Some math behind Patch 4.21
tl;dr at the bottom

Passive - Aspect of the Serpent
on every poisoned unit kill
once every 6 seconds (10 times per minute)
Let's assume for a moment that "Unit kill" only stands for minions for a second here. This means we can calculate this for time: -Minions at mid lane meet each other approximately at the 2:00 mark. By then, that will be 20 stacks on the new passive. This will also mean 12 new stacks per minute with the old method, vs 10 per minute with the new method. Currently: 12x(minutes)=20+10x(minutes) minutes=10 This means, assuming you have 0 interaction with the enemy champion, if you can somehow get a perfect CS score with nothing but poisoned minions, you will actually generate less stacks past the 10 minute mark. On a 4 second cool down with a 3 second poison time on Noxious Blast, I can see this being a kinda impractical analysis, but feasible. If you are an extremely proficient farmer, especially if it were to come to managing your poison, time is not your friend.
Buuuuuut that's bullshit. You're not Nasus, this isn't farming simulator 2014. Let's look at champion interaction:
on Twin Fang cast on enemy champion
for every second that an enemy champion is poisoned.
Calculating for mana, mostly because mana seems to be the only thing close to resembling a shared trait between these two situations, you get 1 stack per 30 / 45 / 60 / 75 / 90 mana, depending on the rank of Twin Fang, based on the old system, whereas you get 3 stacks for 40 / 45 / 50 / 55 / 60 mana, based on Noxious Blast.
Simply put, per point of mana (which is incredibly important to keep track of, I might add, during the laning phase), Cassiopeia is far more efficient at stacking than ever before.
I can't say for sure that "Cassiopeia gains special bonuses at 75/200/400 stacks ⇒ 100/250/500 stacks. The new breakpoints will be hit sooner than the old ones based on the new stacking mechanics (above)." really does hit sooner, mostly because the second calculation is hard to calculate practically based on time, but I will say this.
##These changes on Cassiopeia's passive doesn't promote farming nearly as much as before, avoiding from making Cassiopeia a finite scaling Nasus or Veigar. Instead, the new system implemented is extremely more efficient if your focus is on bullying the opponent. To the lane bully Cassiopeia fans at there, rejoice, this new system is one that caters to you.
E - Twin Fang
! This section cannot be calculated at this time. I would prefer to calculate based on maximum possible DPS, but first I need to know exactly what happens if Noxious Blast or Miasma overlap either each other or themselves.!

Q - Phosphorous Bomb
MISSILE SPEED 1125 ⇒ 1000
For those who can't really comprehend "missile speed" as something tangible in-game, this nerf will cause an approximately a 0.1 second delay when firing this ability at max range. Doesn't sound big, I realize, but I really recommend you Corki players to get used to it. Don't panic, 0.1 seconds is only so long, so you don't exactly have much to actually argue about (at least objectively). Just expect your max ranged Qs to be just that much less reliable; 0.1 seconds longer for the opponent to react.
1125x(time)=825 x=11/15
1000x(new time)=825 y=33/40
y-x=11/120=0.091666~

R - Grandmaster's Might
BONUS ARMOR 25/35/45 (+0.3 attack damage) ⇒ 20/35/50 (+0.5 attack damage)
It meant bonus AD right?
For his Rank 1 ultimate, you need at least 25 bonus AD for this to be a straight buff. Honestly, that's an easy task to meet, so long as you don't build full tanky/never go back by that point, so I really hope nobody complains that this is in any way a nerf. To rephrase, Jax really received some love here.
25+0.3x(AD)=20+0.5x(AD) AD=25

W - Hyper Charge
While I realize this is more of a fix to avoid cheesing like hell as Jayce, this is actually a nerf to Jayce's spell-slinging DPS, which only gets progressively worse as you build CDR.
...Don't most Jayce builds tend to stack at least 25% CDR? Huh...
14x(CDR)=13x(CDR)+1.2 12x(CDR)=11x(CDR)+1.2 10x(CDR)=9x(CDR)+1.2 8x(CDR)=7x(CDR)+1.2 6x(CDR)=5x(CDR)+1.2 (x always equals 5/4. In other words, at normal cool down, it already takes longer to go from one Hyper Charge to the next, and it gets worse compared to more as you buy more CDR)

Q - Arctic Assault
REMOVED: ENEMY HEALTH SCALING - Arctic Assault no longer scales with 4/6/8/10/12% of target's max health DAMAGE 40/70/100/130/160 magic damage ⇒ 80/125/170/215/260 magic damage
Huh...this is actually a pretty big nerf to Sejuani's late game.
At rank 1, this ability used to do more damage if the opponent has more than 1000 HP. Rank 2, 917 HP. Rank 3, 875 HP. Rank 4, 850. Rank 5? 833.
To rephrase, the higher this ability's rank goes, the less health it takes for Sejuani's old percentage health damage to actually do more damage than with the new base values. This becomes stupid when you realize that as levels go up, so does health, ultimately meaning this ability's damage and the enemy's health are going to shoot right past each other come midgame. While I suppose this is an okay change for Sejuani's early game, all this does is make Sejuani's Q fall off harder come late game.
...Actually, don't (big) Jungle monsters have over 1000 hp? Shit, this hurts Jungle Sejuani's early game too!
40+0.04x(Health)=80, (Health)=1000 70+0.06x(Health)=125, (Health)=2750/3=916.66666666 100+0.08x(Health)=170, (Health)=875 130+0.1x(Health)=215, (Health)=850 160+0.12x(Health)=260, (Health)=(2500/3), 833.3333333
W - Flail of the Northern Winds
INITIAL HIT DAMAGE 40/60/80/100/120 (0.3 ability power) magic damage ⇒ 4/6/8/10/12% of target's max health (+3% per 100 ability power) in magic damage
1000 HP, again?
Luckily, this is the exact opposite of before. The moment the enemy has more than 1000 HP, the base damage from Sejuani's new W base scaling beats the old.
It also appears the AP scaling for this ability's burst has gone way up.
40=0.04x(Health), (Health)=1000
~~AREA OF EFFECT DAMAGE 80/120/160/200/240 (+10% bonus health) ⇒ 40/70/100/130/160 (+4/6/8/10/12% total health)
On the other hand however, this is a rather significant nerf. At max rank, the opponent needs over 4000 health in order for the new base damage to catch up with the old one.
80+0.1x(Health)=40+0.04x(Health) 120+0.1x(Health)=70+0.06x(Health) 160+0.1x(Health)=100+0.08x(Health) 200+0.1x(Health)=130+0.1x(Health) 240+0.1x(Health)=160+0.12x(Health)~~
I misread something, please wait for me to rewrite this.
#Nerf, buff, nerf, honestly I'm not sure if I really like these changes. For the most part, Sejuani players are getting straight up lied to about the whole "a lot of Sejuani's damage has been shifted out of her up-front burst (Q) and instead shoved into the damage-over-time of her Flail", at least past the mid game in regards to her Q. Not to mention the rather questionable change to her Permafrost. I guess the mana is nice, but holy shit I do not expect any Sejuani players to like her new Q at all, especially Jungle Sejuanis. I guess AP Sejuanis are may enjoy the initial damage of the flail, but I do find this really sad that these changes manage to flat out hurt Tanky Jungle Sejuani.
A somewhat simplified tl;dr: -New Cassiopeia passive promotes being a lane bully, instead of being a watered down Veigar/Nasus. -Corki has a 0.1 second delay on his Q. -Jax needs 25 AD by level 6, and the armor portion of his ultimate will be a straight buff. -Jayce received a rather noticeable nerf to his Hyper Charge if you want to go spell slinging. -Did Sejuani seriously just get nerfed?!
, any individual shadow for
), exceeds most ranged Auto Attacks, hell it even exceeds Syndra's Q.