Exponential Bias

I'm sick and tired of hearing people say masks are only 10% effective at preventing the spread of Covid and it's therefore not worth wearing one.

For a start, there's a German study (beware of isolated studies) which showed they were around 40% effective and a more recent systematic review and meta-analysis concluded they are effective but, due to it not being possible to conduct randomised trials to exclude other factors, like social distancing, the exact percentage is unavailable.

Regardless of that, let's model a 10% effectiveness on a pandemic in which cases are doubling at each time period, be that a day, a week or a month - it's easy enough to do in Excel. A doubling of cases results in over 2m cases on the 22nd time period - the result of exponential increase. Applying a 10% effectiveness is itself compounded at each iteration. 

I produced the above chart, which shows the effect of a 10% reduction in spread on an exponential rise. As you can see, it's far out of proportion to the small initial effect, precisely because it's compounded and amplified. There are only some 230k cases - a tenth of the original, forecast number.

This 2nd chart shows the result for an empirical 40% effectiveness derived from the single German study. Over the same time period, wearing a mask results in only 46 cases, as opposed to over 2m cases when not wearing one.

Many people simply don't understand that a small change can produce such a huge difference when you're in the realm of exponentiality, which is whenever the R number is above 1. They're wont to apply a linear effect, when it's actually exponential, in line with the infection increase.

Even a 5% effectiveness would result in a 66% reduction in cases. The important caveat, however, is that everyone must wear a mask for these figures to be even remotely relevant, and wearing a mask is the easiest thing in the world to do..