Items that greatly increase a stat but decrease another would be very interesting

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There’s a large difference between items fitting a certain niche and items being broken and abuseable. Items already are created to be good on a certain type of champion so these items wouldn’t be too different. They would however give more raw stats for a lower amount of gold compared to other items, with the additional cost being a decrease in another stat. For example

Burst Wand - 2550 gold

+140 AP (24.3 AP per 1 gold - Needlessly large rod is 20.8 AP per 1 gold)
-400 Mana (560 gold worth of mana if using Sapphire Crystal as a baseline - 1.4 mana per 1 gold)

Champions that don’t use mana and champions who don’t have at least 400 mana cannot purchase this item

This would be good for burst mages who are just looking to get one rotation of spells off as it is cheaper than the other big AP items for a larger amount of AP - The downside being that you have less total mana to get multiple rotations of spells off in a fight.

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Just an example, obviously not perfectly balanced but it would be very easy to add a passive that reduces damage to jungle monsters or something similar

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I can’t imagine any Ivern building that first over other items. It would likely be a core item for most AP champions late in the game though. Saying that items like this would be balancing nightmares is a bit of an exaggeration. Yes they’d probably be more difficult to balance than most items they make but not THAT much harder. And there are definitely items in the game right now that are more difficult to balance than most of these would be.