maxbarry.com
Mon 19
Jul
2021

99%

Max If you do one thing each day that has a 99% survival rate, you’ll likely be dead in under ten weeks. If boarding a plane had a 99% survival rate, a typical flight would end by carting off at least one passenger in a body bag, perhaps two or three. Ninety-nine sounds close enough to 100, but anything with a 99% survival rate is incomprehensibly dangerous.

Go sky-diving, and you’re over two thousand times safer than if you were doing something with a 99% survival rate. Driving, the most dangerous everyday activity, requires you to clock up almost a million miles of travel before you’re only 99% likely to survive. Even base jumping, perhaps the single most dangerous thing you can do without actively wanting to die, is twenty-five times safer than anything that carries a 99% survival rate.

Ninety-nine bananas is essentially one hundred bananas. Ninety-nine days is practically a hundred days. But 99% is often not even remotely close to 100%. It feels like similar numbers should lead to similar outcomes, but the difference in life expectancy between 99% and 100% survivable daily routines isn’t one percent: It’s ten weeks versus immortality.

It’s simple enough to calculate the probability of more than one thing happening: You just multiply the individual probabilities together. The likelihood of surviving for three days, for example, while doing one thing per day with a 99% survival rate, is 0.99 x 0.99 x 0.99 = 0.9703, or 97.03%.

But we find this deeply counter-intuitive. We prefer to think in categories, where everything can be labeled: good or bad, safe or dangerous, likely or unlikely. If we have an appointment and need to catch both a train and a bus, each of which have a 70% chance of running on time, we tend to consider both events as likely, and therefore conclude that we’ll make it. The actual likelihood that both services run on time is 0.70 x 0.70 = 0.49, or only 49%: We’ll probably be late.

We also prioritize feelings over numbers. Here’s a game: Pick a number between 1 and 100, and I’ll try to guess it. If I’m wrong, I’ll give you a million dollars. If I’m right, I’ll shoot you dead. Would you like to play?*

Most people won’t play this game, because the thought of being shot dead is too scary. It’s shocking and visceral, so when you weigh up the decision, both potential outcomes balloon in your mind until they feel roughly equal, as if the odds were 50/50, rather than one being 99 times more likely than the other.

But put the same game in a mundane context — if instead of being shot, you get COVID, and instead of a million dollars, you just go to work as usual — and we tend to return to categorical thinking, where the dangerous-but-unlikely outcome is filed away as too improbable to be worth thinking about. As if close to 100% is close enough.

Between 99% and 100% lies infinity. It spans the distance between something that happens half a dozen times a year and something that hasn’t happened once in the history of the universe. With each step we take beyond 99%, we cover less distance than before: 1-in-200 gets us to 99.50%, then 1-in-300 to 99.67%, then 1-in-400 only to 99.75%. We’ve quadrupled our steps, but only covered three-quarters of the remaining distance. We can keep forging ahead forever, to 1-in-a-thousand and 1-in-a-million and beyond, and still there will be an endless ocean between us and 100%.

You have to watch out for 99%. You have to respect the territory it conceals.

* I pick 73.

Comments

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Suetu (#276)

Location: New Orleans, LA
Quote: "The sky and water looked like separate panels of the same chalk-fogged blackboard. Nature has erased the diagrammed sentences and multiplication tables, leaving a view that was all pan and no orama.--Tom Robbins"
Posted: 61 days ago

This is fantastic. What a compelling way to make your point. A stealth argument, that sneaks up on you. No offense, but I wish you had Andy Weir-level readership, just for more eyes to see this. But thank you for putting it out there.

unreliablenarrator (#8276)

Location: SFR Yugoslavia
Quote: "I have tried so hard to do right"
Posted: 61 days ago

Brilliant! Mark Twain was right about statistics..

Nial Wheate (#5873)

Location: Sydney
Quote: "Charge men; those white flags are no match for our bayonets."
Posted: 61 days ago

This is great Max. A real common-sense explanation of a scientific concept that people have trouble conprehending.

Could you post on Facebook and Linkedin so I can share it? Thanks.

Machine Man subscriber Max

Location: Melbourne, Australia
Quote: "I'm my number one fan!"
Posted: 61 days ago

So to be honest I'm not sure how Facebook works these days, because I'm pretty sure it's terribly evil, but I did post a link to it here:

www.facebook.com/maxbarry/posts/10160155146133690

Feel free to, you know, post yourself, or copy & paste it or whatever.

Machine Man subscriber Alan W (#1427)

Location: Spokane, Washington
Quote: "Corgis are like potato chips"
Posted: 61 days ago

Max and X-Com players get it.

Machine Man subscriber Max

Location: Melbourne, Australia
Quote: "I'm my number one fan!"
Posted: 61 days ago

This is one of those times I wish my site had a Like button.

Drew Kientz (#7438)

Location: New Mexico, USA
Quote: "“Ideals are peaceful. History is violent.”"
Posted: 61 days ago

Whoa. My number was 74. That was close. Now, lemme get that cool million. 😄

Timothy Taylor (#7172)

Posted: 60 days ago

He’s a witch! I too chose 73. Now I’m dead.

Daniel DiFranco (#243)

Location: Philadelphia, Pennsylvania, USA
Quote: "Panic Years, a novel, out now."
Posted: 60 days ago

I chose pi. I'll collect that cool mil next time I see you.

towr (#1914)

Location: Netherlands
Posted: 60 days ago

Living has a 0% survival rate (based on historic evidence, future results may vary, but probably don't), and yet I do it every day ... so far :P

Okay, so I'm cheating a bit by substituting live-time survival rate for event-based or day-based survival rate, although Max is playing a bit fast and lose with the latter two as well.
It also glosses over that event-based survival rate aren't necessarily independent. I can't drive; if I got in a car and drove on the freeway, I'd probably get myself killed. But if I survived, then did it again the next day, and the day after, my chances would get better each time.
The reverse can also be true. There's an infectious disease (I can't remember the name atm), but iirc it has decent survival rate the first two times you get it, but then the third time almost certainly kills you.

Now for the dangerous bit. I don't like how the argument would apply to covid. I'm in decent health and in an age group where it's vastly improbable I'd get seriously ill or die from covid. If it was only a risk to myself, I would probably prefer going out to work and probably getting it (and getting it over with).
But it's _not_ just a risk to myself. Even once I'm fully vaccinated, there's still a substantial chance I can pass the virus along to other people as long as we don't have it under control. And somewhere in that hypothetical chain of infections leading away from me, people could very well die.
So if people want to risk their own lives, fine, it's their life. But risking _everyone else's life_, that's a different story. That's not okay. And it should be part of the equation.

Roger (#8311)

Location: The Moon.
Quote: "Never argue with an idiot. They will drag you down and beat you with experience. ~ Mark Twain"
Posted: 60 days ago

If you chop off 99% of a stick infinite times, there will always be some part of the stick left.

Jake Thiele (#3766)

Location: Missouri, USA
Quote: ""I'm blowing up the whales on the gravy train." --Ozzy Osbourne"
Posted: 60 days ago

For the record (in case anyone is offering) I am absolutely willing to take the 1 in 100 chance of being shot dead with a million dollars given to me if I am not shot dead. I will accept this offer a minimum of once.

syrup6 (#1224)

Location: Arkansas
Quote: ""Truth always rests with the minority, and the minority is always stronger than the majority, because the minority is generally formed by those who really have an opinion" - Kierkegaard"
Posted: 60 days ago

16
See, I'd totally have gotten a cool million. Or, Covid. Depending on how I really fit in to this situation.

VK (#4147)

Location: USA
Posted: 59 days ago

I chose 73 as well. I wonder if that's from the 97.03 percent above? Maybe we're being subliminally messaged to pick that number...

towr (#1914)

Location: Netherlands
Posted: 59 days ago

> but the difference in life expectancy between 99% and 100% survivable daily routines isn’t one percent: It’s ten weeks versus immortality.

Come to think of it, I think that should be 14 weeks and 2 days (100 days total) instead of 10 weeks.

Machine Man subscriber Max

Location: Melbourne, Australia
Quote: "I'm my number one fan!"
Posted: 58 days ago

> Come to think of it, I think that should be 14 weeks and 2 days (100 days total) instead of 10 weeks.

If each day you do something that has a 1% chance of killing you, you aren't guaranteed to die after 100 days -- you might get lucky every day and live for years. But your likelihood of survival dips below 50% after 69 days, or just under 10 weeks, because 0.99 ^ 69 = 0.4998.

towr (#1914)

Location: Netherlands
Posted: 58 days ago

Yes, so after 10 week, you have slightly over 50 percent change of having died (at least once :P). But life expectancy is sum of day * 0.99^day for days in 1 to infinity, which comes to 100 days. You might die sooner, might die later, but on average that's how long you last.
I think ten weeks is the half-life instead of life expectancy.

towr (#1914)

Location: Netherlands
Posted: 58 days ago

Woops, that should be sum d*0.99^(d-1)*0.01
I never said it was easy to remember :P

Machine Man subscriber Max

Location: Melbourne, Australia
Quote: "I'm my number one fan!"
Posted: 58 days ago

Ah yes, I see! You are quite right, thank you.

So if you have the potential to live forever, your life expectancy is quite high, even though you probably won't make it past 10 weeks.

I wonder if a gap like that exists for regular life expectancy. A baby born today in many countries has a life expectancy around 80 years, but I'm not sure at what age the probability of surviving falls below 50%.

towr (#1914)

Location: Netherlands
Posted: 57 days ago

Hmm. I've tried to run it on some US data, and I get a "half-life" of 83, and a life-expectancy of 80. Which seems a bit odd. I think it's because mortality increases exponentially with age (except for the first few years). Or I made mistake.

I used mortality rates per 100 thousand, where the first number is for the first 5 years, then in ten year increments until you reach the >=85 age group: [23.3, 13.4, 69.7, 128.8, 199.2, 392.4, 883.3, 1764.6, 4308.3, 13228.6]

towr (#1914)

Location: Netherlands
Posted: 57 days ago

This actuary table show the same thing: www.ssa.gov/oact/STATS/table4c6.html#fn1
Life expectancy at birth for men is 76 and between age 80 and 81 50% have died. For women it's 81 and 84-85.

Charles (#8298)

Posted: 51 days ago

I see what you did there.

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