You know percentages are funny: it seems to be another one of those things (like exponential growth) where our first instincts are often wrong. The difference is that most people can do the calculations quickly enough so that they won’t persist in believing the wrong thing after you point the mistake out to them. Take what is needed for a stock price going back up to where it was after it went way down: As I recently pointed out to somebody who didn’t do the mental calculations before they spoke, if a stock price drops by 50% (say from $100 to $50), it has to double to get back to $100. Going up by 50% from the depressed price only gets you to $75. But, like I said, unlike exponential growth where it doesn’t seem quick fixes are possible i.e. only learning some more sophisticated math can help, percentage changes are taught early enough and are encountered often enough so a quick mid-course mental correction can happen. My friend immediately more or less said: “Oh that is true, oops”.
So the base (the denominator as it is called in mathematics) you use to take the percentage is all important. It is too easy to mislead people by choosing the wrong number as the base for calculating the percentage or even worse to use “absolute” numbers instead of a percentage. Take testing for Covid 19, I can’t be sure if it is because he doesn’t get percentages or because he realizes how bad they make him look, but only talking about the absolute number of tests done rather than the percentage of people in the United States who have had a test is really really wrong. (Oh, in case you are wondering, on a percentage basis using our population of roughly 330 million people as the base, we are nowhere near the top 10 of countries.)
But what is interesting is that with a little bit of outside the box thinking we can use a different percentage to get a much better picture of where we stand. How? Don’t chose the number of people in the United States as the base (denominator) but use the number of tests done as the base and use the number of positive tests as the top number (the “numerator”). This is sometimes called the test positivity rate. This lets you get a handle on how many asymptotic carriers you have found for example as well as get a better sense of how many non infected people in your country. So one statistic gives you two pieces of information that are both important. Our test positivity rate is nearly 20%. South Korea’s is about 2%. Or in other words, using a test positivity ratio, we are so far behind the curve, we are sitting in the parking lot. (Oh and what’s worse is this ratio hasn’t gotten any better in the last month. Being charitable one might say we are treading water, being realistic we are drowning slowly.)
But in any case when encountering a percentage, remember it’s all about the base.