Statistics – The Statistical Improbability of You

Alan has already debunked “The mathematical Impossibility of evolution” but I thought I would explain a little bit about statistics.

Or rather than explain; I thought providing examples of statistics in order to help you increase your understanding.

The Statistical Chance of You

The statistical chance of you existing is such an astronomical calculation that it is really hard to compute. I’ve spent a while looking at different averages from various sites and and I have to say it was difficult to work out the best approach.

I actually started to write this last year and there were so many variables I exhausted myself and had to stop writing.

As such I decided it would be better to use simple averages, and focus on a high level set of statistics without so many variables.

For example the average age that folks are having their first child varies from country, region, religion etc. I’ve tried to look at a variety of statistics and use an arbitrary figure.

The Statistical chance your fathers sperm was the one that created you

The Average man produces 2-5ml of semen per ejaculation.

1ml of semen contains roughly 1,000,000 sperm.

The average man produces 2,000,000-5,000,000 sperm per ejaculation.

You are the result of 1 of those sperm entering the egg.

that is 1 in 2,000,000 to 1 in 5,000,000. – For the rest of this article lets assume a low average of 1 in 3,000,000.

That is 1 in (3 x 10^6).

Let’s assume you started masturbating at 13, and we will use the average age of first time parents in the 60’s/early 70’s, 23.

You then need to find some way of calculating all the times you masturbate and/or have had sex without having a child. Teenage males, at least one wank a day amirite? (let’s be honest, its probably way more than that)

So let’s say once a day from the age of 13 to 23 (The average age in the 60’s/70’s to a have a first child, rising to 25 during the 70’s and is now closer to 27-33 years) (3 x 10^6) sperm are spent in masturbation and protected sex.

That’s (365 * 10) + 3 (additional days for leap years) * (3 x 10^6)

That is 10959000000 spent already, let’s round up slightly to 11 x 10 ^ 9.

11 billion sperm spent before you even try and conceive.

The Statistical chance your mothers egg was the one that created you

A woman is born with about 1-2 million eggs but by the time she reaches puberty only about 300-400,000 are viable.

Of these only 300-400 get released during a woman’s reproductive cycle.

Regardless, for ease we are going to use the stat 1 in 1 million (1 in (1 x 10^6) eggs have the chance of being you.

It would be even more complex if we were to work out that of the 1 in a million (or even 2 million) which 300-400 get released, and the chances of those being the “correct” egg.

The Statistical Chance that your fathers sperm and your mothers egg created you.

We will examine this from a simplistic angle to reduce the number of variables. In other words we will assume the chances of your mother and father meeting are 100%, and ignore environmental factors that could affect fertility.

So let’s again use the age of 23 for both mother and father as the average age of first time parents.

At that age, women who have unprotected sex have about a 33% chance of conceiving in their cycle.

They also are only fertile for about a week to ten days in a month. If you’re lucky you’re having sex every day, but some less so. The average for couples is only a couple of times a week. (how sucky!) but I think it likely that the man would continue to masturbate during this time, even if he doesn’t admit it. These are unknowns so we will just assume one attempt to get pregnant.

The Maths to Produce the Stats

There is a 33% chance of that 1 in (1 x 10^6) egg being fertilised by the “correct” 1 in (3 x 10^6) sperm after you have already spent 11 x 10^9 sperm. For ease lets include that 1 in (3 x 10^6) in the 11 x 10^9.

=3.03*(1*10^6)*(11*10^9)

that means you have a 1 in 33330000000000000 chance of existing

that’s 1 in (33.33 x 10^15) or 0.0000000000000030%

And honestly, there are so many more factors than that, I’ve done some very rudimentary calculations that don’t cover all the other factors.

We are using averages. We are not even including the 10% chance of miscarriage of a woman in her 20’s, this roughly reduces it to 0.0000000000000027%

It gets even more complex if we throw in variables such as the “wrong sperm” fertilising the egg.

Caveat

The stats above were based on 5 attempts for the first cycle. A woman of 23 may have a 33% chance of conceiving per cycle, but all the sites seem to agree on roughly 96% chance of conceiving within the first year.

That first year would be 12-13 cycles. We will assume 5 attempts per cycle. We will also assume that sex was had for fun outside of the fertile window.

This changes the maths slightly.

In fact statistically speaking by the time you have been trying to hit 12-13 cycles you have a 99% chance of conceiving.

To get the chance of conceiving this cycle C:

If the chance of conceiving per cycle is represented by c
and the number of cycles you have had is represented by n

C = 1 – (1-c)^n

So for a 23 year old, we know they have a 33% chance per cycle, the first cycle would be 33% if they are trying in the second cycle this would be 55% and so on. At the end of a year we are close enough to 100% chance of conceiving. (If we were to include the other variables that could reduce fertility we probably would never reach 100%)

The chance of the egg being the right egg e is:

e = ( 1 in (1 x 10^6) )

So the chance of that egg being fertilised F is:

F = 100/(C*100) * e

However that would equally mean more sperm had been spent, yes?

We have our figure of sperm used up until the first attempt = w (11 x 10^9)
Sperm per emission = s ((3 x 10^6) for the sake of our calculation)

We also need to include:

Attempts per cycle = a (let’s assume 5)
Number of times masturbated and sex when not fertile = m (lets assume 15)

So to get the now to calculate our chance for the right Sperm R

1 in ( (s * (a+m) * n) + w = R

The chance of being pregnant p

p = R * C

The chance to not miscarry (z) and have a viable pregnancy P

P = p * (1-z)

So if we take that all in to an account we can see the chance varying on the number of cycles. The chances of conceiving go up and up and up, however eventually the chances of it being you start to go back down due to the number of sperm spent.

A brief look below at a few examples around the number of cycles and the chance of it being YOU.

1	0.00000000000000270%
5	0.00000000000000692%
12	0.00000000000000765%
15	0.00000000000000758%
20	0.00000000000000740%

Statistical Conclusion

The short of it is, to say anything is mathematically impossible is incredibly ignorant. Your existence is completely improbable but you are still here.

Many folks are waiting much longer to have kids, reducing the chances of conceiving and increasing the number of sperm spent too.

Now you realise how improbable you are when only looking at yourself, excluding so many factors, and consider your ancestry.

This isn’t to say reproduction is unlikely, though it does get harder as you get older, just that the chance of the exact sperm and exact egg that made you was against all odds. Arguably you had equal odds to any other individual sperm or egg.

You’re not just a 1 in a million chance, you’re far rarer than that.

You’re even rarer than my rudimentary and assumptive statistics of between 1 in (11.77 x 10^14) and 1 in (33.33 x 10^15) predict.

From that perspective, we are all special. (awww)

Real world application?

My Mrs and I recently conceived. I was 35 at the time, averaged 3 wanks/shags per day, 5ml.

She is 30, went through 3 cycles before conceiving. Averaged 15 attempts per cycle and probably 30 fun times between each cycle.

That means our child has a 0.000000000000000325149% or 1 in 270645491803279000 of being the person he or she will be.

Ancestral Statistics

Excluding environmental factors and the chances of your parents meeting, both your mother and father each only had between 1 in (11.77 x 10^14) and 1 in (33.33 x 10^15) chance of existing.

So for the 2 of them to exist and have you, we are looking at crazy numbers. Consider a coin, you have a 50% chance of guessing the right side each time. To do it consecutively your probability decreases. 50% becomes 25% becomes 12.5%.

The calculation for the coin is simply the chance C to the power of the number of flips you take. 50%^n

The only variation on our calculation is each generation we travel back we are exponentially increasing the number of people involved. So just you would be 1. Add 1 generation, your parents, that’s you, your mum, your dad.. 3. Add 2 generations, that’s you, your parents, and their respective parents, 7)

g = generations

n = 1 + (2^g)+(2^g)-2

so we are looking at P^n

If we go back 1 generation, so you and your parents, that’s P^3.

Using our 1st time stat for P:

(33.33 x 10^15) x (33.33 x 10^15) x (33.33 x 10^15).

That is 1 in 37025927037000000000000000000000000000000000000000

or 1 in (37 x 10^48)

Added to that, folks today are 27-33 before they have their first child. I used the ages for 60’s/70’s first children – I’m an 80’s kid where the age was closer to 25-27 most places…

Then throw in all the crazy factors of life where they may never have met, chances of miscarriage, stress and other environmental factors, and add this in to each generation there is virtually no chance, mathematically speaking, of any of you existing at all. Yet you do.

By the same notion saying something like evolution is statistically impossible, or non-life to life is statistically impossible just shows how little you understand statistics.

As far as statistics is concerned, you shouldn’t exist.

References

Tools

If you would like to have a play around with the tool I created. perhaps putting in more precise variables and the like then feel free to download it here.

Please note this tool is a rudimentary statistical calculation, real life is far more complex with many more variables. I may over time modify this tool with more specific data and variables.

The last update on the tool was: 19/07/2019

Davidian

I’m Joe. I write under the name Davidian, not only because it is a Machine Head song I enjoy but because it was a game character I used to role-play that was always looking to better himself.

This is one of many things I hope to do with Answers In Reason.

I run our Twitter and IG accounts, as well as share responsibility for our FB group and page, and maintain the site, whilst writing articles, DJing, Podcasting (and producing), keeping fit and more.

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