The correct way to fix zoe.
Nerfing her numbers is the wrong way to balance this champion simply because of how her W works. So how do you balance her? Rework her W!!!! Its that simple. Her W is what makes this champion extremely strong because it basically has no cd. Put a CD OR a ammo mechanic on it. Ive said this so many times but no one seems to under stand that 3 ignites is stupid strong. Her active bolts do not matter because ignite alone is all you need. And thats just 1 summoner.
Proto-belt, gunblade, botrk, redemption, etc are all very strong actives, especially when used early game where it should be impossible to have these items built. So to get lucky and used them multiple times in a row without cd or charges is too much regardless of her base kits damage.
So here is my suggestion: A) everytime she uses a spell with W there is a short CD of 5 seconds before she can use another. CD can be tweaked for balance. This should also allow for her active bolts to be buffed since by default it also will have a CD.
B) give her spell charges. Lets say she has 3 spell charges. She can use up to 3 spells like she normally can currently but once those are used up her W goes on a long CD. Spell drops that drop while her W is on CD drops as spell recharges instead which lowers her W CD if picked up. Once off CD she regains her 3 spell use charges again.
another thing people hate is the fact that her E rewards you even if missed. Bad design no matter how you look at it, but this is an easier fix imo. Simply remove that mechanic entirely or change the zone area into a slow that slowly puts you to sleep if you stand in it long enough. For example instead of the bubble area putting you to sleep instantly it insteads slows you by X%. If you stay in the zone for 2 seconds you are put to sleep. That should be a fair way to keep the mechanic without making it flat out unfair.
That is how id personally balance zoe. Change mechanis first THEN adjust numbers to suit the tweaked mechanics. By now we can safely say that her W and E mechanics are flat out unfair. I get she is supposed to be a champ that ignores game rules, but her ability to use more than 2 summoners is more than enough "unfairness".
. Which is, to be fair, still pretty obnoxious for her enemy.
for example doesnt and neither does
. maybe you can make a case for annie and tibbers with rylais, but that is extreme nitpicking.