Olaf

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Jungle

My Axe is Thirsty

Lane poke dueling and early aggression.

Sorcery

Empowered abilities and resource manipulation

Arcane Comet

Hitting a champion with spells hurls a comet that deals adaptive damage at them. Landing more spells reduces Arcane Comet's cooldown.
Manaflow Band

Hitting enemy champions with a spell grants maximum mana.

After reaching 250 mana, Manaflow Band restores 1% of your missing mana every 5 seconds.
Celerity

Gain 3% extra MS. Gain extra AP or AD, based on your bonus MS, Adaptive.
Scorch

Your first ability hit every 20s burns champions.

Resolve

+65 health and +10 AP or +6 AD, adaptive

Bone Plating

After taking damage from an enemy champion, the next 3 spells or attacks you receive deal less damage.
Chrysalis

Start the game with extra health. After 4 takedowns, consume that health for adaptive AD or AP.

WhyArcane Comet

Olaf's reliable slow with [W] makes your comet a consistent form of sustained poke damage during the laning phase.

WhyManaflow Band

Olaf can have issues with mana when spamming [Q] for poke damage so Manaflow Band helps you keep that up.

WhyCelerity

Celerity's bonus Movement Speed synergizes well with Olaf's [R] as well as Righteous Glory granting you even more Attack Damage when chasing.

WhyScorch

Scorch doubles down on you laning phase [Q] poke allows you to dominate lane with constant harass.

WhyBone Plating

Bone Plating's early game damage mitigation further pushes your dueling pressure in the laning phase to snowball a lead.

WhyChrysalis

Chrysalis' early health allows you to duel your laning opponent early and often. Once you've picked up a few kills and have built health, the extra AD will let you snowball the game in your favor.