Yuumi is the clearest support from all the support champions. She can increase the damage or the ap of the champion she is attached to (adaptive force). She can poke, heal, root, slow and make that damage bigger. She can literally feed one teammate of her team. Or she can make the most fed teammate an unkillable champion. Her perfect time to the game is mid-late game, since she can get some items she do everything she provides much more greater. In the teamfights she is the one who will die last because she is unteachable, and that means that she will always support a teammate at the teamfights until it ends.

The Manaflow Band is the best on Yuumi of the other two ( Nullifying Orb and Nimbus Cloak as they are useful for champion that take damage and walk by themselves)

The Transcendence is the best of the other because it gives you free cdr that you need and the Celerity is useless because you don't walk and the Absolute Focus is useless too since you don't get low.

the Scorch helps you the early poke during the lane phase. Gathering Storm is bot bad but take it when your adc and some teammate are late game champions.

Font of Life is the best since you can activate it. Shield Bash is bad because you don't get damage and the Demolish is bad too since you have no big max health.

Second Wind you actually don't need something from the three so you take health regent. You can also take Bone Plating to Yuumi does the same job.

Revitalize is one of the best runes not only for Yuumi but for all the healers, because makes your shield and your heal greater.

Presence of Mind is very good to Yuumi because she needs a lot of mana and this combined with the Manaflow Band gives her a very big amount mana and mana regent.

Cut Down is an also very good rune for Yuumi because she ha small max health so she deals more damage.

Manaflow Band as i said above you need a lot of mana as Yuumi and this helps with it a lot.

Scorch helps you with the early poke during the lane phase. Previous at the "runes sorcery" paragraph you can see behind because it's the same.

Ardent Censer helpsvery much with your heal and shield you cast and also gives you a high amount of mana regent. Also, gives you and ap and 10% cdr.

Athene's Unholy Grail helps you with the mana regent,ap,10% cdr, its passive is very usefull for all the healers.

this item can protect your teammate. Take it when you want to fully protect an teammate and he will be unkillable.

Zeke's Convergence you can take it when a fed teammate is adc or her damage come of hits like Master Yi or Twitch.

Mikael's Blessing take it when enemy has a lot of cc like Leona or Nautilus.

Redemption I think that this is an situational-core item. I mean that you must try to build it the most times. It gives a team heal and makes the heals and shields greater.

Locket of the Iron Solari take it when you want to shield all the team.

Morellonomicon take it against tanks and champions that have health regent like dr.mundo or Fiora.
Rabadon's Deathcap this item is obvious that you get only for increase your ap.

Rylai's Crystal Scepter it gives an big amount of ap, 300hp and its passive is very useful. By slowing the enemy is easier to catch three times your r and your teammate can finish him.

Void Staff this is the best ap item against tanks. You have 40% magic peration by only building one item.
Twin Shadows this is a very good item. It gives 10%cdr, 70ap and an very useful passive(slow).
Spellbinder gives 120ap and more when you activate it.

Luden's Tempest gives you mana and ap. It is a really good item to poke the enemy so take it fot that. You can buy it and mid-late game it's no need at the early.

Shurelya's Battlesong it give heal and shield power and also speed up your team. Take it when you want to faster an ally that have no speed ups like Nasus.

Early-game

Many players are on their adc with You and Me!. You must hit the minions to try ,at least, take the level 2 and the level advantage. Try to hit the enemies to take the shield from Feline Friendship but be careful don't get too greedy and if not die be low. Because you are Yuumi that's not mean that you don't need health. Try not to get cc because you can die very easy and the You and Me! have cdr after this.

mid-game

Yuumi is not famous about her roaming because she's is not that good but not that bad at the same time. You have speed up, slow and root sow I think you can try to roam. If the first time succeed you can try to do it again. Also you can say your jungler to go for a gank at mid and be on him, to have a sure kill. There's no much to do with Yuumi mid-game just support your adc. If a teammate is ahead and fed except your adc you can go with him and get him even ahead.

late-game

Of coarse at teamfights support the teammate that is most fed, like a fed Nasus with [yuumi]] is unkillable. But see the others teammates because the may need some heal, heal them. If one of your team is split-pushing go with him and your rest team should play defense.

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