On Logarithmic Graphs

2020-04-04

Logarithmic plot of global COVID-19 cases as of 2020-04-04

(Graph source: John Hopkins University COVID-19 Map, highlighted areas added)

A lot of people are not used to reading logarithmic graphs and may come to the wrong conclusions from them. Above is a quick example why. Each red box is a 10x increase of total cases of COVID-19.

Especially when people have seen the very dramatic linear plots of exponential groth before, the logarithmic one can create the impression that things aren't really that serious. What a logarithmic plto does it to squash the vertical axis so that the same distance is a growth by the same factor, e.g. here, each tick on the vertical axis is a 10-fold increase of cases. On a linear graph, one tick on the axis always represents the same change in total numbers, e.g. on the example below, 1 tick equals 100.000 new cases.

A straight line growth on a logarithmic graph is still exponential growth, which is exactly what we don't want because it grows at ridiculously high speed eventually, even if it seems less dramatic at first.

COVID-19 global case numbers as of 2020-04-04, linear plot (Graph source: John Hopkins University COVID-19 Map, highlighted areas added)

Here's the linear graph with he same boxes on it. As you can see the early weeks become really hard to see and compare to the later ones. This is why logarithmic graphs are useful, to analyse an exponential change over longer time.

For a simple "how bad is it now?" glance, the linear graph probably communicates the severity of the situation much better.

So, please treat logarithmic graphs with care, they can be misleading if you're not familiar with them. But they can be very useful to get an idea of the more long term progression of something like our current pandemic.