What’s the Chance of a One-In-A-Hundred-Years-Event?

Last year a bunch of supposedly famous people kicked the bucket.  People were talking about how the world was falling apart (probably in an attempt to block out that they have reached the age where their childhood/teenage idols are in the ready-for-replacement age).

Ignoring the one attempt at quantifying this concluded that was largely bollocks, another, and in my opinion more thorough study, computed whether an extreme amount of people died (yes) and how rare of an occasion it was: the extremity of deaths was roughly a once-in-a-century event (once in two centuries if you count very famous people only).

That sounds extremely rare!  Must be gluten or global warming or something, right?  Ignoring that the Mirror made some surprisingly coherent points (baby-boomers being ripe for the six-foot-under, number of celebrities growing, and our knowledge of celebrities growing) and there’s good reasons we would encounter more hurricanes in populated areas (we have more and larger cities covering larger parts of the Earth, and we have the technology to report hurricanes in desolate parts of the world) how rare is a once-in-a-century-event?

Once way to consider the question is to ask for a given once-in-a-century event, what is the likelihood of a person encountering it in their lifetime?  The probability of encountering it in a given year is 1% or 0.01m and the probability of not encountering it in the same year is 99% or 0.99.  If we say that a person lives for 70 years, the probability of not encountering it during that lifetime is 0.9970 = 0.4948 = 49.48%, making the chance of encountering it during a lifetime just over 50%.

If we assume that senility sets in at 65 and nobody remembers anything before the age of 15, so anything happening after or before that doesn’t matter, a person has 50 good years of building experiences and a 0.9950 = 0.6050 = 60.50% chance of never encountering the event, or just under 40% chance of encountering it.

In other words, you are quite likely to encounter any once-in-a-century events, either 40% likely or 50% chance.

Aside from the maths, there’s also two psychological effects that make rare effects very common: the survivorship bias and the Texas sharpshooter fallacy.

The survivorship bias was discovered by the US army during the second world war.  A bunch of planes were investigated in order to decide where to reinforce them so future missions would be more successful.  It was originally proposed to reinforce the planes where they had most hits, until a researcher noted that all of those planes which had been hit had returned despite being hit.  Instead, the planes should be reinforced where they hadn’t been hit; as it was only possible to analyze planes that had returned safely, they would obviously not have been hit fatally while the planes that caught a severe case of the explodey on the other hand had.

Similarly, we only consider rare events that actually occur.  In 2016 we noted celebrities dying.  In 2017 we notice hurricanes.  In 2018 it might be car-crashes, bees dying or literally anything that happens rarely but is noticeably enough that we start noticing it.  When we only focus on the events that happen, we get a twisted view of the probability: we think that it is much more common and compare it with the perceived rarity of the event.

This is very similar to the Texas sharpshooter fallacy.  The gist of the effect is a person from Texas shooting at a barn (because Texas), and afterwards draws a target around the densest cluster of hits, thereby being able to claim they are a sharpshooter.  This effect was delightfully illustrated by a world-wide hoax “showing” that eating chocolate caused weight loss.

We do the same time-wise with rare events: If we consider 100 once-in-a-century events, we would (statistically) expect once of them to occur in any given year.  Since we only focus on the one that happen, we get surprised because we don’t consider those that don’t.  We only care about the rare event that actually happened after it did and not the 99 that didn’t.

This is all augmented by the law of “close enough.”  Any celebrity of any type counted in 2016 and pretty much any bad weather counts in 2017.  Furthermore, simple confirmation bias also plays a role: once we start noticing celebrity deaths or hurricanes, we are more likely to notice the death of a lesser celebrity we wouldn’t have paid attention to otherwise, or a severe but not really out-of-the-ordinary storm in some bunghole part of the world.

All in all, rare events are extremely common, but our brains wildly miscalculates the probability causing us to get surprised when they happen.  This does not mean there wasn’t an evil plot to abduct or kill beloved celebrities in 2016 and that climate change isn’t causing hurricanes in 2017, but it does mean that those are not the only possible explanations.  Similarly, if 2018 goes by without celebrity deaths or hurricanes, it also doesn’t mean we’re in the clear.

It just means that we shouldn’t be surprised by rare events, and we should probably consult something more reliable than media-statistics when it comes to drawing conclusions.

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