Hello there! This guide makes use of theorycrafting and math to try and get the most out of Riven. If you have any questions, please comment below or take part in the discussion on the official Riot forums, here: http://na.leagueoflegends.com/board/showthread.php?t=1238062

21/9/0 for laning, as described above. See section on Jungling for variation based on a jungling Riven as opposed to a laning Riven.

Flat AD marks and Quintessences are a must. You don't want ArPen because it does nothing for your shield, whereas flat AD reds/quints give your shield a boost while also boosting your passive, and all your other abilities. ArPen boosts just your damage, AD boosts both your damage and your survivability.

Core build: Ionian Boots of Lucidity, and Brutalizer. With these two items plus masteries and runes, you're almost CDR capped 10 minutes into the game. When you upgrade that Brutalizer into a Youmuu's, you will be CDR capped. Riven's abilities are completely free, and completely constrained by cooldowns alone. Thus there's a linear increase in damage/shield survivability proportionate to the amount of CDR you build on her. If you can afford to get CDR boots without being instantly destroyed for your choice, then definitely do so, because 40% CDR on Riven means 40% more damage and 40% more uptime on your shield without any drawback, any mana-cost, any threat of running out of energy, any danger of hurting yourself with health costs of spells.

Do not buy Wriggle's Lantern. It's a great item for champs that don't have sustainability, yes, but Riven does in the form of her shield and her lack of any ability costs. She's a solo top like Jarvan or Singed, who rely on a shield and/or teleport to soak up the damage. If you get both teleport and level her shield after her Q, you'll be able to do just fine in your lane, and the damage items you invest in early will benefit your harass, which can push your opponent right of the lane.

Starting item: Either a Doran's Blade, or if you really want a headstart on that Brutalizer, buy Longsword+1pot (Or sit in base for an extra 10 gold to get a Longsword+2pot). Alternatively, a Regrowth Pendant+1pot is a strong choice if you're worried about lane sustain.

What do I build next? Once you have CDR Boots and a Brutalizer, evaluate how you're doing. If you're absolutely destroying, pick up a Bloodthirster, followed by a Frozen Mallet+Atma's. If you're not doing so well, get the Fratmas first, and then the Bloodthirster.

And after that? If the enemy's building armor, which they probably will be, pick up a Last Whisper, then upgrade your Bruta to a Youmuu's Ghostblade. If they're not building armor at all (maybe you're the only AD on a 4 AP team..?), get an IE instead of a Last Whisper.

What do I do once I have all my six item slots filled? Buy red and green elixers, and an Oracle's so you can squash wards.

Final build:
(Enemy team has built armor): Youmuu's, Bloodthirster, Frozen Mallet, Atma's Impaler, Ionian Boots of Lucidity, Last Whisper.

(Enemy team has not built armor): Replace Last Whisper with Infinity Edge.

(Enemy team has lots of CC/magic damage): Replace Ionian Boots of Lucidity with Merc Treads.

Initial Analysis:

Q: It's a bread-and-butter damaging move. It's got a cumulative 1.8 AD coefficient, some mobility, and comes with a little CC. Always make sure to stagger autoattacks between Qs! I take 1 rank at level 1 then let it sit since many of the benefits (3 passive stacks, the CC) don't improve with rank.

W: It's like Jax's E without any of the RNG factor. However, the fact that your animation stuns you as long as it stuns your opponent(s) means that it only really shines in teamfights when you can get into the middle of a group and disrupt them while your allies dish out some damage, because you won't be doing it. Level this first.

E: I level this after W, because it's amazing. A 1:1 AD ratio shield with a dash baked into the crust is a great ability. It helps keep you tanky mid-game which allows you to build another DPS item and save the tanky items for later.

R: In my opinion, it's an awesome ultimate. It does a lot - AD multiplier and range increase benefits all your abilities, it lasts a long time, and it has an AOE execute. Awesome! It's like a combination of elements of Nasus' ult and Garen's ult.

Your basic skill order is R > W > E > Q.

Level E second, since it's Riven's primary form of mobility, as well as her main form of sustain/tankiness, and its excellent scaling means having it at rank 5 mid-game makes Riven innately durable enough that you can build that Bloodthirster before your Fratma's combo.

If you're in a solo lane, Teleport+Flash.

If you're in a duo lane, Exhaust+Flash, for chasing and for Exhaust's defensive applications (Shut down the enemy carry in teamfights).

If you're jungling, Smite+Flash. Never jungle without smite.

Riven's kit supports jungling. If you jungle, be sure to switch your 9 points in Defensive Masteries, to the Utility Tree for the +EXP bonus. Never jungle without the +Experience from the Utility Tree.

Q+W means you have 4 AoE attacks, your passive is a kind of steroid, and you have a shield. Start at mini-golems for a quick level-2, and then head up to wraiths to nuke them with the full AoE combo. Kill wolves, recall, pick up a Vamp Scepter.

Your next target should depend on what lane you intend to gank. If your teammate in that lane has their own slow/hard CC, pick up blue for the excellent CDR. If they don't, pick up red for the slow. Then start ganking!

A point worth considering is that Riven's passive synergizes with lifesteal, so you'll have very strong amounts of sustain in the jungle if you make proper use of it by staggering your skills and autoattacking in-between.

This FAQ will be updated periodically based on questions asked, either here or on the Riot General Discussion thread. These are all questions posed to me by members of the LoL community.

How do you find her survivability with that build though? Seems kind of like a glass cannon.

Fratma's, plus the strong scaling on her shield and high native stats means she should be good (at least on paper) to take a couple of hits. It's also possible to use exhaust defensively if you elect to go exhaust over Teleport, and one of the reasons I picked Exhaust instead of, say, Ignite, is that very reason.

Stats with this build:
2.6k health.
125 armor.
52 MR (Weakest link).

However!

I'm relying on her shield for most of her tankiness. With this build she has 242 bonus AD, so her shield will absorb 402 damage, on a CDR-capped cooldown of 4.2 seconds.

Absorbing almost half-a-thousand damage every 4 seconds qualifies as one of the best shields in the game. Couple that with the not-insignificant health and armor boost from the Fratma's combo, and she's tanky enough, in my opinion, to dish out some damage without getting instagibbed. Especially since she also has strong escape mechanisms.

Why do you get CD boots instead of Merc Treads? Do you really think the extra CDR is worth it?

It's a matter of personal taste. This build is light on MR and if you're facing a heavy CC/AP team, you should definitely go for Mercury Treads. However, I'm thinking in terms of how Riven's mechanics work. Her abilities are completely free, and completely constrained by cooldowns alone. Thus there's a linear increase in damage/shield survivability proportionate to the amount of CDR you build on her. If you can afford to get CDR boots without being instantly destroyed for your choice, then definitely do so, because 40% CDR on Riven means 40% more damage and 40% more uptime on your shield without any drawback, any mana-cost, any threat of running out of energy, any danger of hurting yourself with health costs of spells.

Have you considered jungling her?

I can see it working. Q+W means you have 4 AoE attacks, your passive is a kind of steroid, and you have a shield. She'd definitely need to build some lifesteal but other than that, her kit seems to support it. I'd probably start at mini-golems for a quick level-2, and then head up to wraiths to nuke them with the full AoE combo. Kill wolves, recall, pick up a Vamp Scepter, get blue for the awesome CDR and start ganking.

Jacket0012 also had this great point to add, on the subject of jungling:
"The awesome thing about her passive is that you can lifesteal with it. it gives her a surprising about of sustainability in the jungle with just a vampscepter..."

was wondering, and you said you like math, what are her cooldowns at 40%cdr?

With max CDR:

Q - 7.8 seconds
W - 4.2 seconds
E - 4.2 seconds
R - 27 seconds, with a duration of fifteen seconds.

or building a champ the right way could we have a final build list at the end? btw i think arm pen marks would be good too its just that she scales so well

You don't want ArPen because it does nothing for your shield, whereas flat AD reds/quints give your shield a boost while also boosting your passive, and all your other abilities. ArPen boosts just your damage, AD boosts both your damage and your survivability.

Final build:
(Enemy team has built armor): Youmuu's, Bloodthirster, Frozen Mallet, Atma's Impaler, Ionian Boots of Lucidity, Last Whisper.

(Enemy team has not built armor): Replace Last Whisper with Infinity Edge.

(Enemy team has lots of CC/magic damage): Replace Ionian Boots of Lucidity with Merc Treads.

I got APen marks and a quint (+12 apen, didnt fill all slots yet) and did quite a bit of damage. I think a Sword of Divine might work nice on her, the attack speed is not really wasted cause you get 20% more damage with ulti, and you get more AAs on it, and the active gives quite a ton of apen for 8 secs enough time to unleash of her combo. And also theres that nifty 100 magic damage in the middle which is nice too. Aaand 100% hit chance.

Or maybe it might be utter ****. Couldn't test it yet on games yet, but it really seems a nice item overall.

I don't think Sword of the Divine is a good item for her at all. Riven scales off of CDR, and AD, and nothing else. SotD gives you attack speed, and an autoattack boost in the form of magic damage every fourth hit. These aren't bad stats for an AD champion, but there are so many better items for Riven to choose. I would personally only even consider it if there's a fed Jax on the enemy team.

One thing that you're missing that is SERIOUSLY next to necessary for her is the Trinity Force. It scales perfectly with her entire concept of spell > attack > spell > attack > spell > attack. And when I say perfectly, it's all but tailored to her. Add in the movement speed, slow and survival, it's very nice.

Trinity's a red herring for Riven, actually. The Sheen proc looks great on paper, but it has a 2 second cooldown between procs. Riven's abilities are used MUCH more quickly than one ever two seconds, so you'll have a lot of wasted non-procs. The MS is nice, the health is nice, the AD is nice, the crit is okay/meh, everything else is a wasted stat. AS scales with no part of the character's kit. The mana and AP are completely wasted.you, and only partial/suboptimal use out of some of the rest.

If you won't take my word for it, here's some math to back me up:
http://na.leagueoflegends.com/board/showthread.php?t=1238815
http://na.leagueoflegends.com/board/showthread.php?t=1240078

Here's a quote from one of those threads, based on the math:

BFS Riven is spending 700 less gold for 400 more damage
BFS Riven has more survivability due to shield being AMAZING
BFS Riven better utilizes the AOE increases of her ult to deal out even more damage
BFS Riven is actually able to complete her combo faster because Tri-force has a 2 second CD between procs, Riven's passive does not.

I have a question, would it be better to have damage per level runes or flat damage runes (like you have)?[
It comes down to whether you want your runes to support your early game, or your late game. Personally, I think that Riven's early game needs more help, so I go for the flat AD marks+quints, because you need that boost to your shield and early harass as soon as you can get it.

I'm interested to hear your opinion for Sunfire Cape on Riven? To me, the fact that Riven will be constantly on top of the enemy(s) and in the thick of things the extra damage every second, including the added armor and health bonuses, seems like a good idea.

I haven't really thought about Sunfire Cape. Since she scales with CDR and AD, all the tanky options I've looked at for her have tried to incorporate AD in some form. Hence, Atmog's and Fratma's seem to be the best options since they will give her both damage, and the tankiness she needs to be in the thick of the fight.

The problem with Sunfire is that the magic damage really isn't all that much. If a champ has 100 MR, then your 35 damage/second is now slashed to just over 17 magic DPS. That's functionally nothing. If you're going to look at options that combine tankiness and damage, you need to find something that will synergize a bit better with her existing kit, and that means combining tankiness and AD, and the only option there is Atma's Impaler.