Some people learn by flipping pages. Some people must gain knowledge through pain. Some people study by television. And then there are those who just observe... See, when you are Good with Numbers you can substitute careful examination in place of careful practice, with the same results: success.
Need to make a million-to-one shot to stop the Doomsday Device from exploding the world, but have never even fired a gun? Just run off some mental calculations about your gun's firing speed, friction, gravity, and the slightly-off-kilter scope (how exactly the analyzer knows all those variables is handwaved), and it's a done deal. Need to defeat a karate master? Logically anticipate where his next strike will come from and remain one step ahead. Need to deduce the Secret Identity without peeking behind the mask? Simply go through all the people with the correct body type, who live in the right area, and who might have the right means and motive to do what they do, and hey presto, it might as well have been an Open Secret all along.
If he has time to explain himself, it always sounds something like "If My Calculations Are Correct". Explaining it gives it a chance to fail. Relatedly, two awesomeness analysts don't really need to explain anything to each other, they can do it by Talking through Technique.
The most common cause of Badass Bookworm, and often results from The Professor having a doctorate in general knowledge rather than any one field. The Clock King can do this thanks to precise attention to detail and patterns. Characters who get to skip the analysis altogether due to some form of copycat power are Power Copying. Exactly What I Aimed At usually comes from this trope. They are most likely screwed if the opponent knows Confusion Fu or is at least enough of a Magnificent Bastard to use the Batman Gambit on a regular basis successfully. The Profiler does this with people. An author may use Super-Detailed Fight Narration to demonstrate that a character possesses this ability.
Compare Sherlock Scan. Contrast with Failed a Spot Check. Not to be confused with this site's very Analysis page.
Awesomeness by Analysis has been suggested to play 4 roles. Click below to see other actors suggested for each role, and vote for who you think would play the role best.