You don't have to be good at math to play a rogue. Anyone can log into WoW and create a rogue. You can get all the way to level 90 and into raids without ever having to do any addition or long division. You can do dailies and dungeons simply by using the highest ilvl gear available and ignoring everything else. Rogues are played with a keyboard and mouse, not a pen and paper.
However, if you want to wring every last drop of DPS out of the class, you're going to have to get your hands dirty with numbers. I love when a class' design forces the player to make tough choices. The choices that we make as rogues, when you think about it, are really just math problems. The secret to making good choices is to do the math ahead of time. You don't want to be faced with an unexpected set of fractions in the middle of a tough raid encounter.
Plan your cooldowns
On your typical tank-and-spank encounter, you want to use your cooldowns early and often. While the best strategy is usually to activate your CDs as much as possible, but there are several situations where that might not be the case. Rogues are a cooldown class, and your use (or misuse) of your CDs will make or break your damage. When approaching a new encounter, you need to know a few things ahead of time.
First, you need to know the fight duration. If you're within the final two minutes of an encounter, you are only going to get one more use out of your major cooldowns. You can choose to delay your final set of CDs to sync up with a particularly advantageous phase or situation, which will boost the effect of the CD. A great example is when facing Jin'rokh, the first boss of Throne of Thunder. You might want to delay your last set of CDs if it allows you to pick up the Fluidity buff from a new pool of Conductive Water.
Stack your CDs with other effects
Speaking of Fluidity, you will also need to know about any special damage buffs or debuffs that you can combine with your CDs. You can greatly increase your damage on Jin'rokh by saving your first set of cooldowns for when you're standing in the first Fluidity pool, rather than popping them off the start. Fluidity is a 40% damage boost and lasts for the entire duration of your cooldown, which means your CD is 40% more effective. Everyone thinks my damage is awful when we pull Jin'rokh, but I'm the one laughing when I pull into the lead when I've got Fluidity.
You also need to know when your raid leader is going to call for Bloodlust. A 30% haste boost is strong enough to warrant aligning your CDs, if possible. Many raid leaders will try to use Bloodlust at the start of an encounter, to ensure that it's synced with potions and cooldowns. Or, they'll try to use the raid CD to push their way through a tough phase or to finish off a boss that gets progressively stronger. Whatever the case, try to align your CDs with Bloodlust.
Make the most of your damage
Finally, you want to consider the fact that all DPS is not created equal. It might look good on the meters if you're popping Shadow Blades and spamming Fan of Knives on some weak adds, but it's not going to make your raid any stronger. You'll often need to use your CDs to help deal with a powerful opponent or to assist with a difficult phase.
For example, when facing Lei Shi, she'll put up a bubble that makes her immune to all damage until someone kills one of her adds. While inside the bubble, she'll be crushing your current tank with Spray. By saving your CDs to line up with her 20% activation phases, you can ensure that you have a cooldown ready to nuke the specified add and to save your tank's life.
Your rotation will be bumpy
If you're playing with Anticipation, you can safely absorb a few bonus combo points from effects like Shadow Blades and Revealing Strike. However, if you've switched to Marked for Death for a particular encounter, you won't have that extra combo point buffer. If you find yourself sitting at 4 combo points, what do you do? Should you use Sinister Strike again and hope it works out for the best? What about if you're playing subtlety?
You need to know your rotation, including the quirks, before you're facing a boss. You need to know that you're fine using a 4-point Envenom as assassination and that Sinister Strike is still pretty safe to use at 4 points as combat. You don't want to be adding up the numbers on one hand while trying to raid with the other. Figure out how you'll respond to any and every combo points and energy situation ahead of time so that you'll be able to react quickly when faced with the decision.
I like to try out any rotation on a target dummy before a raid. I'm not trying to maximize my DPS, because dummy DPS is not representative of an actual encounter. I'm just putting the spec and rotation through its paces to find any bumps or issues that come up. I make sure I'm ready for every possible rotation situation that I find myself facing.
Sneak in every Wednesday for our patch 5.2 guide, a deep-dive into the world of assassination and combat rogue AoE rotations -- and of course, all the basics in our guide to a raid-ready rogue.