Excellent math. For those who aren't so comfortable with the mathematical notation, the point of this comment was that the log of the cases per capita is the same as the log of just the cases, plus a constant offset. This constant offset is present in the linked chart, but is visually compressed - you don't really notice it that much. So if you look at the chart and see how the lines do/don't line up on top of one another, that's partly due to the constant offset.
You are right if you are just interested in the slope. But most people don't just look at the slope, they look at the numbers and what to know, which country is doing better or worse. And that is when the constant (which is different for each country) matters.
Complete opposite. Arguably better would be to look at local population density, but even that is just a proxy for how easily the virus should spread.
Total number is much better than per-capita, because the point is to see how quickly the disease spreads, which it does from a single point. No country is even close to majority infected so weighting by the size of the arbitrary borders enclosing the outbreak is only misleading.
What useful information would it convey, when moving the US 4x farther up the line than China? Or Italy? The point is to show how quickly the virus spreads through a population, which it does with great consistency. Per capita doesn't even tell you anything about how effective the response was been, it only tells you how big the country is. Per-capita would de-normalize this data!
