I'm not seeing why ratio is important compared to magnitude. There is certainly a relationship between number of armed suspect shootings and number of unarmed suspect shootings but it is not clear what that relationship is. It can't be a constant, that just doesn't fit human threat response. Rather, I would expect that the higher the armed suspect shootings (numerator) in an area, the smaller the ratio, meaning that nonproportionately more unarmed suspects are shot as a direct result of a large number of armed suspect shootings. But if that's the case, that will increase the likelihood of unarmed suspect shootings without there being any necessary racial bias. A smaller ratio just reflects a larger denominator increase due to numerator.

If we have equal numerators for each race, but the denominator differs, than that seems like a clear indication of racial bias. But if the numerators are different at all, that potentially reflects an entirely different police interaction dynamic. The expectation that one race is more likely to be armed than another race is, strictly speaking, a racial bias but could also be a rational bias based on encounters rather than prejudice.

What are the numerators? This whole issue may be of course be misguided but I'm simply unable to find the actual numbers from the paper.

> County-level race-specific crime rates (1. aggravated assault, and 2. weapons possession)?

So they are categorizing weapons possession into race-specific crime rates.

> There is no relationship between county-level racial bias in police shootings and crime rates (even race-specific crime rates)

Which is to say crimes related to weapons possession does not correlate with racial bias.