It's the nature of all these figures that you can calculate them relatively easily for known cases but are somewhat more illusive for all infections.

That said I think you can put an upper bound on the number of undiagnosed cases out there by looking at deaths and hospitalizations (in places where that data is reasonably accurate).

There's at least a few ways of getting ballpark figures:

- https://cmmid.github.io/topics/covid19/severity/diamond_crui... (EDIT: this gives some estimates by age correcting the data from the diamond princess cruise which I think is one of the best data sets we have since most passengers got quarantined/tested/monitored).

- looking at data from countries with reasonably strong testing regimes and responses. E.g. Israel or Canada are two I'm following. In Canada 12% of the cases so far required hospitalization (EDIT: https://torontosun.com/news/provincial/ontario-sees-spike-of... )

- Surveillance test data for countries that do that.

20% does sound on the high side from what I've seen read. My mental ballpark is 5%-10%. I'm sure there are local variations (smokers, air pollution, age distribution, general health...)

EDIT: The US has 62 reported deaths. Just estimating based on 0.5% ifr that gives 12,400 cases. Then you have to back-adjust this. Let's say by 2 weeks? That's maybe on the order of 100k+. Obviously this will have a very large error bar but it gives us some intuition. Feel free to poke holes at my math ;)

The 80% figure comes from a study of 72k cases in Hubei. It may have the problem you suggest, but China was/is testing much more aggressively than the United States.

http://weekly.chinacdc.cn/en/article/id/e53946e2-c6c4-41e9-9...

There is also the issue of assuming that social distancing only reduces the number of cases by 90%. Social distancing affects the exponent. Depending on how aggressive it is it could reduce the height of the peak by a lot more than 90%.

I also have no idea the basis for the 10-50x assumption r.e. confirmed/unconfirmed cases.

No, social distancing affects the base, not the exponent.