The first Covid case in Italy was found on February 21st 2020. A couple of weeks later we were entering the lockdown with this number of new daily cases.

The number of Covid-19 new cases was growing really fast every day. We had no clue about what was going to happen and about when it would have ended. Was it going to end soon? How quickly was the virus spreading? I was wondering whether our feelings and expectations would have turned out to be true or not. So, I run a little experiment with 7 friends. I asked each of them the following 2 questions on March 10th 2020:

1. What will the total number of Covid19 cases be by April 1st?
2. When will the number of new cases be smaller than 50 again?

The goal of these questions was to investigate our ability as humans to nearly understand the size and the duration of such an unseen event like a global pandemy. Let's plot the answers we gave to the 1st questions.

Total cases by April 1st

The total number of Covid19 cases in Italy was 110k (precisely 110574). These were our 7 prediction made on March 10th.

We see that 5 out of 7 respondents predicted a number of cases below 60k with 2 respondents even below 25k. Only 2 out of 7 respondents gave more realistic predictions (110k and 130k respectively). Why were most respondents too optimistic? If we look at the very first chart, an exponential growth of new cases was already happening on March 10th. Perhaps, the majority of respondents were perceiveing the growth as linear.

Does our brain have misperceptions about exponential growth? My little experiment gave this insight, but I was curious whether there is some scientific literature about this misperception. I found a paper written back in 1975: "Misperception of exponential growth" by Wagennar and Sagaria.

In this paper, researchers presented the beginning of an exponential time series starting ranging between 1970 and 1974. They asked to predict the value of this time series by 1979. A considerable underestimation of growth was encountered in all groups in all conditions.

not envisioning an accelerated growth of Covid-19 cases? The growth pace increased until mid-March where it turned into a linear growth until beginning of April.