Odds of Walder Frey’s Trueborn Children’s Sexes

[DominusNovus]

Walder Frey has 29 trueborn children (we have no confirmed numbers on his bastards, so we have to set them aside), 22 sons and 7 daughters.  Now, unless he has a bunch of trueborn daughters that were stillborn or miscarried or otherwise not counted, something is weird here.  I ran the odds in a coin flip calculator and got a 1/344 chance of having that ratio of trueborn kids.

So, anything think there’s anything to read into this?

[elder brother jonothor dar]

It's acceptable to kill men, so when the Frey start dropping like flys it's less complicated having a lot of female heirs floating about.

[TMIFairy]

Oberyn Martell has eight daughters and zero sons - do the math for that

The dude in Pride and Prejudice scored 5:0 in the daughters:sons stakes - such things happen.

BTW - GRRM has a dude in the Iron Islands with 10 daughters and 2 sons. The sons were born last and are twins - talk about a fluke!

 

 

[Vaedys Targaryen]

I personally wouldn't think too much about it.

1. Sometimes in real life, these things happen; some couples will have an even number of sons and daughters, some will have more girls than boys, some will have more boys than girls, some will have only girls and some only boys. These things happen and there is nothing strange about it.

2. GRRM is the author of the series and he can make Old Walder have as many sons and daughters as he likes. Maybe it's for plot convenience or maybe he just straight up wants to make it so. Nothing strange about it.

[falcotron]

2 hours ago, TMIFairy said:

Oberyn Martell has eight daughters and zero sons - do the math for that

That's actually more likely, not less—256:1 instead of 344:1.

But really, we see dozens and dozens of families, and even more if you look at the family trees, and the odds of having at least two outlier families are very high. Just like it's unusual for someone to be 5'2" or 6'6", but it would be even more unusual if nobody in the story were that far from average.

[Angel Eyes]

One word: meiosis.

[Philokles]

The odds of 15:14 must be pretty small too when n you have that many combinations. 

[TMIFairy]

3 hours ago, falcotron said:

That's actually more likely, not less—256:1 instead of 344:1.

Wow!

I feel dim witted out of a sudden ...

[The Commentator]

5 hours ago, Vaedys Targaryen said:

I personally wouldn't think too much about it.

1. Sometimes in real life, these things happen; some couples will have an even number of sons and daughters, some will have more girls than boys, some will have more boys than girls, some will have only girls and some only boys. These things happen and there is nothing strange about it.

2. GRRM is the author of the series and he can make Old Walder have as many sons and daughters as he likes. Maybe it's for plot convenience or maybe he just straight up wants to make it so. Nothing strange about it.

True

[Jon Fossoway]

Can't forget Jonos Bracken and his endless stream of daughters.

[Angel Eyes]

12 minutes ago, King Merrett I Frey said:

Can't forget Jonos Bracken and his endless stream of daughters.

And Tytos Blackwood's six sons and one daughter.

[DominusNovus]

3 hours ago, Horse of Kent said:

The odds of 15:14 must be pretty small too when n you have that many combinations. 

7:1

Also, with all these examples everyone is listing, they’re leaving out sample sizes in their considerations. Having a large skew on a large number of samples is much less likely than a large skew on a small number of samples. Thats what makes Walder Frey unique.

[Ferocious Veldt Roarer]

13 hours ago, DominusNovus said:

Walder Frey has 29 trueborn children (we have no confirmed numbers on his bastards, so we have to set them aside), 22 sons and 7 daughters.  Now, unless he has a bunch of trueborn daughters that were stillborn or miscarried or otherwise not counted, something is weird here.  I ran the odds in a coin flip calculator and got a 1/344 chance of having that ratio of trueborn kids.

So, anything think there’s anything to read into this?

No. Because I don't think GRRM ran the same calculator. He just needed a huge bunch of Walder Juniors.

[Adam Yozza]

No because you're thinking about it wrong. The probability of getting that exact combination of sons and daughters 1/344, yes, but that is basically just useless theory because everytime his wife gets pregnant there is a fifty-fifty chance of it being born a son. The sex of the previous child does not affect the chance of the next one being male.

So no, it's perfectly plausable. Just like how Jonos Bracken has only trueborn girls and a natural son. Or how Tytos Blackwood had six sons and a daughter. Or like how Daemon Blackfyre had at least six sons and only one daughter (that we know of). There is nothing more to read into it.

[DominusNovus]

1 hour ago, Adam Yozza said:

No because you're thinking about it wrong. The probability of getting that exact combination of sons and daughters 1/344, yes, but that is basically just useless theory because everytime his wife gets pregnant there is a fifty-fifty chance of it being born a son. The sex of the previous child does not affect the chance of the next one being male.

So no, it's perfectly plausable. Just like how Jonos Bracken has only trueborn girls and a natural son. Or how Tytos Blackwood had six sons and a daughter. Or like how Daemon Blackfyre had at least six sons and only one daughter (that we know of). There is nothing more to read into it.

I'm sorry, but you're not correct in your analysis of the statistics.  Again, sample size matters.  Having a coin land heads up twice in two flips (4:1) is far more likely than having it landing heads up 20 times in 20 flips (1.05 million:1).  When you have a large enough sample size, if you've got a 50/50 split on each sample, your results should trend closer and closer to 50/50, on average.

Odds of Jonos having 5 daughters out of 5 kids? 32:1

Odds of Daemon having 6 sons out of 7 kids? 18.29:1

Garold Goodbrother, 3 sons out of 15? 72:1

These are a full order of magnitude more likely than Walder Frey's 22 sons and 7 daughters.  Just pull up any coin flip calculator and do the math yourself, if you don't believe me.  That said, I did find someone to beat Frey's 344:1 odds: Quellon Greyjoy, with 9 sons out of 9, the odds are 512:1  I think he has the crown, unless anyone can find someone with 10 or more children all of the same sex.

1 hour ago, Ferocious Veldt Roarer said:

No. Because I don't think GRRM ran the same calculator. He just needed a huge bunch of Walder Juniors.

This is likely the correct answer, but it is odd enough to make note of, I think.

[Deepbollywood Motte]

I'm not an expert in statistics but this is how I understand it.

Every time a woman is pregnant the odds of it being a boy or girl is roughly 50:50, how many boys or girls came before doesn't really matter so every combination of sons and daughters is just as (un)likely if you have 29 childeren.

[DominusNovus]

30 minutes ago, Deepbollywood Motte said:

I'm not an expert in statistics but this is how I understand it.

Every time a woman is pregnant the odds of it being a boy or girl is roughly 50:50, how many boys or girls came before doesn't really matter so every combination of sons and daughters is just as (un)likely if you have 29 childeren.

Incorrect. What is equally unlikely is a specific sequence: BBBBG is just as likely as BBBBB, but 4 boys and and 1 girl is more likely than 5 boys.

[elder brother jonothor dar]

4 hours ago, Deepbollywood Motte said:

I'm not an expert in statistics but this is how I understand it.

Every time a woman is pregnant the odds of it being a boy or girl is roughly 50:50, how many boys or girls came before doesn't really matter so every combination of sons and daughters is just as (un)likely if you have 29 childeren.

Partly right the chance of Walder having a boy with his new wife is statistically 50:50 as all previous children are irrelevant.

However for him to have boys to out number girls 3:1 for such a large sample is not 50:50.

So what comes next will always be 50:50 but the total spread will be the cumulative odds of 344:1 in this case, so for every 344 fathers with 29 children 1 will produce the same results as Walder (of course this is an avarage in itself and Walder has proved you can beat the odds)

[falcotron]

5 hours ago, Deepbollywood Motte said:

I'm not an expert in statistics but this is how I understand it.

Every time a woman is pregnant the odds of it being a boy or girl is roughly 50:50, how many boys or girls came before doesn't really matter so every combination of sons and daughters is just as (un)likely if you have 29 childeren.

People get confused by this stuff because we have bad intuitions about probability. You must know that 15 sons out of 29 is more likely than 29 sons out of 29, but what's probably thrown you is one of two things.

First, of course the odds of exactly 22 are pretty low, but the odds for everything are pretty low, and yet if you add up all the unlikely possibilities, it's not that unlikely that you'll get one of the unlikely ones. Having at least 22 daughters, or 23 sons, etc. would all be at least as unlikely, and if we add them all up…

But if you do that, the odds are still only 1/123—a lot better, but still less than 1%.

Second, of course the odds of exactly 22 are pretty low, but no outcome has very good odds when there's this wide a range. Even 15/29 wouldn't be a good bet, right?

And that's true as well, but it's around 1/7—which is a whole lot better than 1/355, or even 1/123.

[elder brother jonothor dar]

6 hours ago, falcotron said:

People get confused

Lol I had to read your post twice to get my head around it