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I just watched the replay file. The 3 main things I noticed were:
-You did not string out your skills with autos. You would go in E-W-Q-Q-Q and run, as riven your autos are a HUGE part of your damage so by not using those you were hurting yourself.
-You did not use your early advantage. When you came to lane you sat back and let him farm with 0 heat, if you would have jumped in with q-aa-q-aa-q-aa you would have gotten him lower.
-You waited to long to try and fight him, by the time you started fighting rumble he was already ahead and started snowballing off of it.
The biggest thing I see you need to do to win this matchup is smarter early trades. watch when his CDs go down, bait his skills and shield back when he tries to come in. If he is at no heat you can typically very easily out trade him, an if you have ult and ignite up probably kill him.
-You did not string out your skills with autos. You would go in E-W-Q-Q-Q and run, as riven your autos are a HUGE part of your damage so by not using those you were hurting yourself.
-You did not use your early advantage. When you came to lane you sat back and let him farm with 0 heat, if you would have jumped in with q-aa-q-aa-q-aa you would have gotten him lower.
-You waited to long to try and fight him, by the time you started fighting rumble he was already ahead and started snowballing off of it.
The biggest thing I see you need to do to win this matchup is smarter early trades. watch when his CDs go down, bait his skills and shield back when he tries to come in. If he is at no heat you can typically very easily out trade him, an if you have ult and ignite up probably kill him.
Nickname, Frozen Mal only gives 20 more AD. Not great for Riven.
Usually you want Frozen Mal on Lee/Darius, but not on Riven, and in that respect their builds differ. They are more tanky, and don't have tanky abilities, whereas Riven has her
Valor. Adding on what Psi said, during fights, when you use your Valor, it increases a LOT with the more AD you have -- that is yet another way that stacking AD on Riven gives you more effective health. Riven is more centered on autoattacking than Darius and Lee (especially Lee), so the lifesteal is just that much better on her. The extra AD through Bloodthirsters not only increases your shield and the damage of your abilities AND your ultimate (2nd part) damage, but it ALSO , of course, increases your autoattack damage AS WELL AS YOUR PASSIVE DAMAGE, which increases your autoattack damage EVEN MORE when you use your spells (which you always do). This results in A LOT of effective health along with a ton of damage that lets you win basically EVERY trade with EVERY champion (unless they are a ton more fed than you).
As to skilling order, like Duff and Wayne said, Q is still viable to max first, it increases your burst by more than it seems since the damage is distributed in 3 stages. I tend to do W>Q>E. All about the damage baby! However, my 2.2k Elo friend TGF Freddy, who mains Riven, does W>E>Q like Psi (I think, but I think the last time I asked him was before the buff to Q). There are many viable ways to skill Riven, it really depends on your playstyle, preferences, and your lane matchup (if you are top).
Also, as Berzerk mentioned, make sure to stagger auto attacks in between your abilities so you don't lose any passive stacks -- that, believe it or not, is where a large portion of your burst comes in. If you don't stagger you autoattacks, that could be the difference between winning and losing a trade, and as a result winning and losing a lane, and as a result winning or losing a game :P
Generally, you want to E into them, auto if you can before you stun or if they are barely in stun range stun, auto, auto, Q, auto, Q, auto, Q, auto. If they are lowish or you think you can full to nothing them, make sure you use your ult BEFORE you shield into them, and ignite them at the beginning of your combo. Then ult to FINISH THEM! YATA!
Usually you want Frozen Mal on Lee/Darius, but not on Riven, and in that respect their builds differ. They are more tanky, and don't have tanky abilities, whereas Riven has her

As to skilling order, like Duff and Wayne said, Q is still viable to max first, it increases your burst by more than it seems since the damage is distributed in 3 stages. I tend to do W>Q>E. All about the damage baby! However, my 2.2k Elo friend TGF Freddy, who mains Riven, does W>E>Q like Psi (I think, but I think the last time I asked him was before the buff to Q). There are many viable ways to skill Riven, it really depends on your playstyle, preferences, and your lane matchup (if you are top).
Also, as Berzerk mentioned, make sure to stagger auto attacks in between your abilities so you don't lose any passive stacks -- that, believe it or not, is where a large portion of your burst comes in. If you don't stagger you autoattacks, that could be the difference between winning and losing a trade, and as a result winning and losing a lane, and as a result winning or losing a game :P
Generally, you want to E into them, auto if you can before you stun or if they are barely in stun range stun, auto, auto, Q, auto, Q, auto, Q, auto. If they are lowish or you think you can full to nothing them, make sure you use your ult BEFORE you shield into them, and ignite them at the beginning of your combo. Then ult to FINISH THEM! YATA!
Thanks to TRUeLM, Plastictree, Scrax, Xiaowiriamu, foggy12, JahGFX, jhoijhoi, msrobinson, JEFFY40HANDS, Nyoike, MissMaw, and me :) for the sigs!
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E in lanes you can't win. Keep in mind that if you max E, even if jungler ganks you porbably can't land kills.