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To consider Poppy a carry, you must consider what she has beyond the normal carry.
Poppy's passive gives her a higher effective HP than almost any non-tank.
Poppy's ultimate gives her immunity to most all CC and most of damage in team fights.
Poppy's Q gives her an incredible nuke, like Gangplank's Parrrley.
She has a decent escape with her self move speed buff.
Overall, Poppy will give you 6 seconds to wreck all hell on the enemy team, assuming you use your ult on the right person. Her overall damage output is strong and she also brings a situational stun. She is relatively strong at chasing, but isn't as good at chasing as Jax or Udyr. She also deals a heavy deal of harrassment damage with her Devastating Blow in laning.
Poppy's passive is great. Effectively, think of her eHP as being roughly 25% greater. Essentially, think of Poppy as being a 2350 HP champion. Please note, this passive also means that HP, armor, and MR all scale worse on her than other other champion.
Poppy's Devastating Blow is, for all intents and purposes, a melee Parrrley which deals physical, rather than magical, damage. When you consider the differences between MR and armor, it deals roughly the same amount of damage. This means that, like Pirate, crit items are great on her. Unlike Pirate, however, she cannot use Haunting Guise or Sorc Boots to up her DPS nearly as much.
Paragon of Damacia
This ability ups your DPS slightly but is far better for running away or chasing. The main aspect of it is the move speed increase. Whenever you need a little bit extra move speed, use it.
This is almost like a mini-Headbutt for Poppy. It's great for slamming people into walls to stun. Be sure to use Paragon of Damacia's active to move into a favorable position to charge the enemy.
Poppy's ult is useful for every team fight. There are multiple ways to use it.
1. Target the opposing carry, exhaust the carry. This essentially makes you immune to almost all damage and CC, given how most carries will lack any hard CC.
2. Target the opposing support. This should relieve you of most of the DPS and CC.
3. Target the opposing tank. This isn't as favorable as tanks tend to have knock ups or some other kind of CC.
Step 1: The Avarice
Start with Brawler's Gloves. Hold off until you can purchase Avarice Blade x 2. Do not purchase Avarice Blades if over 15 minutes have elapsed. These blades will pay for themselves after 25 minutes.
Purchase Boots of Speed during this phase, as well.
Step 2: Infinity Edge
Purchase the Infinity Edge with the Cloak of Agility coming first. Purchase the damage items in any order, but B.F. Sword first is preferred.
Purchase Berserker's Greaves or Mercury's Treads or Ninja Tabi during this phase. Berserker's Greaves will give you the greater DPS and Ninja Tabi's dodge is the only eHP boost which does scales equivalent with Poppy's passive. Mercury's Treads is more reserved for teams which seem to CC you more often out of your ult.
Step 3: End Game
Purchase Last Whisper. This gives you a healthy attack speed increase which should increase your overall DPS. If the enemy has 80 armor, it will reduce it effectively to 48, roughly a change from dealing 56% damage to dealing 68% damage. The effective damage increase is rather substantial.
Purchase Cloak of Agility. Your goal at this point is to reach Phantom Dancer which will give you more crit, move speed, and dodge. Feel free to sell an Avarice Blade to purchase either the Cloak of Agility or Zeal.
Devastating Blow Damage at Lv18 with These Items:
50% Crit Damage Runes vs. 2000 HP: 70% Crit of 1345, 30% Non-Crit of 555
20% Crit Chance Runes vs. 2000 HP: 90% crit of 1145, 10% Non-Crit of 555
If the game has continued on, buy a [item=B.F. Sword] and work from there. It is unlikely your game will go on this long.
4. Masteries + Runes
Crit chance or crit damage runes are both excellent. Damage will scale better near the end while chance will scale better earlier. Both will work quite well.
To quote Heat n' Serve:
"without I.E. (2x crit dmg)
if base < 36.5% => stack more crit chance runes
if base > 36.5% => stack more crit damage runes
with I.E. (2.5x crit dmg)
if base < 56.5% => stack more crit chance runes
if base > 56.5% => stack more crit damage runes
Meaning if your base crit chance from everything excluding runes is greater than the above thresholds, then stacking more crit chance runes will lower your dps. Having more crit damage from items beyond 2.5x will only serve to raise the point at which you reach this threshold of stacking crit chance.
These thresholds are fairly broad, meaning just slightly above or below the threshold, your dps does not differ significantly from the optimal dps.
At the break even point, it is interesting to note that in order to obtain optimal dps, you would need to make a funky combination of crit chance and crit damage runes, rather than stacking all of one or all of the other."
Use 8/1/21 http://leaguecraft.com/masteries/310...31042030031301 masteries if using Heal, else use 9/0/21 http://leaguecraft.com/masteries/3100400100000000000000000000031042030031301.
5. Summoner Abilities
There are several to consider.
Flash is good to set up Heroic Charge stuns. It also has a lot of value as a fleeing maneuver. Given how Poppy has move speed increase from her Paragon of Damacia, she should be able to escape from many every situations.
Exhaust allows you to disable an enemy carry and then use Diplomatic Immunity on them. It is also good for general ganking.
Heal is very effective if used with low HP. Poppy's damage mitigation increases her health is increased, so using heal to stay alive at low HP will increase her eHP the most.
6. Skilling Order
Level 1: Heroic Charge (E)
Level 2: Devastating Blow (Q)
Level 3: Paragon of Damacia (W)
Level 4: Devastating Blow (Q)
From this point, R > Q > E > W.
7. Various Tips
* Golem buff adds greatly to your game. Having a quicker CD to hit them with your Q always gives a large DPS increase. Poppy also has a moderate mana problem and the golem buff will solve it.
* Don't underestimate her ability to burst through many jungle creeps. Her Q's 8% damage increase deals hefty damage to jungle creeps. It's entirely possible to land a strike of over 1500 against Golem or Lizard in this way.
8. Build Example
Please note, in this particular build, there has been at least 1500 gold generated from [item=Avarice Blades] (25+ minutes) and 375 gold has been returned due to the selling of one of the blades.