[vharuck]

In a back-of-the-napkin, spherical-cow, way, it's not too hard.

20% chance it happens in a year means an 80% chance it doesn't. Let's assume (this is the spherical cow) each day has the same chance. We can find it by looking at the chance an adult doesn't get a mental illness in a year. Then, because that's the chance they won't get it every day, it's easier to figure out the daily chance of not getting one.

    0.8 = x^365
    x = 0.8^(1/365)
    x = 0.9993888346422956
    1 - x = 0.0006111653577044462

So, overall, adults have roughly a 0.061% chance each day of getting a mental illness.

Compared to the daily risk for this 90-day period

    0.8 = x^90
    x = 0.8^(1/90)
    x = 0.9993888346422956
    1 - x = 0.0024763016863216247 

So about 0.248% each day for the COVID patients. That's more than four times as high as for all adults.

Remember, this is spherical cow stuff. Numbers to use in other calculations need a more experienced statistical approach, I'm sure. But this at least tells us something's different.

[fulafel]

As a sanity check the "half as high" background number sounds high?

edit: scratch my mistaken numbers - but people would normally (without covid) get many mental illnesses per lifetime?