Katarina gets a pentakill every 61 games

I'm not sure what you are even saying, to be honest. Try rewording it.

When you have a cc heavy kit, or at least one cc skill, you should at least save one spell to interrupt a carry's ability or to disable and eliminate a carry.

Take Sejuani, for example. Her ult is a pretty good intiator, as is her Q. In a teamfight, it's pretty stupid to waste both of them in the span of two seconds. If you're against Katarina, you should be saving one spell just for her. If you blow all your cc on the tank/frontline at the very beginning of a teamfight, you have nothing to defend yourself against.

Katarina is an ability power carry. She is, by default, a priority when it comes to cc. You can't ignore the tank, but you don't have to waste everything on 'em.

I mean, with a champ like Kat, pretty much.

Nope, Yi is different in many ways than kat.

And ok, I'll play your game. Pick Fiddles. Drain her whenever she tries to do something. Laugh at her inability to do it. You could also build early MR. If kat doesn't get fed early, her job is really really hard. Ward bot lane so she can't roam for easy doubles. Have your tank champ peel her. Don't start fights if she isn't there and you don't know where she is. She will jump in and kill you when all your team's abilities are done.

There are plenty of things you can do to completely stop her. She either gets really fed or she sucks, in my opinion. I RARELY see a Kat do well in team fights if not fed early.

Even better, just Exhaust her. I bring Exhaust every time I see her in a game. She never gets kills when I'm anywhere near her.

Also true for yi.

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She's a champion whose performance depends on how bad the enemies are. Just like Master Yi, but better.

This is incorrect though. She's a champion that "can" abuse lack of performance from her enemies. Which is exactly why her weaknesses are completely void when the enemy just makes so many mistakes where it's important to shut her down.