Passive: Berzerker Rage
For each 1% of health missing, Olaf's attack speed is increased by 1%.
This spell is fairly simple and is the reason why he can 1v1 or do jungle extremely quickly. While I don't recommend being constantly low hp to make use of this, it is extremely useful during and after a fight to quickly lifesteal or down a turret/dragon/buff when combined with Wriggles Latern. But the fact that this passive gives so much, allows Olaf to run armor pen runes because having 12-25%
attack speed buff is fairly minimal when you can have a passive that gives 0-99%
attack speed bonus.
Olaf throws an axe to a target location, dealing 50 / 90 / 130 / 170 / 210 physical damage plus 50% of his attack damage to units it passes through and slowing them by 16 / 22 / 28 / 34 / 40% for 2.5 seconds.
If Olaf picks up the axe, the ability's cooldown is reduced by 6 seconds.
Cost 55 / 60 / 65 / 70 / 75mana
This is basically half the reason Olaf is useful, because of the effect of CDR, this skill can effectively have a 1-2 second cooldown, far shorter than ANY aoe skill in the game. Because of it's synergy with is ult and armor pen runes, it will do a huge amount of damage all game and will easily clear waves faster than anything except a super fed AP carry. Undertow sets Olaf apart from the junglers in the fact that it's a reliable ranged CC before level 6 which allows him to do stronger ganks than WW/Udyr as he doesn't need to get in melee range to do it. Simply put, easily one of the strongest spells in the game.
W: Vicious Strikes
For 6 seconds, Olaf's attack damage is increased by 7 / 14 / 21 / 28 / 35 base damage plus 1% of his max health. While active, Olaf gains 9 / 12 / 15 / 18 / 21% lifesteal and spell vamp.
Cost 40 / 45 / 50 / 55 / 60mana
Because of nerfs, this skill is now relegated to being a 1
point wonder as the first point gives the 1%
damage boost according to his health and doesn't change after that. This also gives him a fast way to heal when used with his Undertow as he can clear waves near instantly while taking minimal damage. I max this last because the last 4
points are relatively minimal in effect compared to the first and Reckless Swing requires the points to be useful.
E: Reckless Swing
Olaf deals 100 / 160 / 220 / 280 / 340 true damage to his target and inflicts 40 / 64 / 88 / 112 / 136 true damage to himself.
Despite it's seemingly low numbers, this spell is extremely brutal in damage against anything that stacks armor/mr because it is true damage. When used in combination with Undertow/Melee hits, this is a great source of damage and a great finisher. Leveling this over Vicious Strikes is because it not only increases the damage by a fair bit but it lowers the cooldown on it which essentially makes each next point even better than the last.
Active: For 5 / 6.5 / 8 seconds, Olaf is immune to disables and reduces incoming damage by 20 / 30 / 40.
Passive: Olaf has 10 / 20 / 30 increased armor penetration.
Cost 100 / 75 / 50mana
This spell now gives magic resistance and armor now making it superior for later game. However, it's true strength lies in the fact that you are immune to CC, this fact alone is the other half of what makes Olaf viable. If he didn't have this, he'd be basically a Yi as he'd be perma stunned to oblivion whenever he'd go in to melee. But thanks to this spell, Olaf's damage and durability are mostly taken care of and basically allows Olaf to solo people mid game with only Wriggles.