What is Ex-post-facto Statistics?

A statistician has been described as someone who draws a mathematically precise line from an unwarranted assumption to a foregone conclusion. It is not quite as bad as that, but there are innumerable statistical fallacies ready to trap the unwary and aid the unethical. The fallacy of ex-post-facto statistics is perpetrated when we apply probability laws to past events.


I drew the ace of spades. It was only a 1 in 52 chance, but it came up.

(The same applied to all the cards, but one had to come up.)


We cannot draw too many conclusions from the low ‘probability’ of certain past events. Something has to happen, and if the range of possibilities is large, the probability of each one occurring is small. Whichever one occurs thus has a low probability. The fallacy is committed when we go on to suppose, from the occurrence of events of low probability, that something supernatural was operating:


I met my aunt in Trafalgar Square on Wednesday. Think of the hundreds of thousands going through the square that day, and you’ll realize unlikely it was that we should meet there. Maybe we are telepathic.

(And the same applies to the thousands of others you met.)


The probability of heads coming up four times in a row is only 1 in 16. The same is true of every other combination which might come up; only one thing is certain, that a 1 in 16 chance will come up if you make four tosses. The fallacy goes beyond the evidence, using statistics in an inapplicable way to point to mysterious influences where none are needed. Ex-post-facto statistics often appear in speculations concerning the origins of life and the universe. Exotic calculations are trotted out showing the incredible unlikelihood that things could ever have happened as they did:

How lucky we are that our planet has just the right temperature range for us, and just the right atmosphere for us to breathe. It has to be more than luck.

(Ten-legged blue things breathing ammonia on the third planet of 70-Ophiuchi are even now saying the same thing.)


Similar claims are made of the probability of the right chemicals coming together to form life. The fact is that in our universe chemicals combine in certain ways. If they were different, no doubt different beings in a different universe would be congratulating themselves on their good fortune.

The fallacy is a great prop for those who suppose themselves the children of destiny. Looking at the unlikely events which have led to their present position, they see the unseen but inexorable hand of fate behind them, never realizing that had things been different they could have said the same.

Just think, if we hadn’t happened to be staying in the same hotel, we might never have met and never have married.

(But they might have met and married other people, and thought themselves just as fortunate.)


Your use of this fallacy will depend a great deal on your temperament. It can be deployed at short range to convince others that you are a favoured child of the universe and entitled to receive special consideration:


I believe I was meant to get this job. I saw the advertisement for it in a paper the wind blew against my face in Oxford Street. I feel that something put me in that place at that time so that I would get this job. I’m not saying that should influence your decision, but…

(But it should. Few of us like to confront the remorseless hand of destiny by stamping on its fingers.)


If you have the other temperament, you can always use the fallacy to gain some sympathy:

Just my luck! Of all the parking meters in London she could have checking, it had to be mine. And just at the worst possible time!

(If you can fit going to the pub in between being used as a punchbag by the universe, lines like this should be good for the odd sympathetic pint.)


The above article is from the book How To Win Every Argument by Madsen Pirie. The article is only for educational and informative purposes to explain and understand formal logic and logical fallacies. It is a great book, definitely worth a read!