Probabilities are frequently used to evaluate risk. Unfortunately they are too often manipulated in order to further false arguments. Here I’m going to try to build an intuition for how to analyze safety and risk of a few different events. I’m also going to give you a tool to easily prove whether something is dangerous or not, called the Daily Test!
Consider this list first, which presents the odds of dying in a few incidents, sorted from most deadly to least deadly*.
- Odds of dying after developing symptomatic rabies (no shot): 1 in 1
- Odds of dying after being hit by lightning: 1 in 10
- Odds of dying after a plane crashes: 1 in 20
- Odds of dying after testing positive for COVID (no vaccine): 1 in 75 (I’ve assumed a 1.3% fatality rate to get this number based on aggregate data, but it really also works if you take anything between 0.5%-2%, depending what you choose to believe)
- Odds of dying after crashing in a car: 1 in 150
Most of these incidents are universally considered risky (COVID may be stirring controversy, but the stats speak for themselves, it’s in the neighborhood of the car crash and the plane crash, which are both undisputedly dangerous regardless of your political affiliation).
The tricky thing is that apart from rabies, all of these events present a less than 10% mortality rate. We tend to associate small numbers with small risks, but terrifying incidents all have a less than 10% mortality rate. Does that mean that they’re not as terrifying as we think they are? Not quite.
The Daily Test:
An interesting way to define “safe” is to ask yourself: “If I did this every day, how long would it take for me to die from it?” To calculate the number of days, simply take X in the 1 in X odd, and that is a good estimate. To get the number of years, divide that by 365. Note that when conducting the test, you assume that each time you do the activity in question, you disregard the effects of having it done the previous day; (for the statistically versed, we assume independence)
After a short 10 days of lightning strikes (not possible, but we throw this for the sake of the test), we will die, 20 days of plane crashes are sufficient, we only need 2 months and a half if we somehow caught COVID everyday (remember, this ignores immunity, because we are studying the danger of the FIRST infection being repeated daily independently, rather than multiple infections), and after half a year of car crashes, we will eventually succumb. The reason these incidents are considered dangerous is not that they are a death sentence, unlike rabies, but because they are sufficiently dangerous that we cannot be exposed to them regularly and always expect to get away with it. And in our lives, we are exposed to tens of incidents daily, and if we choose these incidents to have so much as a 1% chance of killing us, then cumulatively, they will kill us in short order, despite not doing so instantly. That’s the true danger of the events mentioned above.
But wait! You might tell me, they’ve always said riding a plane is safer than riding a car. Well yes, but the above list presents the chances of dying in the event of a crash, not on your regular car or plane ride. To get a better estimation of the real risk that these events pose to us, we need to consider the likelihood of them occurring at all.
A few more calculations show us an updated list, when we consider the odds of the events happening in the first place.
- Odds of testing positive and dying of COVID after an exposure (no vaccine): 1 in 750
- Odds of crashing a car and dying in a single ride: 1 in 3 million
- Odds of getting struck by lightning and dying: 1 in 7 million
- Odds of dying aboard a plane due to it crashing: 1 in 16 million
- Odds of catching rabies and dying from seeing a random dog: 1 in 150 million
Well that was dramatic! The list now reflects how seriously we take these risks. There is a reason that driving, going in planes, and seeing dogs, are not considered dangerous encounters: the odds of things going wrong are so low in the first place in the modern world! If things do go wrong, well, it’s a harder ride (see the previous list), but that’s really unlikely, which is why we neither have a rabies pandemic, nor a lightning pandemic. But with hundreds of millions of people interacting, the likelihood of infections is massive, meaning though the event itself isn’t dangerous, repeated exposure makes it so.
Let’s apply the Daily Test to see how long it would take for these events to kill us if we indeed performed them every day. For daily car rides, that’s 8000 years, which, given our human lifespan of 80 years, means approximately 1% of us will die by then. For lighting, that’s over 15000 years, daily plane rides give us over 30,000 years of life, and the dog encounter leave us a whopping 400,000 years (meaning you can cuddle your furry best friend for longer than human history). All these are perfectly safe, since the worst-case outcome is so unlikely!
What about COVID? Well, it would take a mere 2 years of daily exposures to finally kill us. That’s not a lot; it could happen to any of us (disregarding age-related disparity). And that’s why this is so dangerous. It is not a risk we can take daily. That’s the cold, hard truth of it.
The next time someone brings up the COVID 1% fatality statistic, let them know that taking a 1% chance with your life daily means death in 3 months. If they say it’s 0.1% rather that 1%, no need to argue about the exact number! 0.1% still gives us 33 months (or 2–3years). Both 0.1% and 1% are huge risks, even if the numbers look small.
So now you have the Daily Test, a useful tool in your belt to examine the real threat posed by an activity. No longer will you be fooled by small numbers, you now have a rigorous way to evaluate risk, regardless of the event! Now see if you can use that to tell how safe you are once you’re vaccinated (you might be surprised!)
