There has been a lot of conversation about risk lately. What is the risk of having COVID-19? How much is that risk increased by not wearing a mask or not maintaining social distancing? How is that risk affected by where I live and the number of cases in my state or more importantly in my county?
Underlying all these questions is how we understand the concept of risk. What does risk really mean? What does it mean for an individual to have 0.2 risk of being infected with COVID-19?
People’s eyes glaze over when someone talks about probability theory, but I’m going to give some real world examples to show how to understand risk and probability.
The first thing that is very important to understand is that risk (which describes probability of something bad happening) is calculated for a population of people, not for an individual. If we calculate that the chance for some bad outcome is 1%, what we really mean is that if we take a large number of people who are similar in some way (age or diabetes or obesity, etc.) 10 people out of every 1000 are likely to have this bad outcome. The larger the number of people, the closer the proportion will be to 1%.
Probability has nothing to say about what is going to happen to any one individual in that population. For an individual, the risk of a bad outcome is either zero or 100%.
Lets make that a little clearer by using the example of a coin toss. For a non-weighted coin, the chance of heads is 50%. For any single coin toss, however either heads will come up (100%) or tails will come up (0%). As we continue to toss the coin a large number of times, the frequency of heads will get closer and closer to 50%. The same thing would happen if we tossed 1000 identical coins at the same time. We know that the total proportion of heads would be very close to 50%, but probability does not tell us whether any individual coin will be heads or tails.
Does that mean that the idea of individual risk is useless? Not if we understand how risk works. If there are things we can change that put is in a different population that has a lower risk for any bad outcome, then fewer people will have that bad outcome. We still could be one of the few that have the bad outcome, but it is more likely that we will be in the larger group that does not have the bad outcome.
On the other hand, we need to understand that even if the risk of a bad outcome for a population is low, those bad outcomes do happen to some people.
Let us use our example of a coin toss again. What if heads comes up twice in a row? We understand intuitively that two heads in a row could happen by chance, even if the probability is 50%. We can actually calculate the probability of two heads in a row. Since the probability for heads at each coin toss is 50%, the probability of two heads in a row is 0.5 x 0.5 or .25. In other words, if we toss a coin multiple times, there is a one in 4 chance of tossing two heads in a row. What about the probability of tossing 12 heads in a row? That probability is 0.5 x 0.5 repeated 12 times. The answer is 0.00024414062. Even though that is a very small probability, if we toss the coin enough times we will eventually get a sequence of 12 heads in a row.
The point I’m trying to make with this example is that very unlikely things happen all the time. When something unlikely happens to us that is bad, we call that bad luck. If something unlikely happens to us that is good (like winning the lottery), we call that good luck. The idea of luck as a state of being is of course a myth. It is simply the operation of the laws of probability. Unlikely things are bound to happen, but it is impossible to predict to whom they will happen. That is random statistical chance, not luck.
I will give you a real world example from my own experience. My favorite recreation is mountain biking. I have been doing it for 30 years with my only injuries being scrapes and bruises. Last summer I had a major injury that involved a broken shoulder, a concussion, and bleeding in my brain. I have absolutely no memory of the accident (I am fine now, by the way). The risk of injury in mountain biking is 0.6% per year. 10% of those injuries are severe enough to require hospitalization. The risk of injury requiring hospitalization would then be equal to 0.006 x .1 or .0006 per year. That is a very unlikely event. But there is a formula to calculate the cumulative risk of having one accident requiring hospitalization over 30 years of mountain biking. That formula is 1 – chance of not having a serious accident for 30 years: 1 – .998 = .002. Although that risk is 3 times the risk for 1 year, that is still a very small risk. Nonetheless it happened.
With all that as a preamble, I’m going to give you a link to a risk calculator for COVID-19. It lets you put in your zip code, age, gender, and any underlying risk factors you might have. It also asks if you follow CDC guidance for hand washing (reduces your overall risk by 55%) and mask wearing (reduces your risk by 68%). You also enter how many people you contact per week at less than 6 feet distance. Remember that these are just estimates. The usefulness of these risk estimates is to help you understand the risk for the population you are currently a part of and how changing your behavior might make you part of a lower risk population. Here is the link to 19 and Me.