Hi my nick is "IWontPlayRiven". I am diamond 3 riven main since 8 years I guess. I have been trying to come up with this build for past week, and here are some rules I made for it depends on what perfectly skilled riven player has to have...

Ability haste (captain obvious)

Ad

Survive ability (we strictly depend on shield instead of armour and hp)

Dueling potential (1v1/2/3)

Aoe dmg (riven engages are one of the best compared to the rest of bruisers)

W don't do armour or magic resist. Points put in ability haste and ad, then we have faster and bigger shield so we can tank all that dmg.

Same with health. Money spent on ad grants us bigger shield, and additionally we do more dmg. I'm not saying we can't use items with health points, but health is not our priority.

Boots.... Yeah, ability haste boots as second, or halfway first item are big boost for us. But do we really need movement speed at the end of the game? Riven is totally mobile, and as she has more ability haste she can jump all over the map much faster. (remember that we are talking about perfectly skilled player which won't fail any wall hops). But still, running barefoot is not a good option.

That's it I guess. So build i invented is:

Ravenous hydra. 20 ability haste is great, 65 ad, big amount of damage, also we starting to greaten our aoe dmg. Why is it first? We get mythic stats after the second item so It doesn't matter if we do it first or second. Also it makes our dueling potential bigger due to the passive of this item. We do get some livesteal if we fight in group of enemy creeps, also health from omnivamp is bigger if we fight more than 1 enemy.

Goredrinker. The only item we can think of. I'm not going to talk about it much. All that matters is 20 points of ability haste we get out of 4 other legendary items.

Black cleaver. It was never an option to not take this item. 25 ability haste is really big. 40 ad, not very big amount but still we consider items with more ability haste which riven relies on, further we watch for raw dmg. Also we got passive which shreds armour of enemies which we will stack fuly very fast with our combos.

Essence reaver. Another 20 points in ability haste and we are good to go. Only 45 ad points, but as riven depends on her skills, it's amazing to have enchanted attack after each ability. Big dueling potential is in that particular item. Those 20% crit is not what we accually want, (we will come back to this in a minute) but who haven't has used this 1% crit chance?

Navori quickblades. 60 ad is just wow, we keep getting even bigger shield, all this ad we have already combined with our ultimate skill grants us very powerful survive ability (due to ad ratio we have in R1) with our shield, even tho we don't have any armour or health focused items. 30 points of ability haste is as big as it sounds (+another 5 from goredrinker). We want this item because of its raw stats but passive effect is really helpful but we don't want to rely on this. Combined with essence reaver we will have 40% of crit chance so some basic attacks may hit even harder, cause riven's passive counts toward it. (it means that dmg from her passive also will be counted twice). Almost forgot to mention that statistically 2 per 5 attacks will shorten our cooldown of basic skills by 20% of remaining time which is amazing for riven's kit.

Boots. Illonian boots grant us 20 ability haste so it's good power's pike early for really not much gold. We should take them along with caufield's warhammer if we can afford it.

Now runes. I took the best option for us. Conqueror Tryumph Legend: tenacity Coup de grace Transcendence Gathering storm 8 ability haste, dmg, armour

And numbers With this build we have at 18 lvl: 375 attack damage (450 with ult) 173 ability haste which is 63% cdr

Q has 4.76 cd W has 2.56 cd E has 2.2 cd R has 21.98 cd Our shield has 465 hit points (540 after R)

So this is it. Write your opinions and I really enjoy if you give it a shot and write down whether you like it or not.