A recent front-page headline in my local paper read as follows: "County bordering on high virus transmission rate."  A doctor with a large regional health system was concerned that the COVID-19 transmission rate had increased by 37% in one week and stated, "A transmission rate above 5% from the prior week is very scary."

It seems useful to provide some context regarding numbers such as these, considering all the numbers being thrown around regarding COVID-19, the apparent push to create a panic over the delta variant of COVID-19, the obvious push for everyone to get vaccinated, and the fact that the United States is ranked so poorly in math and science.

The first number to be considered is the 37% increase.  It certainly looked pretty bad, but percentages do not always provide an accurate picture.  The county-wide cases went from 11 to 15 during the week in question, an increase of four cases.  So a 37% increase does not seem to be all that concerning, given a population of over 91,000 people.

According to the doctor's statement that a transmission rate above 5% is scary, the next thing considered was what it would take to get to that level.  Going from 11 cases to 11.55 cases, something not even physically possible, would put the county in the "scary" range.  Looking at something that is actually possible, going from 11 cases to 12 cases generates a 9% increase.  So an increase of a single COVID-19 case would put my county well into the scary range, according to the doctor.

Percentages do not always tell the entire story.  Let's look at how underlying numbers and percentages work together.

It is reported that COVID-19 cases have gone up 200%.  Should you be concerned?

Going from 1 case to 3 cases is a 200% increase and is insignificant.  On the other hand, going from 1,000,000 cases to 3,000,000 cases is also a 200% increase and has more significant implications.  It is also worth noting that applying an increase of two cases to the 1,000,000 cases, as was done in going from 1 case to 3 cases, results in a 0.0002% increase.

Consider the situation where reported COVID-19 cases go up 100% and then decrease by 50%.  Do you feel that things are better or worse than they were at the starting point?

Let's look at the numbers, picking 10,000 cases to start with.  The number of cases increases by 100%, which brings the total to 20,000.  Next, cases drop by 50%, which puts the total cases at 10,000 again.  So a 100% increase is comparable to a 50% decrease, and the order of their occurrence is not important.  How do your feelings after seeing the underlying numbers compare with how you felt when just seeing the percentages?

Something else to take away from this example is that as things improve, you are likely going to see smaller percentages reported for case decreases than were reported for case increases.  Consider looking at the underlying numbers to determine where things really stand.

I have no idea what motivated the doctor quoted in my local paper to present the information the way he did.  What I do know is we can sometimes be unjustifiably optimistic or pessimistic by accepting information at face value when it is relatively easy and quick to dig just a bit deeper, whether that information involves COVID-19, taxes, finances, or a variety of other meaningful areas.

Image: Marco Verch.

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