Why Simple Algebra Doesn’t Prove Birth Control Wrong

Welcome dear readers to this newest installment in my efforts to counter the lies and misinformation being spread by the kids over at 1Flesh.org. This week, we’ll be talking about the importance of understanding mathematical formulas before attempting to use them to explain things like contraceptive failure rates.

As always, paragraphs in italics are taking directly from 1Flesh’s site.



Women use birth control for more than just a year. As such, any discussion of the effectiveness of birth control must consider its effectiveness over time. 

Wow. A sentence I agree with. Though I’d add in there that a large number of women actually switch contraceptive methods within a given year, so it might not be quite as important as one would otherwise think to determine long-term efficacy. That being said, it’s still a very worthy topic for research and discussion.

Typical-use failure rates are defined as the expected number of pregnancies in the first year per 100 women using the method.

Not exactly. Typical-use failure rates are defined as the number of unintended pregnancies in the first year per 100 women INTENDING to use a given contraceptive method. These failure rates include method failure, user failure, and a failure to use the intended method at all. Just so we’re clear about that.

That means that for the pill with a typical-use failure rate of 8, that of 100 women using the pill, in a single year 8 of them will become pregnant. A single year.

Hmmm….given that the method y’all push (the Creighton Model) has a typical use failure rate of 35% (that would be THIRTY-FIVE women who become pregnant unintentionally every year), I don’t really think you can be complaining about BCPs. But for the sake of argument, I’ll play along.

Also, y’all are using outdated data, just an FYI. The most recent data on contraceptive methods and failure rates was published by Trussell in 2011.

But given that women will use birth control over time, for more than just a year, shouldn’t we also consider how effective it is over time, rather than in a snap shot of a single year? Let’s take a look by simply using the reported typical use failure rates the contraception folks report for the first year, and extrapolating them mathematically over time.

Hmmmm…. Something tells me this isn’t going to end well, but let’s continue reading, shall we?

Remember those lessons from algebra class about determining the probability of getting 16 heads if you flip a coin 100 times? That can be easily calculated by using the binomial probability formula. Here’s an online calculator so anyone can check the math.


OMG. Are you SERIOUSLY comparing the risk of unintended pregnancy to flipping a coin? SERIOUSLY?

Because, if you are..I mean…


Wait – give me a minute to compose myself.

Photo courtesy RelaxingMusic

Photo courtesy RelaxingMusic

Okay. Composed.

Y ’all DO realize that you ABSOLUTELY CANNOT use the binomial probability formula to determine contraceptive failure rates over time, yes?

I mean, obviously not, because that’s precisely what you’re doing. So I’ll go ahead and say it again. YOU ABSOLUTELY CANNOT USE THE BINOMIAL PROBABILITY FORMULA TO DETERMINE CONTRACEPTIVE FAILURE RATES OVER TIME.

Want to know why?

Because contraceptive failure rates do not remain steady over time. Contraceptive failure rates actually DECLINE over time both due to increased user age/maturity, user discontinuance, and increased efficacy due to practiced use. What does that mean for the binomial probability formula? It means that p isn’t constant. Which means you can’t use the formula.

Note to readers: There are a few lovely charts and tables on 1Flesh’s site here, but as they’re simply explaining a formula I’ve already explained they can’t use, I’ve chosen not to waste my time replying to them. You can see them by clicking the link at the beginning of this post if you so choose. I have, however chosen to address a couple of choice comments because…well, they’re just that hilarious.

8 out of 100 women will have unintended pregnancies in one year, but 34 of those same 100 women will have unintended pregnancies in five years, and more than half in ten years.

Um, nope. Because, again, you’re using an un-useable formula.

Condom use has an even higher failure rate, so typical-use of condoms over five years actually makes a woman more likely to get pregnant than not. Over ten year’s time, it practically ensures unintended pregnancy.

From a study you cite below, cumulativefailure rates for condom usage were as follows: for 1 year 3.3%, 2 years – 7.8%, 3 years – 9.2%, 4 years – 10.2%, and 5 years – 12.3%.

Individuals who do not use any form of contraception can expect an unintended pregnancy rate of 85% at one year. After ten years, I’d say that fertile individuals who do not use any form of contraception will most definitely have experienced a pregnancy.

But based on the data above, I find it absolutely laughable that y’all think that condom use “practically ensures” a pregnancy after 10 years. Again, your inability to understand basic math or scientific data sometimes astounds me, given that y’all like to pretend to be experts.
And what about teens? Teens are not as careful so the failure rates are higher.

You’re absolutely correct. Teens DO have a much higher failure rate for almost all contraceptives. Given that statement, though, can you explain to us all how you can say that birth control efficacy doesn’t improve or decline over time? We’ll wait.

No? Thought not. Moving on.

To be clear, these numbers do not consider the question of whether birth control use improves or declines over time.

To be clear, that means that you CAN’T use the binomial probability formula. Again, because you can’t say that your pis constant.

There has been little research on this issue past 2 years of contraceptive use.  

Actually, this is false.  By two years of research, I’m assuming you’re referring to this study, which found that failure rates declined from 13% to 8% from the first year to the second year (a 62% drop in failure rate, by the way). But there are some other studies with longer time frames, including one that found that, “Rates of unintended pregnancy were inversely associated withage and duration of HC”. Also, please to be seeing the study YOU cite below for more info on long-term failure rates of contraception.

These numbers take the given typical-use failure rate and asks the question: If sexual behavior and birth control use remain constant over time, what is the typical-use failure rate over time?

And that’s why you fail. Because sexual behavior and birth control use do NOT remain constant over time.  Failure rates DECREASE with duration of usage and increased age.

That the statistical result has real life application is apparent. The study “Contraceptive failure rates in France: results from a population-based survey” found that “despite the widespread use of highly effective contraceptive methods in France, one in every three pregnancies is unintended, of which 65% occur while using contraceptives. In the USA, 49% of pregnancies are unintended, half of which result from contraceptive failure.” Looking at all methods of contraception, it went on to show that “overall, 2.9% of women experienced a contraceptive failure in the first year of use and 8.4% in the first 5 years of use,” thus indicating a growth in typical-use failure over time. 

How I do love when y’all cite research that directly contradicts your main premises. It makes me feel all warm and fuzzy inside when you do my work for me.

First, this study contradicts your statement above that little longitudinal research has been done beyond two years. This study was a five-year longitudinal study.

Second, this study established that contraceptive failure rate decreased over time. Using the binomial probability formula, one should expect nearly a 13% failure rate at 5 years. But that’s not what we see. We only see an 8.4% cumulative failure rate.

What did these researchers ACTUALLY discover about contraceptive failure rates?

That while the cumulative percentage of women who experienced an unintended pregnancy increased over the years, failure rates decreased annually after the first or second year of use:

The failure rate for the pill was higher in the first year of use than for longer periods of use (2.4% in the first year, 1.2% in the second, 1.4% in the third, 1.1% in the fourth and 0.7% in the fifth year of use). Conversely, the failure rate for the IUD was highest in the second year of use (3.2%) and declined for longer durations of use (0.4% in the third year, 0.5% in the fourth year and 1.6% in the fifth year of use). Finally, the failure rate for the condom was highest in the first 2 years of use (cumulative failure rate of 7.8% within the first 2 years of use and 4.5% within the next 3 years (third to fifth year of use).

Final take-away? Yes, there is a risk of pregnancy with every sexual encounter, even when using contraception. And, yes, that absolute risk increases with each sexual encounter. But the RATES of contraceptive failure DECREASE over time because, as people age, they tend to become more mature about their contraceptive choices and usage, and because, well, the more you do something, the better you get at it.

After all, practice makes perfect. So practicing the use of contraceptives can help perfect contraceptive usage.

Till next time,

– H

© Heather Parker and Antigone Awakens, 2012-2013.


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