[Touhou] Patchouli Knowledge

Name: Patchouli Knowledge
Title: The Unmoving Great Library
Anime: Touhou

Background Story:
Patchouli Knowledge is a very smart, asthmatic magician from the Scarlet Devil Mansion. She rarely leaves the Scarlet Devil Mansion. She spends most of her time in the mansion's library reading and writing magic books. She's capable of very powerful magic of all kinds, using many elements in a single spell, but due to asthma and general poor health she's often unable to recite her spells. But her passion for elemental magic and books has lead her to reside in the library of the Scarlet Devil Mansion, wherein she acts as its librarian.

Attributes:
Endurance
========== [4]
Swiftness
========== [4]
Potency
========== [8]
Resistance
========== [3]
Speed
========== [3]
Stats Growth:
Endurance
=
Swiftness
=
Potency
==
Category:
Carry
Extra Information:
Attack Range: 500 (Ranged)
Base Attack Time: 2
Base movespeed: 230

Default Skill - Element Sign "Manipulation of Five Phases"
Information:
Patchouli is able to handle the five phases; commonly called Wu Xing, sometimes known as the five elements, with the addition of the sun and moon elements. The order of elements she uses follows the days of the week on a Japanese calendar. Due to this, she is known as the "one-week girl".
--------------------------------------
Ability Type: Passive
Ability Effect: -
Cast Time: -
Cast Range: -
--------------------------------------
Effect:
When Patchouli successfully attacks an enemy unit, she has 15% chance to cast a spell on that target. She can cast the "Fire Sign", "Water Sign", "Wood Sign", "Metal Sign" and "Earth Sign" spells. Each spell has a cooldown time of 20 seconds.

Note:
Fire Sign "Summer Red"
Shoots a large fireball straight ahead and deal (80x0.5Hero Level) instant damage. The enemy unit which was being hit by the fireball will be knocked back at a distance of 100 and will be stunned for 1 second.

Water Sign "Winter Element"
Summons a waterway at the enemy's feet. After 1 seconds, enemies within that 150 AOE will be attacked by the high-pressure water spout, dealing (100x0.5Hero Level) instant damage and making the victim to be thrown up to the air.

Wood Sign "Flash of Spring"
Patchouli creates a shot of high pressure air and throws it at the enemy in front of her, dealing (100x0.5Hero Level) instant damage. The air travels instantly at a distance of 1000. The pressure stops traveling when in contact with a hero.

Metal Sign "Autumn Edge"
Creates 3 sharp blades and manipulates them to rush at the enemies in front of her, dealing (35x0.5Hero Level) instant damage for each blades. The blades won't travel in a parallel direction, but in a spreading pattern.

Earth Sign "Dew Spear"
Summons 3 crystal spears from the ground and erupts for, then rains down immediately after 1 second on 150 AOE on the target, dealing (30xHero Level) instant damage for each spears. Each spears stuns the enemy for 0.5 second.
--------------------------------------
Cooldown: -

1st Skill - Fire Metal Sign "St Elmo's Pillar"
Information:
This spell is a synthesis of "Fire Sign" and "Metal Sign". Patchouli hurls a fireball at the ground under her opponent, which explodes into a pillar of flame. Very fast and can be used to catch people off guard at any range, and its extension into the air makes it one of the more useful cards in Patchouli's arsenal.
--------------------------------------
Ability Type: Active
Ability Effect: Instant
Cast Time: Channeling
Cast Range: 900
--------------------------------------
Effect:
Patchouli channels for 3 seconds, then throws the fireball at the selected area target. If Patchouli moves before she finishes channeling, the fireball will be fired immediately. The fireball itself deals (75/215/360/510/650xTime channeled) damage on the target with 350 AOE. Then after 0.5 second, the fireball will create a pillar of flame from under the enemy, dealing 50% of the damage dealt earlier.
--------------------------------------
Cooldown: 30

2nd Skill - Moon Sign "Silent Selene"
Information:
After holding her book to her lap and spreading a large magic circle around her, Patchouli creates a series of blue columns which circle her and spread out. It is like magic that protects Patchouli like an impregnable fortress.
--------------------------------------
Ability Type: Active, No Target
Ability Effect: DPS
Cast Time: Channeling
Cast Range: -
--------------------------------------
Patchouli summons 10 beams of light randomly around her. These condensed moonlight will orbit around her in a 300 AOE circle with a movespeed of 250. Enemies in that area take 200/300/400/500/600 DPS. In addition, enemies in contact with the beams will take damage from it; Each beams deal 40/55/70/85/100 damage. This spell last for 3 seconds.
--------------------------------------
Cooldown: 30

3rd Skill - Sun Wood Sign "Photosynthesis"
Information:
This spell is a synthesis of "Sun Sign" and "Wood Sign". Patchouli summons a ray of green light that shines on where she is standing. As long as she is in this field, she will be healed by this light. The benevolent light will follow her around.
--------------------------------------
Ability Type: Active, No Target
Ability Effect: DPS
Cast Time: -
Cast Range: -
--------------------------------------
Effect:
The light that Patchouli summons needs 2 seconds to shine. After 2 seconds of shining, the light will heal her and any allies under the light with a rate of (6.5/7/7.5/8/8.5%xPatchouli's Max HP) per second. The light follows Patchouli slowly, with a MS of 150, until it is directly centered on her. The light lasts for 10 seconds and has 200 AOE.
--------------------------------------
Cooldown: 45

Ultimate - Five Elements "Philosopher's Stone"
Information:
Patchouli creates a set of crystals that revolve around her, orbiting around her. Red crystal represents the "Fire Sign", Blue crystal represents the "Water Sign", Green crystal represents the "Wood Sign", Yellow crystal represents the "Metal Sign" and Orange crystal represents the "Earth Sign". The crystal amplifies specials of that element by breaking up into a small set of coloured projectiles, which the colour depends on the crystal used, that fly at the opponent whenever that special is used. The crystal of that element is lost upon use, but is replaced after a short amount of time.
--------------------------------------
Ability Type: Passive
Ability Effect: Buff
Cast Time: -
Cast Range: -
--------------------------------------
Effect:
When this skill is learned, 5 coloured crystals; Red, Blue, Green, Yellow, Orange, will orbit Patchouli as soon as she learns this spell. The performance of Element Sign "Manipulation of Five Phases" will improve. It increases the skill's probability chance from 15% to 30/35/40% and decreases those five skills' cooldown from 20 seconds to 15 seconds. Each crystal will be consumed depending on the element of the skill used, breaking into 10 projectiles. These projectiles will then fly towards the target which the spell was being cast, and each projectiles will deal (15/25/35xHero Level) instant damage with a small explosion of 75 AOE. The consumed crystal will regenerate back after 6 seconds.
--------------------------------------
Cooldown: -

The Default Skill is basically a 15% chance to cast one of the 5 spells. Each spell has a 20% chance of being casted.
Probably the only difficulty would be the cooldown, but I believe it's still possible.

Default

Firstly, don't mind about the bonus damage, cause I have no idea how the stats would be distributed. I might even consider putting just plain fixed damage instead of stats multiplier damage.

1st skill

A 3 seconds channeling which deals only 1.6k, is it too strong or too weak? If it's the latter, then it serves my purpose. For a default skill to deal 11.4k damage, this farming skill should be weakened.

2nd skill

Speed of the beams huh, well okay I forgotten about it, -updated-. Yeah, unmoving lol.

3rd skill

It's made to be a weak healing skill, but it heals her HP via percentage, and not value. At max level would just heal 50% of HP. Yes, this is a skill just to prevent you from being killed by creeps at early levels, and only supporting allies who can save their time from retreating to the base.

Ultimate

This skill only syncs with the default skills. Any more ulti-default combination and 1st and 2nd skill damage would be too imba.

Well... You can be helpful by providing something like a formula to calculate the stats at a specific level?
She would fit more to be a Nuker, Carry than a Nuker, Supporter.