How to Fix all the other game modes
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Remove the map-specific items and put everything on the Summoner's Rift set. This will remove build confusion stopping people from playing.
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Add a First Win of the Day bonus to all modes to give people incentive to play them at least once a day. (Possibly add them to the reward system for crafting)
Simple. Any further balancing of the modes can be done after, since they'll actually have data when people start playing.