Poppy is actually quite the assassin mage mid! Her Q and E allow her to have quite the burst once she makes it past level 3 or gets a sheen. I know her ap ratios sound low although her Q is extremely op! Rank 5 it does 100 base damage (+ 100% total AD) (+ 60% AP) (+ 8% of target's maximum health) and add a lich bane and theres another 70% ap and 50 base damage..


This does not include with the ult bonus that her Q gets Or the Ad bonus she gets from her W. And this is on a 4 second cooldown.. (not including cooldown reduction) She has one of the best low cooldown ap nukes in the game..

Its true she has a hard time farming and is only single target.. Although with a mana regen pendant she can get 5 health potions and 3 mana potions which allows her to farm using her Q and completely ignore the enemy due to her high sustain..

By the time you have to first back you should be at least level 4/5/6, by now she can trade with the enemy mid. With melee mids such as fizz, when they come in range always use Q.. On ranged an E,Q combo is required followed by a W to escape

Pros:
High Damage Late Game
Can easily kill the adc in teamfights
Low Cooldown Q nuke
Fun to play
Strong against melee champions

Cons:
Terrible exchanges pre level 3
Squishy with no spell vamp or lifesteal
Weak against long ranged champions

Poppy is one of the worst farmers in the game due to her very low mana pool and high mana costs.
This can be fixed with a tear of the godess, encouraging poppy to use her Q to farm minions.
Poppy can last hit easier if her W is kept at 10 stacks.

Sheen/Lich bane is a must on poppy. It makes her overall burst much higher.
Tear allows her to farm.
Deathfire grasp makes syncs well with her ult making her abilities do a LOT of damage.
Homeguard enchantment on boots and her W work well together to get back to lane.
Items like Hextech Gunblade/Will of the ancients make her much more durable.