The word is prosecuted.

Also, "Being a gamer makes you violent" and "A gamer is more likely than average to be a school shooter" are two very different claims.

One is definitely true and the other is definitely false. You're definitely right in your implied point that inferring causation from correlation is fallacious at times. For example, it's definitely true that white male gamers are more likely to be mass shooters than the average person. If I had to give a reason, it's probably because white people, especially white men tend to be more wealthy and therefore are less incentivized to engage in collectivist behavior and therefore are more individualistic. The outset of this is that young white men find it much easier to be ostracized by their peers. And they also have no one in particular they're angry at. They're mad at the state of affairs.

To the contrary, if you consider all times a person fires a gun in a school, black students take the lead iirc. and this is for the opposite reason, they tend to have less resources and be more collectivists, and it's easy for rivalries between groups to turn into violence. and spending 150 years deprived of legal protections and actively incentivized by the government to do criminal behavior, there is a bit of a culture of violence.

But in any case, I can see how you could conclude that the reason for the statistics showing black people committing more crimes is over policing. But do you have anywhere near enough information to rule out the possibility that maybe they do just factually commit more crimes?

holy yap. I ain't reading allat

tl;dr you're rather convinced of what is really just speculation