*Cracks knuckles and pulls out champion statistics*
Ok. So you say that kassadin is OP in terms of damage? Let us make various comparisons!
First off, his innate gives him 10% reduced magic damage and transforms this damage into bonus attack speed. This effect lasts up to 4 seconds. A decent comparison would be that of regular MR.
10 Magic Resist gives 9.091% reduce damage from magic based damage, fairly close to the equivalent of the magic reduced by one hit, so nothing too big, although I am not too sure on the exact numbers on the attack speed bonus.
Annie seems like a fairly good comparison in terms of magic damage burst so let us compare base statistics first. Joining her will also be Yi, a melee carry. Reason for both comparisons is how kassadin shares similar traits with both, especially since he is melee.
Health 348 +76 per level
Mana 250 + 50 per level
armor 8.5 + 4 per level
Magic Resist 30 (no mr per level)
Attack Damage 48 +2.63 per level
Attack Speed 0.579 +1.36% per level
Health 444 +86 per level
Mana 199 +36 per level
Armor 16.3 +3.7 per level
Magic Resist 30 +1.25 per level
Damage 55.12 +3.1 per level
Attack Speed 0.679 +2.98% per level
Health 433 +78 per level
Mana 230 +45 per level
Armor 14 + 3.2 per level
Magic Resist 30 +1.25 per level
Attack Damage 50.6 +3.9
Attack Speed 0.638 +3.7% per level
Overall, kassadin's normal auto attack damage is lower than Yi's, stronger than annie's, but compared to annie lacks the safety of range in terms of auto attacking.
Seems pretty inbetween with the two roles.
NOW is the main thing that determines the balance, the skillset.
Kassadin's Null Sphere
80/130/180/230/280 +0.7 magic damage with a silence duration of 1/1.4/1.8/2.2/2.6 seconds.
Costs 70/80/90/100/110 mana
Cooldown 9 seconds
90/130/170/210/250 +0.75 magic damage, can stun due to passive.
Cost 60/70/80/90/100 mana.
Cooldown 4 seconds.
At first glance, Kassadin's has a worse early game output than annie's disintegrate, but later on gets a stronger base. Annie does have an ever so slightly better AP ratio, so if both are just constantly stacking AP, annie may still deal more damage. Kassadin does have the upper hand in terms of range, but annie's cooldown is two times lower than that of kassadins. This counterbalance is then put into equalibrum when you take into consideration that annie would use more mana if spammed at any given moment, but does get more mana via leveling up.
Kassadin's Force Pulse
Deals 60/115/170/225/280 +0.7 per ap magic damage, as well as a 30/35/40/45/50% slow.
Costs 80 mana
Cooldown of 6 seconds (but requires 6 spells to be cast near him to be able to use force pulse)
Range of 400.
Cone Width 90 degrees.
85/135/185/235/285 +0.8 per AP magic damage with potential of stun.
costs 80/95/110/125/140 mana
cooldown 8 seconds
cone width 45 degrees
While Kassadins has a wider width, thus able to hit more enemies clumped togeather, Annie's has a longer range. Kassadins does have a lower cooldown, but can be slightly less reliable since he must gain the spell charges before he is able to use it. Damage output is nearly the same, although annie's is infact slightly stronger, mana cost on annie's is a little bit more intensive, but as stated before, naturally has a slightly better mana pool. The key determining factor is comparing a possible stun, although can only be gained after using so many spells, or a slow, based upon the situation.
Nether Blade doesn't really need much of a comparison. his passive allows him to regain 8/11/14/17/20 mana per auto attack. His active grants his auto attacks 20/30/40/50/60(+0.15 per ap) magic damage for 5 seconds. Although pretty strong, Kassadin is far from a tanky figure, and as such should not often go into melee unless he knows he can go in, get a kill, and get out.
Lastly is Riftwalk, his difining ability. Riftwalk deals 60/90/120 magic damage, and has a cooldown of 6/5/4 seconds. Mana cost is 100, and the range is 400. If he used the ability already within 7 seconds, the ability costs an additional 100 mana, and deals an additional 60/90/120 magic damage per stack. This can stack up to 10 times, thus allowing quite a bit of damage, but also costing a ton of mana for each additional jump. Usually the closer for his melee attacks and for going in for the kill. After gaining this ability his role changes more from a mage to an AP assassin, and as such should be treated as an assassin, stick with your teamates or atleast know you have some sort of backup if he appears so you can burst him down.