I haven't done the count of unarmed people killed (whether or not they were shot) by police, let alone shot by police (whether or not they were killed). What I have done, by using statistics from the Guardian database and the FBI database is compute the percentage of people killed by police who were black in 2015 and year-to-date in 2016:
2015: 306/1146 = 26.7%
2016: 137/569 = 24.1%
The FBI database keeps track of police officers killed or seriously injured by assailants with weapons, and the race of their assailants (when known). The latest data available is for 2014.
2013: out of 26 known assailants who killed a police officer, 11 were black.
2013: out of 72 known assailants who seriously injured a police officer, 40 were black.
2014: out of 58 known assailants who killed a police officer, 13 were black.
2014: out of 80 known assailants who seriously injured a police officer, 26 were black.
So the percentage of police killers who were black in prior years were:
2013: 42.3%
2014: 22.4%
And the percentage of police serious attackers who were black in prior years were:
2013: 55.6%
2014: 32.5%
Personally, I think the best numbers to compare to are the above numbers, although we should wait for the data to accumulate so we can match up years. Although, there is not very much data to go by, it seems plausible that the percentage of people killed by police who are black is lower than the percentage of people who attack police who are black.
If that's true, I think that is evidence that, on average, police are responding with force to real risk in a roughly race-neutral way (maybe even under reacting to the statistical risk from people who are black).
Which is not to say that there isn't systematic discrimination against blacks in policing. It could be that police are seeking out more confrontations with blacks for racist reasons. Or are more aggressive in their confrontations for racist reasons. I don't think that's true, however. The confrontation rate and arrest rate, broken down by race, strike me as reasonable given the higher level of violent crime in black communities.
ETA: Links to FBI data for
2013 and
2014.
And the Guardian police shootings
database.
ETAA: The Guardian does show unarmed shootings by police broken down by race. The percentage who were black in 2015 and year-to-date in 2016 are:
2015: 79/229 = 34.5%
2016: 24/82 = 29.3%
A little higher than killings over all, but within the statistical noise I bet.