Kassadin! I don't like it! Perpetually approved PBE player's thoughts!
LOOK AT DIS GUY.
Okay, so first off, I'm not here to complain. I'm here to suggest. Because the Kassadin that Riot pushed to Live isn't exactly the best solution to the problems that Summoner's Rift players disliked. I mean, he pretty much is the epitome of fixes to Dominion Kassadin due to the quickly stacking ult cost, but that sucker was nerfed already.
I made a post on PBE a while back about how the second iteration of Rework Kassadin the First was a little heavy on the splitpush potential. It was, of course, ignored, and downvoted to hell, because the majority of PBE players, although somewhat intelligent, don't tend to think for themselves. Their minds were stuck "AP burst assassin with a lot of mobility." All of these points in Kassadin's description by the playerbase were things that players disliked, yet they stuck to it. Riot got rid of some of the burst and the assassin while increasing the mobility to make up for the lack of silence which allowed him to lane without risk, even early on, except against champions who had some sort of auto-attack boost. This was, of course, replaced with a magic shield, which once again made it low-risk to play Kassadin. And so on and so forth, but I think I'll skip the now-rambling preamble to go do a spell-by-spell breakdown.
Passive - Void Stone This is fine. Actually, it works thematically, too. The removal of the attack speed boost was necessary to balance out the change to W, because otherwise it would be impossible to outdamage Kassadin as a magic-damage-dealing champion. Noclip makes it easier to work out ult's balance coding-wise because he doesn't jump slightly over units that he clips.
Q - Null Sphere It interrupts channels and grants a magic damage shield. Okay. Interrupting channels is a good idea because otherwise he has no way to interrupt channels and it's kind of a pain in the ass to whap Fiddlesticks in the face otherwise. Except with the latest iteration of Rework Kassadin, he does have a way to interrupt channels, and it's called "kill the hell out of whoever's channeling." So the shield is then superfluous outside of early laning. Dunno what to do about this other than to shift Kassadin's focus off being an AP burst assassin, which would require a lot more... uh, writing, especially controversial stuff.
W - Nether Blade I don't know what you're doing here! 20 + 0.1 bonus ability power magic damage on-hit is actually really useless. It doesn't scale up with level at all, and is almost entirely unnoticeable past level 9! The passive portion sounds like it would be nice to last hit in lane with, but Kassadin's base AD is already the highest in the game! What is the current passive for? In addition, the active at the moment is kind of ridiculously... ridiculous - it's an auto-attack reset that doesn't go on cooldown upon hitting a tower, but it does a ton of damage, works with Lich Bane, and restores mana. But the cooldown stays at 6 unless Cooldown Reduction is purchased, which often comes from Athene's Unholy Grail. This, of course, absolutely breaks Nether Blade, because Athene's Unholy Grail refunds mana on assist/kill, adds CDR, and increases mana regen by a ton - Kassadin can effectively never run out of mana, ever, spamming Nether Blade on Champions in teamfights. The cooldown caps out at 3.6 seconds, by the way. Also, Empower works pretty similarly to Nether Blade's current iteration, except the base damage is higher, the cooldown gets lower with level, and it can be used in tandem with Jax's mobility spell. It also has the same AP ratio and property of resetting autos without going on cooldown upon hitting a tower.
E - Force Pulse What is this still doing in his kit it literally does nothing especially the part where it charges up. I mean I guess it slows and adds a little bit of damage but why is it here in this form. It was even more useless during my favorite iteration of Kassadin because that iteration could build Iceborn Gauntlet and Force Pulse's AP ratio and base damage were garbage.
R - Riftwalk "The community's complaining about Kassadin's ridiculous mobility - let's REDUCE the cooldown on Riftwalk!" The cooldown can hit 1.8 seconds with 40% CDR. Even if the ult cost stacks to 1200 in four casts, theoretically Kassadin's mana can hit somewhere between 4000 and 5000, which combined with Nether Blade and Athene's Unholy Grail makes that increased cost more or less just... not there, so expect to see everyone building Athene's the minute teamfights roll around and never running out of mana, ever, and teleporting every 1.8 seconds. THANKS RIOT.
How to fix the problem:
Preamble Okay, so basically, his AP ratios are too high for the fact that he has an autoattack reset and an ult that times perfectly with Lich Bane's cooldown before CDR. Also his Q magic damage shield and his passive are a bit too much to be together, especially since the Q magic damage shield scales with AP, which he's gonna get loads of, causing a ton of artificial tankiness against magic damage. "Weak to AD" is wrong, too, considering the existence of Zhonya's Hourglass and Rod of Ages. Hello effective 1000 health as part of a core build, how are you doing?
Two paths are available: Gimp the hell out of Kassadin, causing backlash Change Kassadin's "role" to clash with player perceptions, causing backlash because they think he's been gimped
For reference, a Kassadin's build would look something like this:

There's no Void Staff so I'm worried but I suppose the build could be swapped with this:

Then again, those builds are pretty tanky and don't mesh well with "AP assassin" as a concept:

Note Athene's Unholy Grail's presence in every. Single. One. Same with Lich Bane, especially because Kassadin's base AD is freakin' huge.
The first path would deal mainly with the biggest problem factors:
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The combination of the way Kassadin's ult works with the way his W works and Athene's Unholy Grail would work
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Kassadin's base AD plus Lich Bane plus all the low cooldown stuff and auto resets
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Look at me I'm frickin' doing MORE damage than before in burst because my AP ratios are the same or bigger now!
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Magic damage shield that scales on his main stat plus 15% reduced magic damage.
At the moment, mana is still encouraged to be built alongside AP if only because that means infinicast of his ult, by the way.
Anyway, path 1 would see a different or lower ratio on Kassadin's magic damage shield, coupled with lower base values at higher ranks and slightly higher base values at lower ranks. AP ratios would be reduced by 0.05-0.15. Kassadin's base AD needs to not be better than almost every other champion in the game, if not every other champion in the game period. The ultimate should scale up over slightly more stacks in exchange for reducing the mana regeneration on W by evening out its distribution of being really freaking strong over the levels and conditions. The more of these adjustments put in, the lesser their severity - see example below:
Base stats
Armor per level reduced to 2.7 from 3.2
Attack damage per level reduced to 3.1 from 3.9
Base health reduced to not be the same as Dr. Mundo's
Passive
Same
Q
Damage - 80/105/130/155/180 + 0.6 AP
Shield - 60/80/100/120/140 + 0.25 AP. Effectively, he wants to be able to block his own Q cast at level 1. 600 AP means 150 more magic damage blocked. The effective cooldown of this ability with Athene's Unholy Grail is 5.7 seconds, about on par with the amount of time it takes for Yasuo's shield to refresh, proportional to blocked damage.
W
Cooldown - 5/5/5/5/5
Passive - Functions like a weaker magic damage version of Muramana - drains 2% current mana and deals 10/12/14/16/18 + 30/35/40/45/50% AP for each 50 points of mana in the "current mana" pool magic damage on-hit.
Active Damage - 50/70/90/110/130 + 0.5 AP
Active Utility - Restores the lower value between 10% of current mana and 15% of missing mana. Restores the higher value between 40% of current mana and 20% of missing mana against Champions. (is there really a need to have this scale when mana scales in the first place?)
E
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Base damage increased to 85/120/155/190/225
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AP ratio reduced to 0.25/0.3/0.35/0.4/0.45
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Slow reduced to 10/16/22/28/34%.
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Now restores 1% of missing mana per 120 damage dealt by the ability.
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Alternatively, slightly repositions targets away from Kassadin depending on how close they are.
R
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Stacking damage bases changed to 20/25/30 per stack
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Stacking damage ratio changed to 4% of missing mana per stack
Assume Kassadin has 600 AP and a Lich Bane and 3000 mana.
One rotation now applies the following damage and effects:
(Ult is stacked to max)
(Q) 540 magic damage + 290 magic damage shield
Current mana: 3000 - 1125 - 90 = 1785
(R) 120 + 60 magic damage
(R - From Stacks) 120 + 194 (1215 * 0.16) magic damage
Current mana: 1785 - 1200 = 585
(E) 495 damage + 34% slow
(E - ver. Knockback) Nearby enemies are pushed away.
(E - ver. mana recovery) Restores approx 4% of missing mana per enemy hit, prior to damage reduction. Assume 3 targets hit for this demonstration. 300 mana is restored.
Current mana: 795
[[ AA-then-W for speed efficiency:(AA) 81 + 300 + 96 (477) magic damage
Current mana: 779
(W) 108 physical + 430 magic damage
(W restoration) 444.2 mana
Current mana: 1223
Per killed champion, restore 360 mana.
Total damage (single target): 2544, prior to damage reduction]]
[[W-then-AA for damage efficiency: (W)430 + 81 + 300 (811) magic damage
(W restoration) 441 mana
Current mana: 1236
(AA) 108 physical + 168 magic damage
Current mana: 1221
Per killed champion, restore 360 mana.
Total damage (single target): 2616, prior to damage reduction]]
Then there's the option where you can revert him to manatank form like he was on the PBE when I posted a topic on PBE Community Beta regarding that version's splitpush capacity. The manatank form would require quite a few tune-ups as well, but no way I'm going into those when I just typed all this out and I have to go to the dentist in a few minutes.
TL;DR as a PBE player who witnessed all sorts of poo-flinging regarding Kassadin and really didn't like his current iteration before it got passed to Live, as well as having read some posts regarding how Kassadin's current burst is stronger than it was before, something needs to be done. I feel like the retained manatank qualities slapped onto his W and R from the previous iteration clash with his current playstyle because it synergizes too well.