One of the strange things about discussing police violence in the US is that we simply don't know how much of it there is. Despite what you might expect, police in most states are under no obligation to record and report if a person dies in their custody, or even if they kill someone in the line of duty. Back in 2000, Congress passed a law intended to fix this, but as we'll see in a moment, it hasn't quite worked.
Right now, there are only two national sources of data about this. One is the Supplementary Homicide Report (SHR) maintained by the FBI, which is a list of homicides by police that have been ruled justified
by either local law enforcement or the local FBI. (NB: "homicide" is not the same thing as "murder;" it means the death of a person because of the actions of another, which can include everything from accidents to self-defense to lying in wait with an axe)
The other is the Arrest-Related Deaths (ARD) list maintained by the Bureau of Justice Statistics (BJS) at the Department of Justice, created because of this 2000 law. It lists all "persons who died either during the process of arrest or while in the custody of state or local law enforcement personnel." This includes deaths which aren't
homicides as well, such as suicides, drug overdoses, or accidents – but since one frequently asks whether a suicide was a suicide or "the worst case of suicide I ever saw, six gunshots to the back of the head," it's not a bad idea to log all of them. (Really, simply logging these things ought to be mandatory)
Unfortunately, ARD data is collected via voluntary compliance of state and local law enforcement – and quite a few states and localities have openly refused to provide any data, while other localities' data has proven to be so full of holes (e.g. by simple comparison to media reports) that it can only be described as a blatant lie. This failure was so severe that in 2014, the BJS suspended the entire ARD program pending a massive review. 
Congress is discussing passing a new law which would make reporting mandatory, not optional – but given the current state of Congress, passage is far from certain, and the states' treatment of ARD suggests that without some serious enforcement, deceit would be widespread. You would think that "keep track of everyone who died in the course of your job" would be a pretty reasonable thing to ask of most people, but apparently not.
So given two data sources which are full of massive omissions, you might think that we're SOL in figuring out just what the scale of deaths really is. But it turns out that this is not the only situation in which we face such a problem – and there are ways of dealing with it.
The article below was written by a statistician, a member of a team which analyzes mass deaths around the world: Kosovo, Colombia, Syria, and the like. In each of these cases, there are lists of the dead compiled by various sources, and each of them is tremendously full of holes for various reasons. But when you have multiple flawed lists, you can use statistics to estimate how big the original set might have been.
The article explains how this works in very clear language, but let me give you a taste. Imagine that N total people died, but you don't know N. Instead, you just have two lists, one of A people and one of B people. Now, if there were no correlation between these lists, you would expect that the probability for anyone to be on the B list is B/N. That means that the probability for someone on the A list to be on the B list as well is also B/N, so you expect there to be AB/N people on both lists. But since you know A, B, and the number of people on both lists, you can work out a first guess about N.
The trickier bits come from ways to take into account that the two lists often are
correlated; for example, a death with more media attention is far more likely to be reported in both the ARD and SHR than one that goes below the radar. But this is exactly what statisticians have gotten good at for the past twenty-five years, and we can look at how lists like these from around the world do or don't correlate to get a range of how these two lists might relate.
When all is said and done, it's possible to pull out a number: somewhere between 1,250 and 1,500. That's the team's best estimate of the total number of people killed every year in police custody or during arrest in the US. Note that this doesn't try to split up justified versus unjustified deaths, which wouldn't be something you can do from statistics; it just gives us a scale of what's going on.
For comparison, in 2015 there were a total of 16,121 homicides of any sort in the US,  so police-involved deaths would account for about 8% of all deaths. But before you get too relaxed, remember that the overwhelming majority – about three quarters, by best estimates – of homicides are committed by people who know each other. (This makes sense; if you sit and make your better-dead list, it's going to contain people you know, not total strangers. People have more reasons
to kill people they know.)
This means that roughly one third of all Americans killed by strangers are killed by police. That's an extraordinary number. And while I'll reiterate that this makes no attempt to separate the justified from the unjustified deaths, it does give us a sense of scale, and why the reports of police violence sometimes seem overwhelming.
The next step for such an analysis would be to note that police-related deaths aren't uniformly distributed in the population. We could use similar techniques to estimate what fraction of stranger killings are done by police by race. Without access to the full data , I can tell you that the fraction is going to be much higher if you're black, and somewhat lower if you're white. Mental illness is another very strong predictor, although I don't know if we have enough data to estimate the precise effect.
(This reminds me of another interesting article I read, although I can't find the citation right now: while the rate of rape of women is much higher than that of men, the rate of rape by strangers
is actually close to equal. The difference for men is almost entirely accounted for by prisons, where (depending on the prison) rape is considered almost a standard part of punishment. A good general rule is that stranger crimes and acquaintance crimes tend to be very different beasts. This makes it somewhat surprising that our laws don't treat the two more differently.)
So if you're ever wondering why some people see death by police as a major risk, this is why. It turns out that, if you're going to be murdered by a stranger, the odds are pretty good that it's going to be a cop.
 For more, see http://www.bjs.gov/index.cfm?ty=tp&tid=82
 See http://www.cdc.gov/nchs/fastats/homicide.htm
. CDC statistics about death are really interesting.
 I can't give you a back-of-the-envelope answer, because the most naive calculation – using that most statistics of the form "black people are X times more likely than white people to encounter [negative event] with the police" seem to come up with X's around 3 – would tell you that all of them are, which is clearly false. So real statistics work is required, preferably done by real statisticians.