Why I hate the log graph, and you should too

I hate the logarithmic scale which is being used everywhere now to present the spread of COVID-19 around the world. Bear with me while I explain why, but in a nutshell: we’re sacrificing clarity for ease of presentation and seriously under-playing the severity of the crisis being faced by the world.

So the graph being used almost everywhere to show corona virus around the world uses a logarithmic scale on the y-axis. It results in something like this from covid19data:

The problem is that this completely under-rates the problem for many countries.

The log scale is being used for a couple of reasons. The technical reason, and probably the least understood reason, is that it’s a good way of showing exponential growth. For those who read the axis-labels on graphs it tells an important story. But for most of the rest of us, who just look at the lines, it tells a story that’s pretty misleading.

The second, and I would argue most important reason the log scale is being used, is that it allows us to see countries with vastly different raw numbers on the same graph and get a sense of how they are tracking. On a linear graph, because the numbers from the USA are so disproportionately huge, they squish everyone else into a meaningless mass on the bottom fifth of the page.

So, if we look at the United States and Australia together on a linear graph, Australia is just an undifferentiated straight line at the bottom of the screen – dwarfed by the US numbers. It makes for a useless comparison:

The final reason given when you read interviews with those in charge of making the decision on how to display these numbers is that they don’t want to panic people.

And, you see, that’s why I hate these graphs – because by not panicking people they are completely under-playing the severity of the problem. Let’s use the Financial Times tool again and compare the USA and Spain on the log scale:

Now at a glance, it looks like the USA and Spain are following the same path. And, yes, there is utility in knowing that that path exists and so the USA could learn from Spain’s lessons. And, on its face, it looks like the USA is not doing so badly. It’s clearly flattening the curve and moving to alignment with Spain which is, as we all know, coming out the other side of the worst of the pandemic. Right?

But let’s take a look at the same numbers on a linear graph that just displays the raw numbers.

Now that’s a different story. Spain has literally flattened the curve – the USA continues to reach for the stars. If I was in the USA that graph would positively terrify me. It should positively terrify everyone.

There is a time for not panicking people and a time for open-eyed clarity about what is going on. The middle of a pandemic is exactly when we need people to be appropriately panicked. I recognise, that’s a tricky line when you have armed militias invading parliament buildings; but it’s absolutely necessary when we are making decisions about trading off lives for dollars in relaxing lock-down measures.