Hello I am Knhs (The new Boy Genius) Ingame name Knhs1253, I am a gold 3 ADC main and have a level 5 mastery on Ezreal with a 69% winrate with him in ranked. I made this build after Iceborn Gauntlet got a nerf and Tri-Force got a mini rework.

I noticed that Tri-Force had higher sheen damage than Iceborn and since it no longer had the crit in it it could be used in the blue build as what you build in blue build is AD, AS, and On-Hit Damage, so i thought i would try swapping them out.

During my time testing this (in ranked and normals) i saw that although his damage was higher he as less self peel than the Iceborn build so i tried to find a substitute and i found it in Frozen Mallet.

Frozen Mallet and Tri-Force are better than Iceborn Gauntlet because they provide 900 hp all together and if you are against a balanced team of AD and AP then stacking HP is more important than stacking Armour (source:http://forums.na.leagueoflegends.com/board/showthread.php?t=29398), and using this logic the better items for Defence are Tri-Force and Frozen Mallet.

But that's not the only reason you should take these two items, they also give you Tons Of Damage, Tri-Force's Sheen damage is twice as strong as Iceborn Gauntlets and Frozen Mallet gives you AD as well as the HP and slow, what more could you want?

TLDR AT THE BOTTOM

If you look at two Full build comparisons, one with Iceborn and one with Tri/Frozen, you will see that the Tri-Force/Frozen Mallet combo offer more Damage and more Defence overall too.
(Better Defence overall against a balanced team of AP and AD)
(These full builds are basic full builds for an Ezreal currently using his level 18 stats)

Iceborn Build:

Iceborn Gauntlet,
Lucidity Boots,
Mercurial Scimitar,
Manamune/Muramana,
Last Whisper,
BOTRK.

Total AD from build: 165 + ( 2% of total Mana = 51.5) = 217 (Depending on what LW you build Damage might be higher)
Total HP from build: 0
Total Mana from build: 1500 (+ 1075 = 2575 this is including mana at lvl 18 to work out muramana damage)
Total MR from Build: 35
Total Armour from Build: 65
Total On-Hit Stats from build: 6% current HP + 3% current mana (+ 97 + 30% AOE slow if Sheen proc) (Maximum =77.25 ) (Physical damage)
Total AS from build: 40%
Total Armour Pen from build: 45% bonus Armour
Total Life Steal from build: 20%
Total CDR from build: 30%
Total Actives from build: Merc Scim Active (Remove CC) BOTRK Active (steals 10% of targets HP and Steals 25% movement speed for 3 seconds)
Total Movement Speed from build: 0%

Total build cost: 15700

Tri-Force/Mallet Build:

Trinity Force,
Frozen Mallet,
Lucidity Boots,
Manamune/Muramana,
Last Whisper,
BOTRK.

Total AD from build: 165 + ( 2% of total Mana = 46.5 ) = 212 (Depending on what LW you build Damage might be higher)
Total Hp from build: 900
Total Mana from build: 1250 (+ 1075 = 2325 this is including mana at lvl 18 to work out muramana damage)
Total MR from build: 0
Total Armour From build: 0
Total On-Hit Stats from build: 6% current HP + 3% current mana + 30% slow + 10 Movement Speed (30 if you kill a target) (+ 184 if Sheen proc) (Maximum Muramana damage = 69.75) (Physical damage)
Total AS from build: 80%
Total Armour Pen from build: 45% bonus Armour
Total Life Steal from build: 10%
Total CDR from build: 30%
Total Actives from build: BOTRK Active (steals 10% of targets HP and Steals 25% movement speed for 3 seconds)
Total Movement Speed from build: 5%

Total build cost: 16233

Pros: More Sheen damage so higher Q damage + Q applies Slow (2x as much)
More Hp
More Movement Speed (stats and passive)
A more frequent Slow (every AA instead of every Sheen proc)
Better for Solo Q mind set (Solo Q Solo Carry, self peel tankier but same/more Damage)

Cons: Lose the AOE slow
Less Mr and Armour
Less Lifesteal
Less Mana
Lose Merc Sim Active
Build costs 533 more gold

The reason i take these Runes and Masteries are because the 3 AD you lose in the marks you gain back in the masteries after you level up a few times in game and on top the of the 3 AD you gain you also gain extra AP and since Ezreal has quite a few AP scalings in his kit this increases your overall damage but lets you stay healthy with the lifesteal in the the Runes
which means you don't need the lifesteal in the Masteries and the 3 AA marks make up for swapping an AA Quint for the lifesteal one.

Your damage is also increased by Fervor which stacks on your Abilities which are very spammable with the sufficient Mana you gain from this build and the Sorcery Mastery increases Ability Damage by a further 2%.

Meaning at Level 18 when your Qs base damage is 115 and has a 110% bonus AD (165 in the builds we looked at) so 181.5 so altogether 297 + Tri-Force Sheen proc which at level 18 would deal 184 Damage = 481 and 2% of 481 is 9.62, WOW.(this damage stacks up when you're in game and basically negates the loss of the 5 AD from the build, this damage will also be increased if you choose to go Steraks as your final item and will also increase the Sheen proc)