[rjsimmon]

The FBI does indeed gather such statistics:

FBI Stats 2014 (Table 14)

Total for 2014 was 444.

[MeganC]

http://www.washingtonpost.com/sf/investigative/wp/2015/12/26/2015/12/26/a-year-of-reckoning-police-fatally-shoot-nearly-1000/

Per the Post:

The landscape of police shootings is surprisingly thinly explored. The FBI is charged with keeping statistics on such shootings, but a Post analysis of FBI data showed that fewer than half of the nation’s 18,000 police departments report their incidents to the agency.

The Post documented well more than twice as many fatal shootings this year as the average annual tally reported by the FBI over the past decade. The FBI and the federal Bureau of Justice Statistics now acknowledge that their data collection has been deeply flawed. FBI Director James B. Comey called his agency’s database “unacceptable.” Both agencies have launched efforts to create new systems for documenting fatalities.

[MeganC]

Dr. Williams literally just replied to my email and says this was his source:

https://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2012/crime-in-the-u.s.-2012/offenses-known-to-law-enforcement/expanded-homicide/expanded_homicide_data_table_14_justifiable_homicide_by_weapon_law_enforcement_2008-2012.xls

[Chaguito]

IIRC, the FBI statistics refer to “arrest-related-deaths” and are the only official way of estimating deaths by police action. I don’t know where the ThinkProgress number come from, since I haven’t read it in detail.