How effective are face coverings in reducing transmission of COVID-19?

In the COVID-19 pandemic, billions are wearing face masks, in both health care settings and in public. Which type of mask we should wear in what situation, is therefore important. There are three basic types: cotton, surgical, and respirators (e.g. FFP2, N95 and similar). All are essentially air filters worn on the face. Air filtration is relatively well understood, however, we have almost no direct evidence on the relative role played by aerosol particles of differing sizes in disease transmission. But if the virus concentration is assumed independent of aerosol particle size, then most virus will be in particles > 1 $\mu$m. We develop a model that predicts surgical masks are effective at reducing the risk of airborne transmission because the filtering material most surgical masks use is highly effective at filtering particles with diameters > 1 $\mu$m. However, surgical masks are significantly less effective than masks of FFP2, N95 and similar standards, mostly due to the poor fit of surgical masks. Earlier work found that ~30% of the air bypasses a surgical mask and is not filtered. This highlights the fact that standards for surgical masks do not specify how well the mask should fit, and so are not adequate for protection against COVID-19.
Comment: 11 pages + references, 7 figures. Resubmitted version with substantial additions over original