Most of the time, when the police shoot someone they are justified in doing so (cue shouts of outrage from those DUers who believe the police have horns and tails).
The relevant statistic is ratio of unjustified to justified shootings of whites and blacks, because that would indicate how much more trigger happy the police are when their target is black than white.
Unfortunately, neither the police nor their critics can be trusted to divide shootings into "justified" and "unjustified" reliably, making it very hard to work that number out.
If I had to guess at it, I would expect it to be about 3 or 4 times higher for blacks than for whites, based on the fact that blacks commit about 6 times more homicides per capita and are about 20 times more likely to be shot, and guessing that likelihood of murdering someone is likely to be at least correlated with likelihood of being the victim of a justifiable shooting by police. But, obviously, there are a lot of "guesses" in that sentence.
On edit: and also a basic mathematical mistake, as well as the guesses - (a+b)/b is not the same thing as a/b. So that estimate would only hold if the fraction of police homicides that were justifiable were small, which is not the case.
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