Infertility math*

This post was primarily inspired by a recent, lovely post by Jane at Mine to Command who confronted the myth that stress causes infertility. She delves into the medical literature on the subject, so I won’t provide my own (undoubtedly less eloquent) rehashing of what she’s said there. Go read it! Then come back, if you like.

The myth that stress causes infertility is a pervasive one. And, its logical consequence – namely, that infertiles should “Just relax, and you’ll get pregnant – has lead to a laundry list of charming little chestnuts of advice including:

  • Just adopt, and you’ll get pregnant.
  • Go on vacation, and you’ll get pregnant.
  • Get drunk, and you’ll get pregnant.
  • Don’t try so hard, and you’ll get pregnant.

and so on…

This myth originated – and continues to be fueled – by the observation that indeed many infertile couples get pregnant when they stop trying.

Although I’m not a medical practitioner and haven’t consulted the scientific literature on this particular topic, my intuition (aided by some basic mathematical understanding) tells me that this observation is probably true: many infertiles do get pregnant when they “aren’t actively trying”.

Before you chase after me with torches and pitchforks, please let me explain…

While I do think that the probability of getting pregnant while not “trying” is significant (in some cases rivaling the probability of getting pregnant through medical intervention), the often-touted “logical consequence” of this observation – that infertiles should stop trying to get pregnant…in order to get pregnant – is complete and total hooey!

I’m a chemist, but I nearly minored in math. I’m particularly grateful that I took statistics (both math stats and biostatistics), which comes in quite handy in situations like this…

So, why do so many couples get pregnant when they aren’t actively trying?

As Jane pointed out, this is kind of a silly question. Anybody who is having sex without birth control is, on some level, trying to get pregnant. So immaculate conception and birth control failures aside, everyone who gets pregnant is technically trying. But any infertile knows that there’s a wide spectrum of “trying”, all the way from “pulling the goalie” (aka unprotected intercourse) to spending tens-of-thousands of dollars for the privilege of being poked with needles, pumped full of hormones, subjected to minor and/or major surgery, and violated on a regular basis by an ultrasound wand, among other things…

Statistics provided by reproductive endocrinologists – the infertility experts – tell us that our odds of conceiving are significantly increased by all these interventions. Consider the following per-cycle odds of conception for several common interventions:

Intervention Per-cycle odds of conceiving** Source
timed intercourse 5%
natural cycle IUI 5-10%
medicated IUI Up to 20%

I couldn’t find any odds for “not trying”, but I think it’s safe to say that they would be less than 5% per cycle.

So, how on earth is it possible that so many infertile couples get pregnant after they’ve stopped trying, even though their odds are so much less – more than 9 times less compared to IVF?

The key words here are per cycle. The odds, per cycle, of success from IVF are nine times that for timed intercourse (and >9 times that for ‘not trying’). But how many cycles of IVF do people actually do? Looking around the blogosphere, I can find lots of examples of people who have done IVF two, three, four times. But at over $10K a pop, few people have the financial means (or an IVF clinic willing to risk hurting its SART stats) to do many more cycles than that.

On the other hand, an infertile couple might have 5-, 10-, 20-years of “not trying” to get pregnant. For a woman who ovulates regularly every 28-days, that corresponds to as many as 65, 130, or 260 cycles of not actively trying to get pregnant.

So, how do we do the math to figure out the odds of getting pregnant by “not trying” versus using a technology such as IVF?

Let’s take an example of a couple that tried IVF three times unsuccessfully, adopted a child, then had unprotected sex for ten years:

First, let’s calculate their odds of a pregnancy resulting from three rounds of IVF. (In statistics, it’s actually slightly easier to calculate the odds of something not happening, and then to convert that to the odds of that thing happening…)

  • According to SART, the average odds of a pregnancy resulting from one cycle of IVF for a woman under 35 are 46%. We can express this value as the decimal 0.46.
  • That means the odds of not getting pregnant from one IVF cycle are 100-46 = 54% or 0.54.
  • The odds of not getting pregnant after two rounds of IVF are 0.54 x 0.54 = 0.29 or 29%.
  • The odds of not getting pregnant after three rounds of IVF are 0.54 x 0.54 x 0.54 (or 0.54 to the third power, 0.54^3), which equals 0.16 or 16%.
  • Now, to get the probability of a pregnancy resulting from three IVF cycles, we just subtract from 100% the probability of not getting pregnant: 100-16 = 84%. (Not bad odds! It seems our hypothetical couple – like many of us – was on the unlucky side of these stats…)

Now let’s calculate the odds of getting pregnant from ten years of unprotected sex.

  • For the sake of argument, I’m going to estimate that the couple’s per-cycle odds of pregnancy are a mere 1% (0.01). (Given that the per cycle odds for infertile couples practicing timed intercourse is estimated at 5%, I think 1% odds for “not trying” is actually pretty conservative…as long as the couple is having sex…) If the odds of a pregnancy are 1%, that means the odds of not getting pregnant are 99% or 0.99 per cycle.
  • The odds of not being pregnant after two cycles are 0.99 x 0.99 = 0.98, or 98%.
  • The odds of not being pregnant after three cycles are 0.99^3 = 0.97. In other words, there is only a 3% chance of a pregnancy resulting from three cycles of “not trying” – not even close to the 84% odds from three cycles of IVF.

Like interest on a long-held bank account, things start to get interesting as these paltry odds compound over large numbers of cycles…

  • The odds of not being pregnant after 13 cycles (one year) are 0.99 to the thirteenth power (0.99^13) or 88%. That means the odds of a pregnancy resulting from those 13 cycles is 12% (100 – 88 = 12). In other words, more than one tenth of “infertile” couples will be pregnant after a year of “not trying”. (Thereby supplying ample anecdotal “evidence” for annoying fertiles to misinterpret and hold up to their infertile friends…)
  • The odds of not being pregnant after 130 cycles (0.99^130) are 0.27, or 27%.

In other words, after ten years of “not trying”, this “infertile” couple had a 73% chance of achieving at least one pregnancy. (And remember, that pregnancy could occur randomly at any time during the ten years of not trying…)

How do you suppose most people interpret this series of events?

The facts: a couple failed to get pregnant from three rounds of IVF, adopted a child, and then got pregnant after a few years of not actively trying to get pregnant.

I can think of a couple of likely interpretations:

“After becoming parents through adoption, they were finally able to “just relax” and get pregnant!”

“In adopting, they were able to resolve the karmic imbalance that had previously interfered with their attempts at pregnancy!”

Nonsense! The real reason is far less romantic:

Over the course of many years of regular unprotected sex (albeit without officially “trying”), chances are that at least once, healthy sperm would meet with healthy egg at the right time to fertilize, and travel through the fallopian tube to find a uterus in just the right condition for implantation.

As Jane would say, “it was just their time.”

For women with diminished ovarian reserve (like me) the odds of conceiving by IVF are far below the 46% average I used in the example above (see this post for the depressing stats). Yet it’s not known how significantly DOR affects our chances of success through natural conception (which only requires one good egg each month…) In such cases, it’s easy for me to believe that the odds of conceiving from 100+ cycles of “not trying” could exceed the odds of conceiving from a handful of IVF cycles!

Am I saying we should all “just relax” and abandon assisted reproductive technologies?

No way! I can think of several good reasons to take a more aggressive approach:

  1. I don’t want to wait ten years to have a decent chance at a pregnancy! (Since I didn’t start until 33, I don’t even have 10 years of trying left in my old lady ovaries anyway…) I want my child yesterday! I want to change her diapers, not ask her to change mine. ART gives me the best odds of a child soon!
  2. Unlike in my simplified example, our odds of success are not static. My odds of pregnancy with my eggs – whether via ART or natural conception – are decreasing every month. With that fact hanging over me, it’s hard to justify waiting around for years for a natural conception. I can always try (or “not try”) for a natural conception after trying other family-building options (IVF, adoption, etc.) But ten years from now, if natural conception doesn’t work, I can’t go backwards and do IVF (at least not with my own eggs, which will have long dried up by then…)
  3. It’s not an either/or situation. If the odds of a pregnancy in my hypothetical example were 84% for three rounds of IVF, or 73% for 130 cycles of “not trying”, the total probability of a pregnancy – given that this hypothetical couple used both methods – was an almost unbelievable 96%! (1 – 0.16 x 0.27 = 0.96). Carefully timing intercourse instead of “not trying” should increase the odds further. Trying a combination of aggressive treatment (using ART) and regular unprotected intercourse will give me the very best odds of a biological child.
  4. There’s comfort in knowing that I’ve “tried everything”. If things don’t work out, and I end up on the unlucky end of all these statistics, at least I won’t wonder whether I might have been a genetic parent, “if only I’d tried X…” I’d rather go ‘all in’ now, and then move on to the next family-building option (or child-free living) without regrets.

As you’ve probably figured out by now, my plan is to continue with high-tech treatment…and to break out the Marvin Gaye around ovulation time every month in between!

It’s a plan that will mean a lot of two-week waits,…

a lot of peeing on sticks,…

and charting temps,…

and reading signs…

You’ll understand if I get tired of all the effort and decide to “take a break” and skip the meticulous timing for a few months…

And if, by chance, I happen to get pregnant that cycle,…

For heaven’s sake, DON’T use me as an example of how you “know this girl who got pregnant as soon as she stopped trying!”


*I can’t write about Infertility Math without acknowledging this brilliant post by Aramis at It Only Takes One.

**Odds shown are for infertile couples (that is, couples who have been trying unsuccessfully for at least a year) in which the woman is less than 35 years old. Other factors can dramatically change these odds. For example, when fertile couples are included, the per-cycle odds are much higher – as high as 25% per cycle for timed intercourse. For older women, the per-cycle odds are lower in each case. Also, note that these stats show approximate pregnancy rates. The live birth rates are (sadly) lower due to miscarriage…

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  1. I read somewhere that the practice of considering a couple infertile after one year of unprotected sex is actually causing people to rush to fertility treatments and that it more often takes 2 years of unprotected sex. So there is definitely a likelihood of getting pregnant between IVF cycles.

    I’ve tried not to get too wrapped up in the numbers after I realized my insane logic of ‘if I had a 10% chance with IVF’ then I’d probably have to do 10 cycles was extremely faulty.

    • You’re right about not getting wrapped up in the numbers. 95% odds of something are meaningless if I fall into the unlucky 5%! And, of course, all these calculations assume that each event is independent and not influenced by the earlier result…which is not true for infertility…

      But I found it therapeutic to use math to help explain why a person getting pregnant while “not trying” should NOT be used as “evidence” to support recommending “not trying” as a strategy for getting pregnant…

  2. Oh how my head spins…. but what you said makes sense. There’s bound to be some infertile couples who would get pregnant after “not trying” for many years. I admire your ability to put it all in words. Now let me go eat some sunflower seed butter to ease my dizziness from all the math…..

    • Sorry for making you dizzy! Now you know how I feel when my colleagues start spouting sociology or philosophy jargon at me. 😉

  3. Makes sense to me! 🙂 If I was in your exact position, I would make the same choices. And I sincerely hope it pays off for you!!!

    It’s funny, though- as a woman who has just given up the quest for a second child, I am fully capable of turning the statistics upside down, and using them to support the decision that we have made. I have a bit of a love/hate relationship with statistics for that reason- those of us with a serious love for numbers can often present them in ways that can support any hypothesis. Even as I was writing a recent post about why we stopped ttc, by the numbers, I was so conscious of the fact that all of those numbers could be flipped around to support why we should keep on trying. Statistics are funny that way.

    In any case- I think you’re incredibly smart. You’re hedging your bets, and laying all your cards on the table. In hindsight, there are a few things I wish I had done differently that may have afforded us a bit more time. I don’t wish that kind of regret on anyone. As always, I’m thinking of you, and praying for a happy ending!

    • Yes, I have to be careful with the stats. But understanding what they mean – and what they don’t mean – definitely helps to avoid overemphasizing their significance…

      Out of curiosity, would you be willing to share what you wish you had done differently?

  4. I loved this post (and not only because you called one of mine “brilliant” at the end of it, though that helps). 😉 It just puts the whole “you need to relax and stop trying” argument to shame. I’m going to print this out and shove it in people’s faces next time I hear them say it. Plus, as I said on Jane’s post, you never seem to hear about the people who stop trying and then never have kids. They just get forgotten, but they’re out there.

    • Indeed, confirmation bias is pervasive in these sorts of arguments. The couples who adopt and don’t get pregnant after, or who stop trying and never have kids don’t make for very good stories. (After all, they probably didn’t want it that badly anyway!) [Insert sarcastic tone here, in case it wasn’t obvious!]

  5. This is such a good post. I like your reinterpretation of the “they just stopped trying and got pregnant” argument. Luckily most people in my life don’t say things like this to me. Although, I harbor a deep, irrational, secret hope that once we move and get away from our stressful DC life, we’ll magically find ourselves pregnant. I think the chance of that is 0%, yet still, I find the thought creeping in.

    • I think the chances of that are NOT 0%! 🙂

      I’m all for using anecdotal examples to help fuel irrational hopes (hence my obsessive trawling of the blogosphere for pregnant DOR ladies!) It just gets old when people use those stories as a basis for offering unsolicited advice… I’m extra sensitive since I work full time at a job that some people (like my otherwise lovely in-laws) consider too stressful!

  6. Ellen

     /  July 18, 2013

    I agree! I won’t want a baby 10 years from now–I need one right now! That’s why I went straight to IVF without trying IUI first. If it doesn’t work, then I need to get on with my life immediately.

  7. Thanks so much for referencing my post and for writting a brilliant follow up! You set the standard for evidence based posts! Husband and I were outlining that if we fail IVF, we figured we would leave the door open for a year before restating birth control. I was contemplating going “laisez-faire” as the whole CBFM/timed intercourse is stressful, but I needed the reminder that going LF would not increase our fertility in any way. Given how hard it is to determine my fertile time WITH assistance, going LF would be like trying to find a needle in a haystack. Maybe we’d get lucky, maybe we wouldn’t. Scheduled coitus may be a drag, but it increases our chances. I did want to add as a follow up to my post, I definately support anything to reduce stress, not just for fertility, but for overall health! I don’t want to come accross as ‘pro-stress’ I’m choosing to defer starting IVF after the stress of my in-laws visit as a preference, I don’t think it would impact out success rates if we did it before or after. Except if we started before and it failed, I’d have another reason to resent my inlaws. Finally, I once had a patient who explained that they tried for three months and didn’t get pregnant, but the next month “we relaxed and it happened” I explained that they were within range for normal fertility, but I was really tempted to ask, “So how exactly did you relax…?”

    • Thank YOU for writing such a great post. 😉 And I’m totally with you on reducing stress…mainly for the sake of my sanity!

  8. In response to your question- I don’t mind at all sharing what I wish I would have done differently. But my situation is quite different from yours- while my ovarian reserve is now pretty crappy, it wasn’t always, and I had no trouble getting pregnant after the birth of my daughter. I just couldn’t stay pregnant.

    I wish I had pushed for RPL testing after 2 losses instead of 3. At our ages, we would have been entitled. I wish that when I finally got the requisitions to have RPL testing done, I had gotten off my ass and done it sooner. I had the paperwork in hand for 6 months by the time I had the bloodwork drawn. I wasn’t feeling brave enough to go looking for answers. Not to mention the fact that I stupidly made the assumption that nothing was going to be found anyway, since I had already had a child. But something was found. Had we known sooner, it is possible (though we’ll never know for sure) that loss #3 could have been prevented. I wish that when I got pregnant the last time, I had pushed my FS to start my heparin sooner. My gut was telling me that implantation was a serious problem for us, and that heparin would have helped. I deferred to his ‘expertise’ though, and allowed him to wait to see two appropriately doubling betas before starting it. I lost that baby after seeing a slow HB on two ultrasounds. So close. Hearbreaking, and I will always wonder if things would have been different had I stood up for myself.

    Basically, my regrets all boil down to wasting time, making assumptions, and not standing up for what I believed. Don’t let it happen to you… though you’re a smart woman. I’m sure you don’t need to be told. Pay attention to your instincts, and fight for what you believe. Regret is an awful thing to live with.

    Wow, that was a total downer comment, wasn’t it? Lol…

    • Thank you for sharing that. “Pay attention to your instincts, and fight for what you believe” is good advice that is always easier said than done. I’ll keep your words close as I go through this journey.

  9. Brilliant post. I will be sending this to my husband who told me about a friend of his… We were in the middle of timed intercourse … he wisely never repeated the comment or anything like it… but this kind of evidence is much more reasonable than the daggers I glared at him.

    • Hmm. Is it worse that he gave annoying anecdotal “evidence”, or that he did it in the middle of intercourse?! Yikes!

  10. Hello from ICLW! I would LOVE to send this post to everyone who has ever been told to “relax” so they can make copies and pass it out and say MATH SAYS YOU’RE AN IDIOT. What satisfaction..

    • Welcome! (To my blog, and to the IF blogosphere in general.) Yes, I’d love to tell people – in all kinds of contexts – that math says they’re idiots. On an unrelated note, I wonder why I have such a hard time making friends… 😉

  11. Ha! I love, love, love this post! (Hi from IComLeavWe). I want to submit #5 on the list: ‘Start writing an infertility blog, and you’ll get pregnant’ (or does it just seem that way to me?!).

    Anyway, my issue has never been getting pregnant, I seem to do that with ease, but I have had 6 miscarriages (out of 7 pregnancies). I have tried to do the statistics related to my pregnancy failures, but it just ends up feeling very depressing when you fall into the .0001 (or worse) percent of people with luck as bad as yours.

    • Welcome, and thank you. Ah, I wish #5 were the case for me! 😉

      Yes, statistics can be a double-edged sword. No matter how good the odds were in theory, it’s no comfort when you fall in the unlucky minority…

  12. Wow! These is pretty amazing stats. Thanks for posting. So glad I found your blog through ICLW.

  13. Not being a mathematician, I’ll have to trust you on that number-crunching – but it makes sense. At least (in summarized form) it will make a good retort to any rude/ignorant advice!

    Since our case involves both POF and male factor, I definitely feel like the numbers are not on our side, however you look at them. At least not for a “natural conception”: I admit after finding out what we are dealing with we rather lost our mojo for such things as timed intercourse and hopeful two week waits. I still hold out hope that there are things we can do to increase our chances with ART. I think in the long run it is healthiest to be honest with yourself.

    • You’re totally right. The odds of conception are different for each diagnosis. I mostly just wanted to point out the compounding effect of trying (or “not trying”) over a long period, even when the per-cycle odds were very low. I should have mentioned that it’s still worth considering the psychological effect of trying month-after-month without success. In many cases, it may not be worth it…

  14. Ahhh I can not even begin to count the ways I love this post. I will however copy and save it to my favorites.

    The next person that tells me “You just have to relax and not stress..” Is getting a copy!

  15. Reblogged this on journeyformybaby – IVF, Infertility and Pregnancy Blog and commented:
    I came across this blog post and found it very interesting! I often felt I was doing something wrong because I couldn’t “just relax”. (Until I learned of our very substantial issues.) Anyways, I wanted to reblog it because I feel it gives hope to couples trying or “not trying”. Enjoy!

  16. Wow this is amazing! Hope u don’t mind. I HAVE to reblog this!!

  17. Good lord, I want to like this post 10 times!!! Thanks for putting the effort into figuring out something that I’ve thought about in a disorganized way for a while now. I despise when people tell me this. Even if it were true it’s impossible to relax under the circumstances. Thanks for the post :).

  18. It depends how many times a year you have sex as well. If you have sex twice a year you are most likely not trying but the chance of getting pregnant is very slim. Therefore all these couples that claimed we’re not trying are lying as they most likely had regular unprotected sex just were not focused so much on if they fall pregnant or not. In fact they were trying otherwise the woman would be on birth control or they wouldn’t have frequent sex.

  1. My worst fear | the infertile chemist

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