Why Trinity Force on Riven is utter trash compared to Black Cleaver (current cleaver) math.

I'll go ahead and write down some math as to why trinity force will never in any way shape or form be an optimal item for Riven.

The stats that TriForce holds are: +250 health +40% attack speed +25 attack damage +5% movement speed +250 mana +20% cooldown reduction

• (200% base ad spellblade dmg at a 1.5s cd)

The stats that black cleaver holds are: +250 health +300 health +50 attack damage +20% cooldown reduction (and 40% armor shred after a full fast combo).

Looking at main stats purely we see that triforce has a

• 40% aspeed increase, this is pretty useless on Riven as she is a caster and her main focus as a champion isn't to mow down turrets.

• Triforce gives 25ad while cleaver gives 50ad. Cleaver just outclasses triforce in when it comes to Riven's main stat.

• Triforce yields mana, which is literally useless.

• Triforce and BC share the CDR stat.

• Triforce yields a 200% base ad spellblade effect every 1.5 sec. Since Riven is a caster this holds a value to her. Let's look at the dmg it will do in a full fast q combo. using this video: https://www.youtube.com/watch?v=Er1yVjuxe5w the q combo takes around 2.5 to 3s to fully complete. Considering the spellblade only scales with base ad we don't need to take builds into account. Riven's base ad at lvl 18 = 107. 107 * 2 = 214. Riven will in this time do one AA Q AA Q AA Q AA, in this time frame Riven will AT MOST proc spellblade twice. Let's look at the math if we're facing a 100 armor champion. At 100 armor a champion has 50% physical damage reduction. Riven will with this deal:

• (nonpassive AA) = 132/2 =66dmg, Q = (90 + 60% ad and Triforce yields 25 ad, 132*0.6 = 79.2 + 90flat = 169.2/2 = 84.6), AA(passive stacked aa = 50% of total ad = 132/2 = 66 + 66base = 66+32= 98 + spellblade = 214/2 = 107 + 98 = 205) + 84.6 + 98 + 84.6 + (98+107=205) = 827.8total dmg in a fast q against a 100 armor champion using spellblade.

-----------

• With BC if the target already has 6 stacks in him, he will have 40% less armor. 100 - 40% = 60 armor = 37.5% ad dmg reduction. an nonpassive AA with this = (107 + 50ad from bc = 157ad - 37.5%) = 98.125dmg, Q = (157*0.6 = 94.2 + 90 = 184.2-37.5%) = 115.125dmg , AA(+passive) = (157 + 50% of ad = 157 + 78.5 = 235.5 - 37.5%) = 147.1875dmg + 115.125 + 147.1875 + 115.125 +147.1875 = 885.0625total dmg in fast q

So in total, Black cleaver deals more dmg to opponents with a base of 100 armor, this math still holds vs opponents with larger quantities of armor, since cleaver is an armor shred, it will at all times deal more dmg vs triforce. However vs squishies with around 60 armor, the shred is rather negligeabel and doesn't matter what so ever if you build BC or Triforce, as they will die within ms of you getting ontop of them. Not to mention that BC allows your ADC and other teamates who deal physical dmg to also do increased dmg.

TL;DR Dont' buy triforce.