care is ALSO 3 yrs old, and his birthday is THREE days later on August 28th! Now it gets interesting….we have our twin babies who are now 9 months old. A Boy and Girl…ALSO foster care and pending adoptions to us soon! THEIR BIRTHDAY’s are the same day as our Daughter AUGUST 25th!!!! HOW CAN THAT BE EVEN CALCULATED ON THE CHANCES????? If anyone could figure it out and let me know -I would be very thankful!