One of the worst examples I can think of went like this:
Someone is running down the street, maybe 30m from me. I shoot them, get a few hits in, and they take a right and disappear in a side street.
It’s hard to accurately time what happened afterwards, but I know I had time check damage, to feel disappointed I had missed one last shot, wondered whether to follow or head elsewhere, and started moving my aim away. I know humans can think quite fast, but it was a significant delay.
And then bam, I got my kill cross. The cross appeared where they were just before making a right, their body was far away from that corner.
My understanding is that that my shots are resolved on my computer, then sent to the server for validation. Maybe my packet got delayed, maybe the server took a long while to decide, but whatever THEIR ping was, stable connection or not, would not have made a difference: I got them in the street, server agreed, if belatedly, and signal is sent to tell them they’re dead, It must have felt like crap.
I don’t know how other games manage to resolve these issues more efficiently, apart from having more servers. But having been able to compare the game on low ping (when ME servers were still a thing) and high, the difference is night and day. It’s mostly painful for me, but once in a while, I’ll be ruining someone else’s day… :(