You dabbled in the College of Necromancy but didn't love the corpses.  The College of Evocation was a bit strict.  You moved from College to College but never quite found you niche.  Too dull, too dogmatic, too boring.  Before long you realized you could do this whole "Wizard thing" without the strict confines of Wizard Colleges.  Unfortunately your expertise didn't exactly translate to mastery.

Other Wizards look down upon the dropouts.  Some are outright hostile, not wanting their secrets getting out to the uncultured.  Not that it bothers you, as you are busy finding yourself and doing your own thing.

Dropouts rely on instinct and raw power, instead of precision and predictability.  

Dropouts are also able to adjust on the fly because they are not adhering to strict guidelines.

Tools of the Inventor

At 2nd level, you gain proficiency with a tool and a musical instrument.

Experimental Armor

Your passion for magic is unmatched.  Your control is less than ideal.  To combat these dangers you developed some special armor as a precaution, but also to prove to the establishment Wizards that you can do enchantment your way and don't need to sit through hours of lectures.

Starting at 2nd level, you gain proficiency with light armor and gain a suit of experimental armor — a magic item that only you can attune to. While you are attuned to it and wearing it, it grants you resistance to force damage.

The armor is light armor and provides an AC of 12 + your Wisdom modifier. It weighs 8 pounds.

You can create a new suit of it at the end of a long rest by touching a non-magical suit of studded leather armor, which magically transforms it. Doing so removes the magic from your previous experimental armor, turning it into non-magical studded leather.

Reckless Casting

Your dabbling in all the arcane subjects has given you a vast knowledge of spells.  However, since you didn't spend enough time studying them thoroughly, you can't quite remember which is which.  You know a large number of spells, you just don't always know which one you will cast.

• Roll on the Reckless Casting table for cantrips and cast the resulting spell as part of this action.
• Expend a spell slot and roll on the Reckless Casting table for its level, cast the resulting spell as part of this action.

If the spell you cast isn’t a wizard spell, it is nonetheless a wizard spell for you when you cast it with this feature.

Additionally, you may prepare one spell per spell level prepared that you can cast at will (still uses spell slot).

Reckless Casting

d10	Cantrip
1	acid splash
2	chill touch
3	fire bolt
4	light
5	poison spray
6	ray of frost
7	shocking grasp
8	gust
9	thorn whip
10	Roll twice and cast each cantrip, but if you roll another 10 on either die, you cast nothing, wasting your action.

d10	1st-Level Spell
1	burning hands
2	chromatic orb
3	color spray
4	compelled duel
5	false life
6	fog cloud
7	ice knife
8	magic missile
9	thunderwave
10	Roll twice and cast each spell, but if you roll another 10 on either die, you cast nothing, wasting your action but not the spell slot.

d10	2nd-Level Spell
1	heat metal
2	darkness
3	enlarge/reduce
4	aganazzar's scorcher
5	invisibility
6	levitate
7	Melf’s acid arrow
8	scorching ray
9	shatter
10	Roll twice and cast each spell, but if you roll another 10 on either die, you cast nothing, wasting your action but not the spell slot.

d10	3rd-Level Spell
1	blink
2	fear
3	feign death
4	fireball
5	haste
6	mass healing word
7	lightning bolt
8	melf's minute meteors
9	stinking cloud
10	Roll twice and cast each spell, but if you roll another 10 on either die, you cast nothing, wasting your action but not the spell slot.

d10	4th-Level Spell
1	blight
2	giant insect
3	Evard’s black tentacles
4	conjure minor elementals
5	greater invisibility
6	ice storm
7	phantasmal killer
8	stoneskin
9	vitriolic sphere
10	Roll twice and cast each spell, but if you roll another 10 on either die, you cast nothing, wasting your action but not the spell slot.

d10	5th-Level Spell
1	cloudkill
2	cone of cold
3	danse macabre
4	far step
5	hold monster
6	insect plague
7	mass cure wounds
8	steel wind strike
9	wall of stone
10	Roll twice and cast each spell, but if you roll another 10 on either die, you cast nothing, wasting your action but not the spell slot.

D10	6TH-LEVEL SPELL
1	chain lightning
2	disintegrate
3	eyebite
4	globe of invulnerability
5	investiture of flame
6	investiture of ice
7	investiture of stone
8	investiture of wind
9	otto's irresistible dance
10	Roll twice and cast each spell, but if you roll another 10 on either die, you cast nothing, wasting your action but not the spell slot.

D10	7TH-LEVEL SPELL
1	crown of stars
2	finger of death
3	mordenkainen's sword
4	power word pain
5	prismatic spray
6	reverse gravity
7	whirlwind
8	project image
9	forcecage
10	Roll twice and cast each spell, but if you roll another 10 on either die, you cast nothing, wasting your action but not the spell slot.

D10	8TH-LEVEL SPELL
1	abi-dalzim's horrid wilting
2	antimagic field
3	dominate monster
4	illusory dragon
5	maddening darkness
6	maze
7	mind blank
8	power word stun
9	sunburst
10	Roll twice and cast each spell, but if you roll another 10 on either die, you cast nothing, wasting your action but not the spell slot.

D10	9TH-LEVEL SPELL
1	invulnerability
2	meteor swarm
3	power word kill
4	prismatic wall
5	psychic scream
6	shapechange
7	weird
8	wish
9	storm of vengeance
10	Roll twice and cast each spell, but if you roll another 10 on either die, you cast nothing, wasting your action but not the spell slot.

Corrective Casting

At 6th level, you learn to channel magic through your experimental armor to augment spells in a variety of ways. When you cast a spell while wearing that armor and attuned to it, you can expend one additional spell slot of 1st or 2nd level to alter the spell. The effect depends on the spell slot you expend.

A 1st-level slot allows you to manipulate the spell’s energy. When you cast a spell that deals acid, cold, fire, lightning, or thunder damage, you can substitute that damage type for another one from that list.

A 2nd-level slot increases the spell’s raw force. If you roll damage for the spell when you cast it, increase that damage by 2d10 force damage against one of the spell’s targets (your choice) this turn.

Reassessment

At 10th level, you have attained a greater mastery of spell preparation. As a bonus action, you can replace the spell you have prepared with another spell from your spellbook. You can’t use this ability again until you finish a short or long rest.

Controlled Chaos

At 14th level, your ability to improvise magic grows stronger. Whenever you roll on a Reckless Casting table for a spell other than a cantrip, you can roll on the table that is one level higher than the expended spell slot or at a higher level.

Show Off

(Replaces Signature Spells)

At Level 20 you show your mastery of the arcane.  Once per long rest you can expend a spell slot to roll an automatic 10 on the spell table.  You must still follow the rules for rolling a 10 on the subsequent rolls.