Hello My name is reflects and I play on oce and I main Kat with 1mil+ mastery. I am here to show you my way of playing katarina if you want to learn and play katarina like me.

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Page 1: Best used for snowballing
(Primary) Domination Tree
Electrocute (Burst damage is the key to this champion)
Sudden Impact (More magic pen since katarina has the ability to blink)
Eyeball Collection (Gains more ap apon kill, assist, or shutdown)
Ravenous Hunter (More lifesteal goes well with your abilities as well with Gunblade.)
(Secondary) Sorcery Tree
Absolute Focus (Does extra damage when you're above 70% health nothing too special.)
Gathering Storm (The longer the game goes on the easier it'll be to do damage unless you're already in front.)

Page 2: Good if you're still learning katarina
(Primary) Domination Tree
Electrocute (Burst damage is the key to this champion)
Sudden Impact (More magic pen since katarina has the ability to blink)
Eyeball Collection (Gains more ap apon kill, assist, or shutdown)
Ravenous Hunter (More lifesteal goes well with your abilities as well with Gunblade.)
(Secondary) Precision Tree
Triumph (Gives back health after killing someone to save you from those risky moments like ignite.)
Coup de Grace (Does bonus 7% bonus damage to people under 40% health so easier to kill squishies.)

Talking about these 2 Rune pages?

Rune page 1: Sorcery

Pros:
1. Good for snowing balling after first kill.
2. Gives an easier Second chance of getting back into the game after losing because of scaling with Gathering Storm.

cons:
1. No extra defenses.

Rune page 2: Precision

Pros:
1. Keeps you some what safe after kills.
2. Beginner friendly Rune page.

cons:
1. No good scaling Late game.
2. Worse than the other 2 rune pages displayed since Precision got nerfed a while back.