Evelynn is unsuccessful in low MMR because her kit is bad and players need to overcompensate for it.
We can fix this by giving Eve's R a reset mechanic. If the ultimate, that does extra damage to low health targets, deals the excecute threshold's double damage Eve's R cooldown should be refunded, temporarily as if darius's R. Master Yi, Katarina and Darius already have mechanics like this. Eve, like all of these champions is actually a damager. Yi's reset enables him to do more damage, katarina enables her to do more damage, Darius's enables him to do more damage and gives him a not too bad steroid. Unlike all of these moves with their desireable affects, eve's R takes her out of the fight and basically gimps her damage overall. Perhaps Eve would do a reasonable amount of damage or be kind of threatening if she could ult 3 or 4 times in every fight. Thoughts?