This is a really thoughtful analysis — thank you for laying out the assumptions so clearly. One small correction on the expected-value math: in the footnote, the calculation treats “not getting sick” as +$1,000 and “getting sick” as –$1,000, which effectively double-counts the benefit of being healthy.
In expected-value terms, I believe it is standard to treat one outcome as the as the baseline and assign it a value of $0 (e.g., only assign a cost of -$1,000 to the “sick” outcome). In that case, the expected value of masking would be the ppt difference in risk from mask less no mask, multiplied by the value you place on not being sick. So the true benefit would be half of what’s shown in the post (e.g., $333 rather than $666 for the 50% to 16.7% example).
The qualitative conclusion still holds—masking has positive expected value—but the magnitude is overstated because of that sign convention.
This is a really thoughtful analysis — thank you for laying out the assumptions so clearly. One small correction on the expected-value math: in the footnote, the calculation treats “not getting sick” as +$1,000 and “getting sick” as –$1,000, which effectively double-counts the benefit of being healthy.
In expected-value terms, I believe it is standard to treat one outcome as the as the baseline and assign it a value of $0 (e.g., only assign a cost of -$1,000 to the “sick” outcome). In that case, the expected value of masking would be the ppt difference in risk from mask less no mask, multiplied by the value you place on not being sick. So the true benefit would be half of what’s shown in the post (e.g., $333 rather than $666 for the 50% to 16.7% example).
The qualitative conclusion still holds—masking has positive expected value—but the magnitude is overstated because of that sign convention.