I'll just hop right in with describing the effect:
After a short delay, Amumu runs in a straight line while crying. His tears falls like mini-Phosphorous Bombs or Arcane Comets around him, targeting nearby enemies. He can shed two to four/five/six tears this way based on how far he runs. Only every other tear can target the same enemy. Tears prioritize Cursed enemies and then closest enemy. They do not prioritize champions, so headbutt em' first if you want them to get hit. Or just combo this with your ult. If there is only one enemy nearby, every even tear just flies in a random direction instead (with a chance to hit the single enemy, too).
He keeps his current crying animation to show the range of where Despair targets enemies, but the tear initial homing and AoE can extend beyond that.
A small picture to help with visualization. O = Tear AoE. This is the 'normal' version of how it would work. However, tears can also fall in front of or behind Amumu, so it could also look like this:
With more ranks, you can shed more tears in the same amount of time:
But no matter the rank, if you only run a minimum distance, you'll only get two tears:
I thought maybe non-smart cast indicators could show a number saying how many tears you will shed based on how far you pull the indicator. If not, players would just have to get a feel for it.
While running, Amumu would have a Movement Speed modifier, like Slow Resistance, Unstoppable, extra Movement Speed, or a minimum amount, but he wouldn't be able to perform any other action for about a second or until the effect ends. If he is CCed during this time, he continues to shed at least the first two tears for that second he wouldn't have been able to do anything anyway.
He would also ignore unit collision and could get a slight damage reduction effect (around 10 to 20%, possibly based on rank).
I thought tears could deal a combination of his base Attack Damage and a percentage of enemies maximum Health. He's locked out of actions during the run, after all, so it has to deal a minimum amount of damage comparable to his auto attacks. The other bonuses are the Movement Speed modifier, ignoring unit collision, damage reduction and AoE damage.
- Tear Amount: 2 -- 4/4/5/5/6
- Tear Damage: 80% base Attack Damage + 4% of target's maximum Health (+2% per 100 Ability Power) magic damage
- Cost: 40/50/60/70/80 Mana
- Damage Reduction: 10/12.5/15/17.5/20%
- Movement Speed Modifier: ???
- Max. Range: 650 (he can cancel Despair after 1 second, which would be about half max range)
- Cooldown: 12
- Passive: Whenever Amumu damages an enemy champion with an ability, reduces Despair's Cooldown by 0.5 seconds. The reduction amount is further reduced by Cooldown Reduction (so with 40% CDR it only reduces by 0.3 seconds instead).
It would probably need a minimum range, too.
The rank-up values and the passive are supposed to discourage maxing W first, as it's mostly an AoE damaging ability suited to mid to late game teamfights. If ranking it first is always a good choice, something is probably wrong. Ranking up E or Q first reduces *their* cooldowns which means he can hit enemy champions more often with them, which means he gets his W back up faster is what I mean with the passive discouraging ranking it up first.
Overall, this just increases Amumu's skill cap and adds Gameplay that fits with both his fantasy (a kid running somewhere crying, despairing over hurting people reduces Despair's cooldown) and his current kit. It could help make the champion feel a little more modern and distinct, similar to what they did with small ability updates like Xin Zhao's.