AD items
Attack Damage-oriented items are the opposite of support ones: AD champions seek for slot efficiency and want big items. Some items, however, don't fit that description. Let's focus on Executioner's Calling and similar ones.
http://i.imgur.com/8hbJbkas.jpg
Executioner's Calling
Purpose: Heal reduction
Problem: ADC items need to be more slot-efficient and lategame-oriented, and crit chance is an ADC stat. Current EC is built on pretty much noone.
What this item needs to be: Either a mid-tier fast item building into something bigger or a better lategame scaling one.
Who should build it: Top laners facing immense sustain or bruisers wanting to shut down carries.
My suggestion: Make it an Advanced tier item building into a Legendary one when combined with Avarice Blade and/or Vampiric Scepter. This leaves more time to stack Avarice, gives the upgraded EC a better
lategame prevalence and allows to build EC right when it's needed. This concept of EC needs to be not cost efficient in bare stats and the Grievous Wound application to occur under lower % of health to avoid
abusing it in ranged AD lanes (or make it melee only?).
Example build: Brawler's Gloves + Longsword, granting about 15 AD and 10% crit for ~1100 g. Needs a new item to build into - generally an AD+crit one. Avarice + EC + Pickaxe seems like the way to go here, but another concept would be tweaking Spellbreaker (Hexdrinker + EC).
http://i.imgur.com/rbD4sCQs.jpg
Atma's Impaler
Purpose: Tanky DPS; metagolem
Problem: We've got better bruiser items (BC, Hydra, Gauntlet, Sunfire) and this one was always painful to fit into the build - it grants two stats nowhere to find in any other item that very few champions can utilize while granting third stat basing off fourth stat.
What this item needs to be: "I'm tanky. Now I want to deal damage"
Who should build it: AD Bruisers
My suggestion: Replace Avarice Blade with pretty much anything else. Bruisers do not scale with crit chance.
Example builds: Chain Vest + Kindlegem or if we're scared of Renekton Chain Vest + Catalyst the Protector
http://i.imgur.com/MB1X4fgs.jpg
Runaan's Hurricane
Purpose: AoE ranged ADC damage
Problem: ADC as a role is about maximizing single-target DPS, which makes the item underwhelming in most situations. Arguably the least problematic of the bunch.
What this item needs to be: AoE when needed, not a lackluster when no AoE possible.
Who should build it: Anyone but Teemo
My suggestion: Merge it with another underused item, Sword of the Divine. This way Hurricane will gain two purposes: you either focus on one target or deal damage to multiple ones. New core item on Twitch.
Example build: Same, just with 10% less AS and SotD active. Passive is lost (along with AS) while active is on cooldown.
http://i.imgur.com/oJQqJ4gs.jpg
Guinsoo's Rageblade
Purpose: "Hi, I'm Jax, and I'm so fed that I've decided about to embarass you with this thing. Imagine if I had a real item"
Problem: Extremely niche and impossible to balance because of two champions who can abuse it
What this item needs to be: Hybrid item that would be attractive to not only Kayle and Jax, but also some other champions
Who should build it: Any champion that can be played AD and AP - Ezreal, Twisted Fate, Varus, Kennen
My suggestion: Remove AS and stacking component. Add crit chance related mechanics to prevent Jax and Kayle from abusing it. Make it an item that enables hybrid builds on more champions. Hybrid penetration or weird scaling, perhaps? (possible weird scalings: crit chance applies to spell damage, if spell crits it deals true damage?)
Example passive: Critical strikes reduce your target's magic resistance by 20% for 2 seconds. Magic damage reduces your target's armor by 20% for 2 seconds.