Because I’m me, I’ve been doing the math on my bad luck. And because this is my blog, I figured I’d share it with you. If you hate math, this might be one to skip, but I find it to be a helpful perspective.

My question: Among all women who have been pregnant four times before, what is a typical outcome, and how common is my type of outcome?

Assumptions: I’ll assume that first-trimester miscarriage has a ~20% probability, since that seems to be in the middle of the 15-25% estimates. It depends a bit on week of gestation, but mine have been in the 6-8 week range, and I think 20% is probably about right for that gestational age; I also think first-trimester miscarriages at that gestational age are pretty typical. As for 2nd trimester losses, it depends a little bit. The overall risk is something like 1%, but the risk of losing a chromosomally normal fetus like I did is about half that, or ~0.5%. If I were being totally self-consistent, I’d make the probability of live birth ~79% and first-trimester loss ~19% to account for the ~2% of pregnancies that are lost in the 2nd and 3rd trimesters, but it won’t change my answer much so I’ll keep using round numbers for at least these initial back-of-the-envelope calculations.

**What is a typical outcome for a woman with four pregnancies? **

The highest-probability event in any pregnancy (other than mine, that is) is a live birth, with a probability of ~80%. The probability of having four live births in a row is (0.8)^4, or about 41%. So, fewer than half of women with four pregnancies will have all live births. That jives with my experience — most women I know with three kids had one miscarriage along the way. So let’s explore the probability of three live births and one miscarriage.

There are four ways to have one miscarriage in four pregnancies: either your first pregnancy can result in a miscarriage, or your second, or your third, or your fourth. So the overall probability of having one miscarriage among four live births is 4*(0.8)^3*0.2 = 41%. That means that just according to the typical probabilities, *80% of women who have been pregnant four times will have either one or no miscarriages, and it’s more or less a coin toss between those groups. *

**What about the other 20%?**

The other 20% are women who are less lucky. They might have had two or three or even four miscarriages, typically in the first trimester. But which fraction is which? The easiest to calculate is having four miscarriages in a row: (0.2)^4 = 1.6%. So, how unlucky do you have to be to have four miscarriages in a row, just by chance? Unluckier than 98.4% of other women. If you somehow manage to collect 100 women who have been pregnant four times in a room, you would expect about 2 of them to have had this outcome by chance.

But what about the other 18 women who had more than one miscarriage? Most of them will have had two miscarriages. There are six ways to do that (1st and 2nd pregnancy, or 1st and 3rd, or 1st and 4th, or 2nd and 3rd, or 2nd and 4th, or 3rd and 4th), so the probability is 6*(0.8)^2*(0.2)^2 = 15% So a whopping 3/4 of the 20% of women who had more than one miscarriage had two miscarriages, and there are only 5 women in our hypothetical room of 100 G4 women who had three or four miscarriages out of four pregnancies, just by chance.

That’s actually more than I might have expected. I mean, I don’t know very many women who have had four pregnancies, but of the ones I know, they mostly had one or two first trimester miscarriages along the way. I think the largest total number of pregnancies I know of in my normal everyday life (not counting blogland, which is a very biased sample), is a grad school mentor of mine who once shared that it took her six pregnancies to have her three kids. (I was appalled at the time, but now I’m 2/3 of the way to her total number of pregnancies and I only have one kid to show for it, so there’s that.) But the point is that if you somehow collect 20 G4 women in a room — this is the size of a typical seminar course that I might teach at my college — you would expect only one of them to have had more than two miscarriages just by chance.

**What about later losses?**

So far I’ve ignored 2nd and 3rd trimester losses, because they are so improbable that they make up a pretty tiny fraction of all pregnancy outcomes. For example, the chance of having one late loss out of four pregnancies is 4*(0.98)^3*0.02 = 7%. That’s not nothing, unfortunately, but it’s also fairly small — it’s about the same as the chance of having 3 or 4 first trimester miscarriages out of four total pregnancies. The more times you get pregnant, the more likely you are to have an improbable outcome like a late loss, alas. The good news is that for a typical woman, even if she gets pregnant four times, she has a 93% chance of never experiencing a late loss — and probably it’s actually significantly better than that, since I’m assuming that all pregnancies are equal, whereas the research shows that women who have had one late loss are more likely to have another, so in reality it’s almost certainly skewed so that women with generally poor reproductive outcomes account for a larger-than-chance share of the late pregnancy losses, and a truly typical woman is less likely to ever have a late pregnancy loss.

**So, how unlucky am I?**

Let’s explore the probability of my particular reproductive outcome: four pregnancies, one late loss, two early losses. We’ll assume that the order is random, although it might not be — for example, the adhesions from my first pregnancy could conceivably have contributed to my early losses in later pregnancies, or I could have some sort of weird immune-mediated thing that got worse after a live birth. But those are fairly speculative possibilities, so I’ll just assume that the order is random. In that case, the probability of having an outcome like mine (one late loss + two early losses, random order) is something like 12*0.02*(0.2)^2*0.8 = 0.8%. So, if you got 100 G4 women in a room, *maybe* one of them would have a history like mine, but maybe not. You’d need a thousand to get me some buddies for sure.

And I’ve also been generous in defining what “like mine” means. If you narrow the definition to the loss of a chromosomally normal fetus in the 2nd trimester (plus two early losses), that brings the numbers down by a factor of 4 to 0.2%, which means that I’d need a room full of 1000 G4 women to maybe have one friend who’d been through something similar. This thought experiment is also interesting because it brings the probability of having an outcome like mine below the threshold of 0.3%, which means that my outcome is 3-sigma bad, or that there’s a 3-sigma probability that my obstetrical history is not just due to bad luck, but rather to some other contributing factor that predisposes me to poor pregnancy outcomes. That’s significant enough to get you publication in a journal in my field (though not in all fields).

Now, of course, when you get down into the weeds of these small-number probabilities, there are a lot of outcomes that look similar. Another outcome that has a probability of 1-2 women in a group of 1000 G4 women is having two late losses and two full-term births, and you can add a bunch of different permutations that also give you similar answers. But the point is, by the time we get into the land of both late losses *and* multiple losses, we’re down in the tenths digits of the percentages, which is a fairly lonely land to be in. It’s also increasingly absurd to be told that your problems are due to “bad luck” and told that you should just try again — when you’re out in 3-sigma land, while it’s certainly true that your outcomes *could* be due to bad luck, the probability is low enough that it seems like any reasonable person with at least a slight grasp of statistics would want to do more investigation. It’s easy to say that investigation is a waste of resources when you’re talking about two first-trimester losses out of four pregnancies (roughly a 1 in 5 chance), but not when you’re talking about an outcome that only a few in 1000 or even 10,000 women will experience (since most women don’t get pregnant four times and therefore aren’t even represented in the above numbers — you actually expect overrepresentation of poor pregnancy outcomes in G4 women for exactly this reason).

So there you have it. I am so statistically significantly unlucky that it seems unlikely that my issues are due to random chance (i.e., they are probably more than just “bad luck”). However, I’m not as dramatically unlucky as I guessed going into this exercise (I guessed that I’d be 4-sigma unlucky, but I’m not that unlucky). So, that’s good news, I guess? The other good news is that I live in a time when the internet exists to connect me to all the other women having a tough time out in 3-sigma land, so it doesn’t feel as lonely as if I’d been a prairie mama trying to deal with this all in isolation, never knowing another woman who had been through something similar (waving at you, blog friends!). Though in that case I’d probably already be dead and/or completely infertile from the infection I contracted after my 2nd-trimester loss, or from hemorrhaging due to retained products of conception before the infection — huzzah for 21st century medicine! It’s keeping me alive, even if it’s not telling me how to keep my babies alive.