Is there X amount of mass shootings that would change gun supporters' minds, or is that the wrong way to think?

Nah, that’s certainly not true.

Here is a post where I compare some U.S. health statistics negatively in comparison to the rest of the world (this is interesting specifically because you quote and agree with me in that thread)

I don’t have a problem with the general idea of comparing statistics from one country to another and drawing conclusions. But not all statistics are aptly compared, or are aptly compared in the context of particular arguments.

I think comparative crime rates are some of the most difficult to draw the sort of conclusions that I suspect gun control advocates would want to draw because there are so many culturally specific factors to crime. I think that’s true for healthcare for example too, but I think less so than crime.

I also think crime and gun crime overlap a number of areas in which America just is not that similar to most OECD countries, so choosing to narrow down only on the gun part, creates misperceptions.

For example policing in America, which is a component of crime management/statistics, is quite different than in most countries, both structurally, legally, and culturally. As another example, our approach to incarceration and rehabilitation is also markedly different from most OECD countries. As another example, the way we fund our K-12 (aka primary) education, and the wild disparities this creates between school districts, is fairly uncommon in the OECD. Our large population of racial minorities for which there is strong historic racism and discrimination against is somewhat different from most of the OECD–most of our OECD country pals are “Nation-States”, i.e. ethnic nations that formed or primarily make up a specific state. All of them of course have some degree of ethnic heterogeneity these days due to migration, the EU allowing free movement (and most of the OECD is in the EU)–by my count about 27 of the 38 OECD countries are “nation states”, the rest are mostly in the Western Hemisphere, or AU/NZ. Also worth noting the U.S. has a lower homicide rate than several of our Western Hemisphere OECD cohorts–Colombia, Mexico, Costa Rica.