For me, the problem with Ekko isn't even 100% how high his base skill values are... His problem is where his scaling lies.
Take his Q, for example:
Outward Magic Damage: 60 / 75 / 90 / 105 / 120 (+ 20% AP)
Returning Magic Damage: 40 / 65 / 90 / 115 / 140 (+ 60% AP)
What does this tell me? This tells me that Ekko needs only 233 AP to double his base damage for the returning of max level Timewinder. However, that outward projectile is going to stubbornly stay at a weak state, only doubling in damage after 600 AP!. This means that Tank Ekko's Q outward shot, the easy part that's almost guaranteed to hit, would never have been much better anyways. Meanwhile, the real power that lies in the skill (somewhat...), the return, has much more power when he's high AP, he just doesn't have the tankiness to really bully an enemy into it.
So, what are the AP values that his ratios double in effectiveness (in relation to level 18 Ekko)?
Passive: 237 (requires stickiness)
Q: 600 (easy hit) - 233 (telegraphed hit)
W: 300 (Passive, low HP assassinate) - 106.6 (prediction shield)
E: 350
R: 300 (telegraphed damage) - 300 (self-heal; only percentage portion counted)
I will note that this is a lot of AP ratios. However, I'd say that he only really has 3 ratios that don't require some high amount of prediction, which I can count in his actual combo: E (350), Q out (600), and generally, the passive (237). Meanwhile, his main 2 telegraphed values are low: his return boomerang (233), and the miniscule amount needed for shield (106.6).
So, what does this mean? This means that in order for Ekko to deal his base damages, he needs no skill. Now, I don't mean no skill as in he can set his dog at the controls, but we're close. Q out, E, and passive, and he does 450 damage with base values only. In order to double that, he needs 321 AP to get 900 damage out of that combo, and even that is discounting the inherent damage from autoattacks which aren't going to improve a bit from AP. However, his telegraphed skills need 233 AP and 106.6 AP to double up, no AA involved. These are the abilities that require the actual gameplay proficiency to use, corralling the enemy into their return Timewinder, and timing your Parallel Convergence to a spot you won't get caught out. So basically, you put the power in his keystone, difficult-to-use abilities, but only after investment.
But here's where the problem comes in. AP Ekko, despite having a very high ceiling because of this, also has a high fizzle rate. Now, this probably is why Ekko has 8 AP ratios and feels so bad. If Ekko makes his main combo, he generally only needs one of his two (or more) potential "fizzles" to hit in order to secure the kill most of the time. This leaves a LOT of damage potential if, say, he somehow lands both. Or maybe he completely misses his target, but hits another enemy trying to protect. Or he gets a 1.75 second stun thrown in to root the enemy and secure his fizzles from happening altogether. Now, Ekko is designed to basically be a crap-shoot who hits his main combo, and then depends on a flurry of possibilities to knock the enemy low enough to kill. But, there's one thing that makes Ekko 10x better at landing this combo: tankiness. Tankiness gives him the freedom to AA without feeling overwhelmed on the front lines. It allows him to guide his Timewinders better. It helps to feel safer when trying to hit your bubble. Basically every potential fizzle in his kit suddenly becomes attainable when he's not squishy. You can guide the enemy into your Timewinder, or simply use it as a corral for your stun/shield. You can also lead the enemy, who is already slowed from Timewinder, to get hit by the return with near certainty (with a little aid from E). Ekko has a lot of intended combos which are just not available to him in his AP form because his reliable combo has been stripped down to base values, and he has limited capabilities once people learn his tricks.
So, all in all, Ekko needs to have stability tossed into his kit. Either he builds the stability through HP, or AP. If he goes tank, that is his stability, and his base values need to fall on stable skills to accommodate that. Meanwhile, his stable skills need to have high ratios to make assassination feel more stable for AP Ekko, but drop the impact of the randomness in his kit by lowering the ratios on his crap-shoot skills. If you want to balance Tank Ekko in, you can try raising the base values on his crap-shoot skills. All in all, here's what I would do:
Passive - 20-190 (+80% AP) > 20-100 (+80% AP)
Too much free damage. Needs to fall off lategame.
Q out - 60-120 (+20% AP) > 40-120 (+40% AP)
Q in - 40-140 (+60% AP) > 40-120 (+40% AP)
This makes bases 20 weaker all game, but frontloads much of the AP ratio on the outer Timewinder. Bases aren't too high here.
W passive - Not changed? Don't have any real opinion on this at this point. Might change to flat because he and Fizz use % missing HP tied with AP ratio too well.
W shield - 80-160 (+150% AP) > 40-120 (+100% AP)
W stun - 1.75 seconds > .75 seconds
(NEW) - W damage (if stunned) > 40-120 (+50% AP)
Shift some shield and stun to damage. This utility was more than warranted, anyway. Also, shield was never utilized by AP because 150% ratio was nuts high. 100% is more usable on AP Ekko, maybe a bit lower, but gets some damage to tie with it without being too utility OP on stun. As another option, would like it if bubble acted like blinding ground, forcing vision of enemy units to be only within the bubble until outside, similar to Graves' Smokescreen, but with clear vision within the bubble.
E - 40-140 (+40% AP) 20-100 (+60% AP) [possibly with cooldown compensation].
R - Reworked, essentially to be a less-telegraphed W bubble. Ekko still flies to the position he was 4 seconds ago, but instead of bursting obscene amounts of damage, he gives a small bit for plopping the bubble, and then the typical stun/shield, with possible healing on top if the consistency with the old kit was needed. Would be nice if the bubble-smokescreen idea from W was in effect here, too. Possibly add another effect on top, like a damage amplifier or something within this bubble, if needed. Generally, though, keep the inherent damage low on this. Edit: Maybe just rework R into this and make a new W. Not 100% sure where to go with this.
It's not perfect, but I feel this is more the direction Ekko needs to go in order to be healthy with such wildcard type skills available to him. I'd like to reduce the kiting or something, but I feel his E and W should be a viable combo, and R is going to be too expensive to just toss. I'd like to modify the innate, too, as he's one of the easiest champs to reliably combo in laning phase; basically throw Q's all day until one lands, and then E-Auto before they can leave vision. Ekko shouldn't feel the win on the trade that easily, I think, considering this will basically be granting him Rengar-esque instakills lategame. My opinion is to increase stack time a lot and remove passive stacks from autoattacks that aren't his E. That way he has two choices: either stack by landing all 3 hits on Q and E, or land 1 Q and pop passive when cooldown comes back. In the latter case, the enemy always has the option of backing off until stacks reset.
TL;DR Ekko's reliable-hit skills have bases that are too high, keeping those ratios low, and forcing the telegraphing skills to be too impactful. Having more powerful reliable skills after AP investment makes room for more meaningful utility outside those skills without relying on those skills to be a hail mary (and therefore enabling tank strategies which already steer the battle the direction they want it to).
