The search for evidence into "institutional racism"

Months ago Sean at Ideas and Data tackled the facts about racial bias in police shootings:

In contemporary political discourse, there’s an awful lot written about black people being unfairly killed by police. Such writings are normally in response to a particular incident of this supposedly occurring. Of course, these are merely anecdotes and in a nation with 300 million people you can come up with a new anecdote every month for something that basically never happens. You can also create a general impression of racial bias if stories about white people being killed by police are less sensationalized than stories featuring black people.

If we turn from anecdotes to data, this narrative very quickly falls apart.
As we've seen the past 2 weeks, the loudest people don't want to pivot from anecdotes into data. They want outrage and the facts don't back it up.
The CDC says that around 27% of people killed by police are black. A sociologist used data from Killedbypolice.net to argue that number should be 30%. The FBI puts it at 32%.

By contrast, Black Americans account for 13% of the total population, 38% violent criminals, and 53% of murders.

Black people also account for 40% of those who murder police officers, and so probably instigate around 40% of potentially lethal confrontations with the police (FBI, 2014).

Thus, black people are underrepresented among those killed by police relative to their representation among those who commit violent crimes, who commit murder, and who kill police officers.