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,
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.