Cassiopeia Q and Karthus W feel like wasted opportunities in terms of hyperscaling

So all AP casters have the basic quadratic scaling on their abilities, ability power, which is added onto your base damage based on scaling, and CDR, which increases the amount of times your total damage comes into play, multiplying the linear damage increase from AP items.

However, in concept Karthus W and Cassiopeia Q (and to an extent W) have a design element that allows them to scale quadratically with CDR only (and with AP this becomes cubic): Windows of increased damage from abilities, activated by an ability.

If you don't know what I mean by this, basically Cassiopeia Q poisons enemies, causing them to take more damage from E, while Karthus W decreases enemy MR inside the wall, causing them to take more damage from Q (and E)

Normally, when you increase the CDR of a normal mage like Lux who has 4 activated abilities and a passive that just adds flat damage on her damaging abilities if she autos a hit enemy, they follow the rules above. More AP is more damage, more CDR is more use of that extra damage. Cassiopeia on the other hand, if she gets CDR she gets more Qs and Es as expected, but since she gets more Qs, the enemy spends more time poisoned, and in turn more Es are casted with bonus damage beforehand even considering the fact E CD is reduced as well. Karthus has the same in that more time wall is up = more Qs with reduced MR on top of Q cooldown itself being reduced.

On the opposite side of the spectrum, you can have mages who don't scale with CDR damage wise as well (but keep in mind CDR is inherently valuable so even with these champs you'd probably still buy CDR items). These mages are those that have interactions where their abilities actually spend time being unaffected by CDR, namely Anivia (actually her E makes it complicated but that's for another thread, Aurelion Sol, and other channeled mages. If Anivia spends 1 hr channeling her ult at a time (theoretically), reducing the 6 second cooldown to 3 would have relatively little effect on DPS compared to an ability which goes on cooldown instantly (where the DPS is doubled). Many mages have both like old Swain with his damage buff and his ult, and Karthus E + QW (which is slightly ironic)

Keep in mind that this is from a purely mechanical perspective, in a vacuum. In general battlemages mages will see an increase in damage directly as they can see the difference between 30 Es and 60 Es in DPS easy, while if you're a burst mage you only get one ult (and burst mages tend to be ult heavy while battlemages rely more on their spammable basics) every teamfight unless it's extremely extended, and maybe the next teamfight is so far later that you would've had your ult even without CDR, and you were only in range for light poke when enemies were nearby and waveclearing the whole time. In general the benefits of CDR are less tangible (but still there) on burst mages. This connects with the paragraph above in that abilities that are not in cooldown, are not affected by cooldown reduction. Hence abilities that you hold onto a lot are not as good with CDR.

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But that brings us to the main problem: in practice these abilities don't work this way at all. Karthus W MR reduction is not very good at all and in terms of DPS might actually be counteracted by the fact a bulk of your damage will be from E (which scales bad with CDR) and R (which you hold onto instead of using the moment it comes off cooldown, thus reducing its CDR scaling). Karthus always went RoA over morello's, and many Karthus mains don't bother hitting the 40% CDR cap. Cassiopeia is similar, her Q poison has a 3 second duration and 3.5 cooldown. Her 'cubic scaling' caps out at 15% CDR where her Q reaches ~3 cooldown and your poison is up 100% of the time if you're skilled enough to hit it every cast.

So really, what could've made them have damage scaling closer to an ADC (bad early, good late) is pretty much wasted. Instead Karthus and Cassiopeia (well before aggro chances) are very effective lane bullies who scale decently into late game.

Other parts of their kit like 6 item Cassiopeia and Karthus death passive do make them good late game champions, I guess. But they're always second to the marksmen

What's odd is that Syndra, a burst mage, has something similar in that more CDR = more orbs = better ult.