The ProPublica data indicates a magnitude greater than yours. Can you cite something to support 2:1?
The Pro-Publica's 21:1 data, if even accurate, are only for teenagers. The 2:1 I got from quickly glancing at the numbers in the chart in the same Vox article. Actual calculation yields 2.88:1 (still far less than the 5:1 discrepancy in homicide rates!) That is much less than 21:1 so if both sets of numbers are accurate it would imply black teenagers being way out of control compared to white teenagers and also that there is probably not much difference in police shooting rates among black and white 20+ year olds.
Why do you think that black teenagers are more out of control than white teenagers?
A minor point. Blacks don't murder five times the numbers of homicides as whites. Possibly you meant to say that a black man is five times more likely to commit a murder than a while man?
Let's see. According to the FBI data for 2013;
whites murdered 2509 Whites + 189 Blacks + 32 others + 25 unknowns = 2755 total
blacks murdered 409 Whites + 2245 Blacks + 27 others + 17 unknowns = 2698 total
others murdered 49 Whites + 20 Blacks + 96 others + 3 unknowns = 168 total
unknowns murdered 38 Whites + 37 Blacks + 4 others + 23 unknowns = 102 total
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totals murdered 3005 Whites + 2491 Blacks +159 others +68 unknowns = 5723 total
These are not the totals for the entire country, some of the more than 17,000 police agencies in the country don't report to the FBI, but the ratios are considered to be representative, which is good enough for us.
So whites kill 2755 ÷ 5723 × 100 ≈ 48% of the people who are killed in the US.
So blacks kill 2698 ÷ 5723 × 100 ≈ 47% of the people who are killed in the US.
So whites and blacks kill about the same number of people, not that blacks kill five times more people than whites.
We can normalize the numbers to see if your 5:1 ratio holds for the propensity to kill.
Since the numbers reported are under counts of the number of murders in the country we just use the percentages as representative of the number of murders each group committed since we are only interested in the ratio.
Blacks are 13.2% and whites are 77.7% of the US population.
(47% ÷ 0.132) ÷ (48% ÷ 0.777) = 5.8
Your 5:1 actually understates the greater propensity to kill of blacks.
The question becomes then does this justify the larger number of blacks killed by the police?
It would seem to when the police are apprehending people suspected of murder. But does it really? Aren't the police trained to arrest even armed suspects of murder without killing them? After all isn't there the presumption of innocence, even in cases of murder?
And even though blacks have a greater PTK, the odds of a policeman encountering a black killer drops off dramatically when the police deal with a black citizen in matters other than murder.
The population of the US in 2013 was 316.5 million. Assuming that the FBI statistics are accurate it means that the chances of a policemen meeting a black killer other than in a murder investigation are one in (316,500,000 × 0.132) ÷ 2698 = 15,485.
1:15,485 would seem to be the more pertinent set of odds than your 5:1, wouldn't it?