Kid Buu from Dragon Ball Z was able to learn any technique instantly just by watching someone else use it.
This was also how Goku first learned to do his trademark Kamehameha blast in Dragon Ball.
Which in itself is derived from Sun Wukong's (the character Goku's based off of) own ability to immediately figure out a technique by just watching it.
Vegeta himself is an excellent example of this trope, when he learns how to sense ki by having witnessed the Z fighters do so.
Back when Yamcha was the main Butt Monkey and Tien was the current Jerkass villain, Yamcha threw his very first on-screen Kamehameha. Tien was less than impressed, and fired one right back at him. Master Roshi spent 50 years perfecting this technique.
Goku managed to perform a smaller version of it after seeing Master Roshi do it once for the first time. The second was Yamcha who used it, during the second Tenkaichi Budokai, presumably after seeing Roshi and Goku in the past. Next came Krillin, on that same tournament, who did an improvised yet effective one, again after seeing Goku and Yamcha. Finally, Ten Shin Han launched a powerful one merely after seeing it once. Roshi never taught any of them said technique and was quite surprised when they managed to pull it by themselves.
Android 16 seems to have a knack for analysing the power and abilities of others, immediately sensing Piccolo's fusion. In a show where everyone is constantly underestimating their opponent, this sticks out.
Frieza to a certain degree too, as he copied Krillin's Destructo Disc and turned it into the Death Saucer after seeing Krillin use it just once. Krillin cut off Frieza's tail with it though, so he wouldn't have forgotten about it easily.
And he added homing capability to it.
This ability to copy techniques and instantly comprehend motion is the main source of the Sharingan's power in Naruto.
The main character (post time-skip) develops his own form of battle analysis, using his Shadow Clones in Trial-and-Error fighting until he forms a winning strategy.
For example, when facing the Third Raikage in battle, he learned from Hachibi that both of them fell from exhaustion while their jutsus were still active. That gives him the idea that maybe the Third Raikage's Nukite damaged him. Testing that theory out, he entered Sage Mode since he couldn't use his Nine-Tailed Chakra Mode at the moment. Creating a Rasengan, he used his sensing abilities and Frog Katas to dodge the Third's strike, spinning around and hitting his arm with the Rasengan. Which sent it crashing into his chest, leaving him open for sealing.
Kakashi, according to Word of Guy: "You're second to no-one when it comes to analyzing." Though he has the Sharingan, his stamina keeps him from making full use of its copycat power, so he relies more on its observational abilities. He is, as far as we know, the first person to understand how Tobi's jutsu works.
This is how Vash the Stampede in Trigun is so awesome with his gunmanship. In one episode, he even surreptitiously throws a rock between gun duelists to deflect a bullet in mid-flight away from a lethal trajectory.
He, does, however, have the advantage of being over a hundred years old and has had plenty of time to hone his skills. Still, his physical abilities combined with his high mental abilities are what allows him to pull off such stunts.
Indeed, Vash was even able to dodge bullets by noting the trajectory of a gun just as the wielder began to pull the trigger, giving him a head start on moving out of the way.
Ranma from Ranma One Half has a super-human ability to utilize and adapt to even the most complex martial moves using this trope.
The Gamer: Han has a unique ability that turns his life into an RPG Mechanics Verse, and he even gains the ability to observe people and see unique things about his stats. He can also learn powerful techniques from books describing them a-la Skyrim.
In Yu-Gi-Oh! GX, Daichi Misawa analyzes his opponent's known cards via computer before a duel and writes complex math formulas on his walls to develop new strategies. Kagurazaka, a one-shot character in Season 1, manages to do this by copying Yugi's deck, and was implied to have done so with several more duelists. There's also Dr. Zweinstein in Season 2, who is implied to have spent most of his time since Duel Monsters came out mastering the game through analysis and "duel physics".
Then in Yu-Gi-Oh! 5Ds, we have Team Unicorn. Breo studies the cards and tactics of prospective opponents, memorizing and organizing it into sensible data. Jean, the leader, builds this information into plans that foresee how to counter what the opponents will do. Andore isn't given to thinking beyond the present, but he's a first-rate improv duelist, able to put down any opposing comebacks in one turn and with very few cards. Since their only on-screen duels are against the protagonists, Failure Is the Only Option.
Yu-Gi-Oh!: Want to beat Yugi at a game he's never played? A game of your own creation, no less? You will lose; even if you're lucky, it will take him a maximum of two turns to figure out the game to the point that he's able to invent a strategy to kick your butt. As mentioned elsewhere, the card game taking over was unintended. He is king of games, plural, and being able to do this is his thing.
Also, while this aspect wasn't quite as prominent in the second anime, Yami is incredibly good at analyzing his environment and developing strategies against brutal gang members. One of the prime examples is the "trigger" trap in the chapter where Jounouchi gets tortured by Hirutani's gang with stun guns. Yami lets one of the guys hit him so that he can lead the gang to puddle, telling them that a time bomb is going up unless they find a trigger. Hirutani quickly figures out that if they use the stun guns in the rain, they might actually hurt themselves. This wasn't the trigger though. The trigger was the arm of one of the gang member's, who was lying by the puddle after getting kicked by Jounouchi, stun gun still in his hand that is kept up by a metal pipe. Above his head, Yami had tied his Millenium Puzzle so that water drops on his face, waking him slowly. The moment he stirs, the metal pipe that held up his arm falls to the side, and he drops the stun gun into the puddle.
Ryosuke Takahashi of Initial D, one of the hero's main rivals, is said to be the only racing driver who trains on the computer—not through simulations, but apparently by mathematical analysis of the performance of different cars.
To further prove his awesomeness, in 4th stage once he asks Takumi to wait for his opponent for a few seconds, lowering his speed in the first part of the race, having understood just by watching him that the opponent is awesome by analysis himself. The opponent is in fact so good that in the little time he studies Takumi's car by following him he realizes Takumi's weak point. Ryosuke does that on purpose so that their opponent can prepare a strategy in the following race, to teach Takumi to understand his weak points and improve his ability. This means he is so smart that he actually uses another awesome by analysis character as a pawn, predicting all of his further reasoning and reaction. He's 3 steps ahead of a common awesome by analysis character. This kind of foreshadowing rivals that of Lelouch or Light Yagami.
Kotomi attempts to pull this off during a baseball game in the first episode of CLANNAD After Story. Results are mixed.
Subverted in the Visual Novel when Kotomi attempts this with a claw machine.
Manabu Yukimitsu from Eyeshield 21 is not the most athletic guy, but his ability to analyze the moves of his teammates and opponents alike makes him a skilled receiver. He even manages to score the Devil Bats' first touchdown against the supposedly impenetrable defense of the Shinryuji Nagas.
Hiruma and Mamori aren't too shabby either.
Takami, quarterback for the Ojou White Knights also runs on this trope.
Parodied by Sasuke Kanagushi of the Dokubari Scorpions, who pays attention to the little details in the opposing players' position to accurately predict their moves. Unfortunately, he was up against Hiruma who Takami says "His enemy's just plain too evil." How Hiruma tricks him? Using blush and lipstick.
Awesomeness of Lelouch from Code Geass extends to this trope, too: in the second season, he pilots a Humongous Mecha so complex to handle, that people with normal intellect (like his "brother" Rolo) can barely utilize a third of its full combat potential. Granted, there are stronger mechs in the show but for a Non-Action Guy like Lelouch even keeping up with them is impressive.
He also pulls this in the first season when a detailed study of the "White Armor"'s fighting style allows for prediction and preemptive countermeasures which almost result in the Lancelot's destruction - "almost" because a missed strike at the cockpit reveals its pilot to be his childhood friend Suzaku, inducing a brief Heroic BSOD in Lelouch.
And he does it again late in R2 when he rapidly calculates (partly in his head, partly using his Frame's computer) several dozens of environment parameters under extreme time pressure to cancel out the a FLEJA explosion. Even the inventor of FLEJA, Nina Einstein, admits she wouldn't be able to do it fast enough.
He also records a video that gives the appearance of talking to Schneizel (already a Magnificent Bastard in his own right) in real-time, purely by calculating all his responses beforehand- including exactly how long he would laugh for.
The homunculus Wrath in Fullmetal Alchemist, has a superpower called "the Ultimate Eye". It means that he is able to analyse all possible factors in his vision and calculate the perfect battle strategy to any situation. He is defeated by one of the heroes stabbing him through the body of a terminally wounded ally, which left a large blind spot in his field of vision.
All alchemists are this in general since they often have to understand and utilize the material in their surroundings to use their ability.
Special mention, however, goes to Ed, as he manages to defeat "The Ultimate Shield" of Greed by realizing his armor was composed of Carbon, and realigned that Carbon from a diamond-esque stratum to one of graphite - i.e. pencil lead.
In the manga, he also manages to recreate Greed's trick using his automail and figures out how to use his own soul as a Philosopher's Stone by using the energy from Envy's to escape Gluttony's stomach earlier on.
One chapter of The Kurosagi Corpse Delivery Service involved a crooked insurance agent who convinces people to sign up for insurance (with him as a beneficiary), then murders them via probability: he uses a special notebook to calculate circumstances that are most likely to kill them in a freak accident, then lures them into such situations and collects the money. He tries to kill the members of the Delivery Service this way after they make contact with one of his victims. His demise comes about due to a personal weakness - his deduction is that he'll die in a plane accident, so he cancels his flight, but accident is not synonymous with "crash"; a screw falls off the plane and hits him in the eye. At terminal velocity.
Damn near the entire main cast of Death Note pull this sort of thing off on a regular basis. The least intelligent of the main cast are members of an elite task force of detectives, while Light, L, Near and Mello are able to pull off incredible feats of deduction. L narrows Kira's location down from anywhere in the world to a single district in Japan with one TV commercial.
Index herself. Within a space of roughly three seconds, she correctly identifies the history, style and everything about a giant rock monster that had just appeared. The awesome part comes when she takes partial control of it by apparently reciting letters at it and causing it to miss/punch itself. Oh, and this is without her using magic, because apparently she can only do that under special circumstances or something and doesn't know she can at all. Considering that her mind contains knowledge of everything to do with magic, it's more a matter of her having a really fast ability to access that stored knowledge. (Considering that she holds 103,000 books worth of magical knowledge in her head, it's still a pretty impressive feat.)
She still has to figure out what's going on and decide what to do. It's analysis and just happening to have a gigantic resource to draw on. In a later fight, she manages to completely analyze a powerful magic item kept deliberately secret from her in a matter of minutes.
Also Accelerator. Yes, he won the superpower lottery, obviously, but it's entirely reliant on his knowledge of mathematics ie. if he wants to stomp his foot and make a gigantic rippling wave of doom, he needs to know how to actually do that. He knows how to shot web.
Not just Accelerator. ALL Espers have to calculate and know what they're going to do, before they do it. Both Kuroko and Awaki need to calculate what they're going to teleport and where using eleventh dimension mathematics, not three-demensional (Length, width, hight) mathematics. In short, The Raildex universe is a World of Awesome by Analysis
Touma still counts, I mean he perfectly calculated the trajectory and velocity of a flying F-15 jet coming near him in like five seconds, he also subconsciously finds ways to counteract the abilities of his enemies. Like how he is able to block Misaka's railgun which goes three times the speed of sound, or Accelerators black wings of badass by using his own weakness of not being able to negate strong powers instantly.
During the Railgun Sports Festival arc, one of the villains manages to lead a team with few and generally weak Espers with the strongest being a single Level 3 to victory over Tokiwadai, where the only Esper below Level 3 was a Level 2 with extensive combat experience by exploiting the limitations of their powers and personal phobias. He later gets into a real fight with several Tokiwadai students and attempts the same technique, but they anticipate this and fool him into underestimating them.
Urahara Kisuke became immune to bala attacks from Espada #10 Yammy, solely by analyzing those attacks, including the way he moved his arms.
Espada #8 Syazel Apporo could easily deal with Abarai Renji from observing "video" of his earlier fights and negated quincy power simply from having collected information on Ishida's previous fights.
Ishida is known in-universe for doing this, most notably in his fight with Cirucci Thunderwitch. Later on during the Lost Agent arc, Ichigo actually holds off fighting the Arc Villain because he's waiting for Ishida to analyse the fight and come up with a plan. At least until he gets bored of waiting, anyway.
Resident Mad Scientist Mayuri lives by this trope. He analyses everything and everyone before he'll get involved to the extent where he was able to defeat Szayel Aporro by having analysed the fight via spy-bacteria he'd secretly infected Ishida with. It allowed him to replace all his bodily organs and tendons before going to the fight just so he would be immune to Szayel's powers.
Ichigo, Leeroy Jenkins-extraordinaire, has been noted for having a talent for seeing through his opponents techniques the longer he fights them. He's known in-universe for his uncannily accurate insights into his opponent's hearts.
Prior to turning into an Eldritch Abomination, one of Aizen's main and most impressive skills was analyzing people around him and using their emotions and ideals to his benefit.
Coyote Starrk was able to work out Ukitake's shikai after seeing it only three times, and was able to predict Kyouraku had a two-sword release form because even with one sword in his hand, Kyouraku was fighting like a dual-wielder. His assessment was based on minute adjustments Kyouraku was making with his two hands in battle. He figured out Kyouraku's colour-game almost instantly.
Hachi is able to work out how to defeat Barragan simply by listening to Barragan's Badass Boasts and figuring out that if Barragan's power genuinely was absolute aging then he had to be protected from being destroyed by his own power, which allowed him to use his Functional Magic to make sure Barragan was exposed to a dose of his own power.
An even more appropriate example is the villain Amiba (or Ameeba, or Amoeba, or whatever) , who is able to get a grasp of any martial art by observing its practitioners. He uses it to impersonate Toki, and manages to pull off the sham for awhile, until he gets outed by Rei. However, his versions of whatever martial arts he copies aren't quite as pure as the original, and Kenshiro is able to fight out of his techniques, while saying that if the real Toki had hit the same pressure points, Kenshiro would never, ever have been able to get out.
Parodied with a mook in Soul Eater who could predict and analyze the next 20 moves of an opponent in battle, and do the necessary calculations on how to deal with it. The first thing he did when faced with his opponent was to surrender, because his analysis told him that he had no chance to win anyway.
Also played straight with Maka and Kidd. Maka's ability to analyse and discern who and what her enemies are (as well as how to beat them) makes her a serious threat to anyone, while Kidd (when he's not stressed out over his OCD) proves that his ability to extrapolate a fight makes him a brilliant strategist. And then there's Stein (who has a bloody doctorate in Awesomeness by Analysis). Soul also has his moments too (remember the piano soul resonance idea?)
Kiyomaro Takamine of Gash Bell does this a whole lot, but the best example comes from his and Gash's fight with Robnos, in which he takes apart his opponent's tricks in succession, as follows:
Once he learns that Robnos's laser beam attack reflects multiple times, he calculates the angles instantly and hides himself and Gash in the attack's blind spot.
When Gash still gets hit by the attack, Kiyomaro deduces that Robnos has a clone, explaining why he survived Gash's lightning attack without a scratch.
After Robnos and his double merge into a giant with a much more powerful laser beam, Kiyomaro defeats him by jamming a metal pole in his head and using it as a lightning rod when Robnos stored energy for his attack.
He almost meets his match with Koral Q, a mamodo with spells specifically designed to counteract all of Gash and Kiyomaro's tricks. Kiyomaro pulls through by inventing a new trick on the fly.
Dufaux much? His ability Answer Talker, which he shares with Kiyomaro is KNOWING EVERYTHING. He actually just walks into an attack from Ropes, sustaining no more damage than a big hole ripped in the shoulder of his jacket. He then proceeds to pin Apollo to a wall and burn his book, only casting his first spell the entire battle if I remember correctly. If not, only one mid-level spell to defeat their trump spell.
And Momon. And everyone. Really, it's about the premise of the show here.
Also in StrikerS, Teana's personal "graduation fight" consisted of knocking out three combat cyborgs at once by predicting their moves. She didn't have much choice but to think very hard, either: all three were way above her in both combat skill and power, and she was crippled, to boot.
Same goes for Yue. She's able to recognize an illusory dimension and KO a griffin dragon by analyzing their properties. It helps that her artifact is a Great Big Book of Everything.
Jack Rakan as well. After witnessing Negi's speed and concluding that he can't match it, he is still able to hit, block, and dodge him. He explains that he is able to predict where he will move to.
Rakan's abilities come from fighting another Lightning guy and using what he learned from that battle, he even says so himself.
Satsuki, the local (evil?) brainiac of X1999 begins her day in the limelight with a tennis match. Not only can she instantly analyze the angles of the ball and react accordingly, but she can also read her opponent's physique and (successfully) conclude that she cannot return the serve without "an 11 percent increase in muscle mass."
The Prince of Tennis, anyone? There's a whole style of tennis based on analyzing your opponent's moves, abilities, statistics, etcetera, and then using it to beat them. It's called Data Tennis. It's utilized most extensively by Yanagi Renji and Inui Sadaharu, although it is used to a lesser (or at least, less successful) extent by Mizuki. Konjiki Koharu and Dan Taichi also show a tendency for Data Tennis, though in Koharu's case it is largely overshadowed by his Comedy Tennis, and Dan is yet to actually use his data in a match (largely because, at least in manga canon, he is yet to HAVE a match).
Jokingly subverted by all of Inui's non-Tennis sports attempts. When playing billiards, the others assume he'll be good at it, even going so far as to say "It seems like a game he'd be good at, neh?" He then proceeds to lose horribly. Another time, when they go bowling, he chooses a light ball because it should be easier to control... but in bowling, a light ball tends to get excessive spin, making it ironically DIFFICULT to control. He spends the whole game making one point per turn, because he can only get the ball to hit the far left pin.
Every time this happens, he grimaces, gets Scary Shiny Glasses, and thinks a stunned "Illogical..."
Seems to be a characteristic of Fukumoto Nobuyuki main characters. Akagi defeats seasoned professional mah jongg players just by watching them play, and ultimately wins by making a play that most would consider suicide. Kaiji is able to grasp the nature of the one-sided gambles he finds himself in and creates plans to help get him out of tough situations.
Siegfried and Odin also use a variant: they dodge and counter their opponent's attacks by learning their "rhythm", which allows them to predict the opponent's next move. In both cases Kenichi attempts to trip them up by performing random stunts unrelated to fighting (Siegfried) or radically altering his fighting technique at quick intervals (Odin).
Emerald from Pokemon Special can tell where a Pokémon was born just by looking at it. While the skill has no practical use by itself, Emerald also has a special dirt-firing gun. He can calm down any rampaging Pokémon by firing the dirt of its home at it, soothing it with the dirt's nostalgic scent.
Pearl can also tell what move a Pokémon is about to make before it makes it by observing its movements and stance, allowing him to figure out a counter beforehand.
Black can use his Munna to clear his mind completely, and can determine what sort of Pokemon he's up against using various clues.
In the anime, Tracey has this ability as one of the perks of being a Pokémon Watcher.
Also in the anime, Max thinks he's this, but the few times we see him battle he has trouble getting his plan rolling quickly enough. Granted, he's seven and has no actual experience whatsoever.
The male lead of Lock On is no fighter, but is so good at his career in photography that he can easily read the movements of any martial artist to roll with an attack, break a fall, or even stop an attack before it can gain any momentum.
Kenshin from Rurouni Kenshin is good at reading his opponent's moves and can even apply this to dodge bullets. However, one of his weaknesses is that he is a little over-reliant on this, meaning that he can be thrown off by opponents using unorthodox moves, like when Jin-e passed his sword behind his back to his other hand or when Saitou threw his broken sword as a distraction before whipping Kenshin's sword out of his hand with a belt.
It also hurt him in his battle against SoujiroSeta, who was emotionless/ki-less, and therefore, unreadable. Kenshin flounders during the first half of the fight, but is able to turn it around when Soujiro suffers a nervous breakdown.
In Mx0, Taiga is a Badass Normal in a school of mages and everyone believes that he has the strongest magic possible for plot related reasons; because of that he gets in near constant fights that he wins by carefully observing the magic being used against him, its limitations, and putting terrain to very good use. He is so good at this that people in his school still believe that he has the strongest magic of any student.
Toru of Iris Zero. In a world where people suddenly began developing special powers called Irises (when someone with an iris sees someone or something, they see something else along with it that goes along with the power. One girl sees a devil tail on anyone who is lying, another sees an X or O over someone's head when seeking out someone qualified for a position), Toru has no Iris at all, making him a titular Iris Zero. However, he is so skilled at analyzing others that he was able to convince people that his Iris was being able to tell what other people's Irises were. Had he not been outed by the one person who could tell when he was lying, he'd still be doing it. He's so good at this that one character, whose Iris has yet to be revealed, admits that Toru is the only person he's ever met who was actually able to figure out what his Iris is. Ironically, Toru isn't very good at solving "emotionless" puzzles, that is to say, IQ test type puzzles, but he's exceptional when solving problems that involve other people.
In the sports mangaBaby Steps, Eiichirou's primary method of learning tennis is through careful analysis. When the natural talent Natsu looks at his notebook for the first time, she is amazed to see that he has taken careful notes of everything she's told him and every move he's made, complete with drawn diagrams, angles, and trajectories.
From Black Cat we get Eve, who admits after her battle with Leon, that he is stronger than her, she still manages to beat him up, simply by knowing how he will react.
Erza Scarlet from Fairy Tail was able to figure out the weaknesses of Midnight's powers after three exchanges.
The first Fairy Tail master, Mavis, takes this Up to Eleven.
In Digimon Tamers, one of the D-Reaper's agents was able to replicate the Digimon's attacks after seeing them only once.
Luffy from One Piece is extremely good at figuring out ways to dodge, parry, or even counter attacks after seeing them once, or at least very little. Thanks to that, he was even able to assimilate the CP 9's Soru technique and use it himself.
Tatsuya, the main character of Mahouka Koukou no Rettousei, has barely any magical power, yet uses sheer breadth of spell knowledge, unarmed combat, magical gadgets and Anti-Magic techniques to make what he has fight on-par with the others.
Kankuro:That Onimaru Miki didn’t knock that train out of her way, she dodged it, nya! I understand at last! That body of Onimaru Miki that’s as strong as a rock still can’t beat a train! I finally got it nya!
Hiroto Kuragane's main ability of the 2011 Kendo manga, Kurogane, used to help offset his lack of physical abilities.
Holyland chapter 168 explains that the ability to "read" an enemy is the real source of Masaki's ability, more than any of his physical prowess.
Yusuke Urameshi is better at this than one would expect from your average street punk. Of note, he mastered Genkai's Spirit Wave technique after his first use of it, correctly deduced which of his friends was a doppelganger based on their personalities and traits, fought on even ground with the world's greatest martial artist after only one prior battle with him, and found the weak point of Yomi's Deflector Shield technique, using this opportunity to bring a fight with a demon several times more powerful than him to a near draw.
Cyclops is similarly good at pool, seeing as he's had to memorize complex trigonometric techniques to make sure his optic blasts go wherever he wants. Its implied/stated to be part of his powers.
Mr. Fantastic of the Fantastic Four lives on this trope. Being stretchy and somewhat more resistant to bullets than the normal person would not be the most impressive superpower (though still better than no powers at all), but when it's backed up by a brain that can build nearly anything, including a planet-buster-buster, he's a lot more dangerous.
Bruce Banner has this too when he isn't the Incredible Hulk. To the point that Norman Osborn considers Banner a bigger threat than The Hulk.
Marvel's Anti-Hero-Villain Taskmaster can do this with any physical skill he has seen at least once and is physically capable of duplicating (and some that he shouldn't be). However, what makes this Awesomeness by Analysis is that he's founded a thriving business teaching other supervillains, (his latest job is training the recruits/draftees of The Initiative and latter Osborn's Camp HAMMER) something he couldn't do if he didn't gain a deep insight into the skills he picked up.
In fact, he's so good at it that governments have been shown to hire him to train law-enforcement to take down supervillains.
This power, however, requires the subject to act sanely and in a recognizable pattern. Daredevil once defeated him by acting at random (eventually tricking Taskmaster into stepping into traffic), and he is powerless against Deadpool's Confusion Fu.
Also from the Marvel Universe, the Inhuman Karnak has the superpower to find the one weak spot in any material or object, allowing him to shatter it with a (non-superpowered) karate chop.
He is a bit stronger than a normal human, because of the superior genetics of the Inhumans. Still, he has been shown to damage Ultron with a well-placed strike. And pushing the awesomeness even further: this is not a "superpower." He was never exposed to the Terrigan Mists, like other Inhumans, so his abilities are the result of training and discipline. Eat your heart out, Batman.
This is also the power of Top 10 Detective King Peacock, although his justification is rather odd. (He talks to Satan. Apparently.)
Over in DC, Batman is said to have a second major in this, as he is very very much a detective and criminologist when his preplanning everything didn't succeed immediately.
An example of this trope in action comes in Batman: Year One when Bruce Wayne first encounters street hooker Selina Kyle and quickly realizes "She knows Karate...Only Karate."
Which may have been a shout-out to the Adam WestBatman series, in which Catwoman is rendered incapable of using karate against Batman because it's a defensive martial art and he refuses to attack her (?)
Same goes for Batman's evil counterpart Prometheus, who has created technology that analyzes an opponent's fighting style, allowing him to simulate it perfectly.
Batman villain Bane became a master of several martial arts and sciences simply by reading every book he could get his hands on. After Bane holds his own against world-class swordsman Ra's al-Ghul, Ra's criticizes his lack of flair and implies that Bane learned sword fighting entirely from reading books on the subject.
The Midnighter of The Authority starts every battle by first running the whole thing through the supercomputer in his head a few million times, analysing every possible outcome, so he'll know precisely how the battle will go, and what he'll have to do. He's particularly fond of telling people that he's already beaten them a few million times, so doing it once more will be simple.
He even put this on a business card once in an effort to save time. This failed, as the card ended up in his forehead. Ow.
And it fails when a supervillain summons the Joker. The Joker, despite being human, is so psychotic and unpredictable that the only thing Midnighter can do is stand there staring at him.
Another failure came about in the miniseries Human on the Inside, in which Midnighter's opponent thwarted him by declining to make the first move, reasoning that Midnighter could only derive the possibilities for the fight once his opponent made an opening move. Fans seem divided over whether that's really how the power was supposed to work.
Shockwave in the Marvel Transformers series (not to be confused with Shockwave in the cartoon series, who was different) was like this, able to calculate probabilities of situational outcomes to exact percentages. It didn't hurt that he was, y'know, an actual computer.
The IDW Shockwave is no slouch at this either, and not just for calculating probabilities or discovering weakness, either. During a fight with the Dinobots, he is astonished by the irrationality of their attack, and deducts that it's driven by anger, an emotion that he finds irrational and normally pointless. However, once he sees how it seems to drive up their ability to fight, he patches together a "rage" emulator into his mind, and goes absolutely berserk, single-handedly dominating the Dinobots, and then puts this so-called "anger" on the back-burner for later analysis.
Skids of Transformers: More than Meets the Eye has the ability to learn and master new skills quickly. He has used this to analyze opponent's fighting styles and overcome numerous, powerful enemies.
American Pi in Troy Hickman's series Common Grounds has this as her superpower.
Destiny Ajaye in the upcoming Top Cow series Genius has this ability which she uses to co-ordinate gang warfare on a national scale.
In Watchmen, two such characters exist. One is Ozymandias, the other the God-like Doctor Manhattan. The latter is Blessed with Suck when he can analyze everything, even the future he will take, and finds everything to be meaningless on a grand scale.
Finesse from Avengers Academy has a similar ability to the Taskmaster's: the ability to master any physical skill she sees performed. So much so that she actually wonders if she might be Taskmaster's daughter.
This is supposedly how Helix sees the world in IDW's G.I. Joe series. It is the explanation for her kickass combat abilities that make her a match for Snake-Eyes.
The New52 version of Superboy taught himself to talk and communicate by watching others do it.
Freddie Benson has this as his main power in iFight Crime With Victorious, and it doubles as healing and triples as an Adaptive Ability. He uses this to diagnose the functions of his own ability and the abilities of his friends.
Neville Papperman performs a similar task with his "fear-sense", but he does this by figuring out the person's vulnerabilities and concerns over their power and working out how it functions. He analyses their fear, which typically relates to their new-found power.
In A History Of Magic Queen Himiko studied other Puella Magi to learn their skills and abilities.
In By Royal Command, Trixie turns out to be an excellent profiler and personality reader, as part of her chosen occupation. When she receives an incredibly indecent letter without readable signature and the claim of being written by a princess, Celestia asks her what she could determine about the author - Trixie determines that the writer is female, extremely educated, was socially undeveloped for most her life and only lately started to develop interpersonal relationships outside of her immediate family, and has no sexual experience whatsoever. It doesn't take much work for Celestia to figure out who that is.
In Mass Effect Human Revolution, Adam has a Sherlock-like ability to read an opponent's fighting style and plan an elaborate counter. And just like Downey's rendition of Holmes, it falters when he can't read the foe or isn't given the time and space to plan.
In A Great Endeavor, Twilight ends up as an advisor to the Allied forces at Bastogne, initially treating the strategy "as a big logic puzzle".
Film - Animated
Basil has a very pronounced moment of awesomeness near the end of The Great Mouse Detective. He prattles on about some sort of forces and equilibrium, and defeats Ratigan's fiendish Rube Goldberg death machine by setting it off at precisely the right instant, setting off a seemingly unpredictable chain reaction that frees him, his partner, and the little girl.
And then, just to rub it in Ratigan's face, he grabs Dawson and Olivia, cheerfully cries, "Smile everyone!" and poses with the two of them with a massive shit-eating grin on his face, in front of the camera that would have photographed the moment of the final blow.
Although Dawson deserves some of the credit; Basil's wrapped up in self-pity before Dawson finally snaps him out of it by frustratedly yelling that if all Basil's going to do is lie in the trap feeling sorry for himself, they might as well set it off.
In How to Train Your Dragon, Hiccup is able to observe how dragons behave close up and with that indepth observation, he is able to do things with dragons that his village thought were impossible.
This is how Mikey catches the scare pig in Monsters University: calculating the right moment to throw a football to knock over a row of bikes to catapult a garbage bin into the path of the pig.
Film - Live Action
The Bad Ass "Tetragrammaton Clerics" of Equilibrium are masters of the Gun Kata: through analysis of thousands of recorded gunfights, they know where bullets are most likely to be at any given time, and they simply aren't in those places. Likewise, they also don't aim so much as they shoot at all the places where people are probably standing.
This is how it's described, anyway. The way they do it in practice is to stand mostly-still in the middle of the room and shoot in rigid lines; so unless their targets are always aiming at the Clerics' arms, it's difficult to imagine it working as advertised. The movie does, however, open with a silhouette of a man practicing a much more fluid, much less static form of Gun Kata; it was originally how they Clerics were supposed to fight, but was later ordered to be changed.
This is the whole premise of the Thai martial arts film Chocolate, in which an autistic girl is able to become a face-kicking machine by memorising techniques she sees when watching Bruce Lee movies and observing lessons at a nearby Muay Thai school.
The Hunt for Red October has Seaman Jones, whose sensitive ears can tell if people are singing on a distant submarine, can pick up unique submarine sounds that the computer thinks is a result of geology, and can tell if a torpedo is Russian just by listening to the pitch it makes as it passes over.
In Ice Princess, Michelle Trachtenberg is a math and physics nerd who applies her skills to becoming a figure skater, utilizing it to figure out how fast an ideal spin is and how much power she needs to apply to do it, and so on. She goes from 0 to competing for a U.S. Nationals spot in a few weeks.
That said, it is implied that her character has skated recreationally for many years, and so at least has a little advantage in the area of previously-gained experience.
This is subverted in the film Im Juli. The main character, a physics teacher, must get a car across a river with a conveniently placed ramp. He does some calculations in the sand, drives the car off the ramp, and sails through the air... only to land in the middle of the river.
It's played with in Road Trip - Ruben calculates that the car will need to be going 50 miles/hour to jump the broken bridge. After EL spits over the gap - and causes the bridge to collapse further - he revises it to 75. They make the jump fine...but the car's axles break and, after they all get clear, it blows up.
In the Kid N Play movie Class Act, uber-nerd Duncan becomes a star football player by using geometry and physics to kick perfect field goals.
Richard B Riddick's badassitude stems not only from his fighting skill but also from his deductive reasoning. In The Chronicles of Riddick it is hinted that the entire series of events that transpired at the Crematoria prison was a Gambit Roulette masterminded by Riddick.
The Crematoria prison escape begins with Riddick giving a detailed description of what they guys currently escaping the prison are doing, and concludes by saying it's a good plan. When another prison asks him how he knows their plan, he replies, "It was mine."
Sherlock Holmes has always had shades of this, but the 2009 movie makes it explicit by showing his analysis, step by step, of how to beat the living shit out of an opponent. The 2011 sequel, A Game of Shadows takes this even further with Holmes and Moriarty deadlocked in an Awesome by Analysis duel in their minds before a single punch is thrown.
Victor Creed, a clawed and beastlike creature with abilities similar to Wolverine in X-Men Origins: Wolverine faces John Wraith, a man who can instantly teleport. Creed uses his brain, not his mutant power, to predict the exact location of John Wraith's next teleport destination. Creed catches Wraith's spine mid-teleport, and comments on how Wraith's weakness was his predictability.
In Ink, the pathfinder is able to cause a car accident to happen despite barely being able to affect the physical world by being in sync with the flow of events. He creates a Rube Goldberg machine made out of people in order to shake up someone who sorely needs it.
For all that the franchise plays it straight with many characters, Star Trek II: The Wrath of Khan averts it for Khan himself. Spock observers that "he is intelligent, but inexperienced" in space combat, and notes his "two-dimensional thinking". Kirk then proceeds to kick Khan's ass in space combat, defeating or bypassing every single one of Khan's ship's advantages and taking advantage of Khan's unfamiliarity with the equipment and how to use it to best advantage. In this case, raw intelligence simply cannot defeat experience, knowledge, and sheer treachery.
"I'll say this for him: he's consistent."
Juror #9 in 12 Angry Men, once convinced to examine the testimony and evidence more clearly, uses clues from the witnesses' appearances in court to poke holes in their testimony. The biggest example is realizing an eyewitness was glasses-dependent, and couldn't have seen the crime well enough to identify the murderer.
Downplayed in Man of Steel by most Kryptonians, but Zod is able to figure out the mechanics of flying and how to use heat vision, as well as using the heat vision's cool-down period against Superman.
In the Discworld novel Jingo, Lord Vetinari pulls off a juggling act despite never having attempted it before.
His excuse for this is that he's spent decades juggling different parts of his city's political and murderous groups. However, the fact that he's a trained assassin with excellent reflexes probably helps... Furthermore, it would be quite in character for Vetinari to be lying about not having done it before.
He does, however, appear mystified that anyone should think it amazing that he can do this. Although juggling is something only The Fools Guild does, not assassins. (Alternate interpretation: juggling badly is something only Fools do...)
The two schools are next door to each other. Considering the Fools Guild teaches Battle Clowning (imagine a martial art based on typical clown motifs) Vetinari probably stealthily observed lessons or may have even taken part in them in disguise.
Discworld also shows this in Lord Hong of Interesting Times, who is capable of learning and doing everything perfectly. No one else seems to focus.
In The Arctic Incident, Artemis Fowl performs an acrobatic slide across the ice-slick roof of a moving train by calculating momentum, angles and friction.
In The Lost Colony, he saves Holly's life AFTER SHE'S KILLED in the middle of a glitchy time-spell breakup (which tears the island they're on apart) by calculating exactly when and where the next time-glitch is going to occur. He fires a gun at the precise moment needed for the bullet to travel into the past and hit Holly's killer.
Literary (and to some extent, historical) example: In Claudius the God (the second part of I, Claudius, though it is downplayed in the TV adaptation), Claudius — who was frail and had spent years playing the fool before being forced to take the throne — leads the Roman forces to victory against the Britons through his extensive knowledge of historical tactics and his heavy use of intelligence about the enemy's social structure and favored tactics.
Grand Admiral Thrawn, from The Thrawn Trilogy, with the ability to find a species's weakness just by looking at their artwork. And, for that matter, figure out their general biological traits (dominantly left- or right-handed, number of fingers or limbs used, perceptual or biorhythmic flaws) as well as traits of those who created or even just favor a particular piece. Notably another character who was supposed to have his tactical insight couldn't do a number of things Thrawn could, and never so much as looked at a painting.
Thrawn also had one "failure", where the inferences he'd made after looking at the art proved utterly wrong. In a dialogue with Pellaeon, Thrawn specifically says that his failure to understand a species's art led to him being forced to eradicate said race. Years later, he thinks he's finally starting to grasp their psyche. Such a pity.
In Outbound Flight, there's a scene where Thrawn and three Corellian captives/guests come to look at a very beat-up nonmilitary spaceship that came into his territory, attacked, and was disabled in such a way that all those aboard died. Thrawn asks the Corellians what they think, and one doesn't care, one thinks he killed poor people and/or refugees, and the third looks at the height of the dead aliens, looks at the wall and a point where sealant patterns change texture, and concludes that the people who repaired/maintained the ship were much shorter than the current owners. A bit of information later and he speculates that this was a slaver's ship. Thrawn is pleased.
A few pages later, Thrawn, who at this point in his life apparently likes explaining things, says he knows of this ship and this people only by reputation, and that, "The crew complement is smaller than one would expect for a vessel this size. That indicates that they weren't expecting trouble, but instead intended to go straight home. [Thrawn knew while fighting them that they were undercrewed, because...] I deduced it from the fact that their defense was sluggish and mostly ineffectual. They did little but launch missiles. A fully crewed vessel would have had laser gunners in place and would have shifted the defense pattern of their missiles. Clearly, they were expecting their escort to do any fighting that became necessary."
Thrawn always liked explaining things. He just did so in more detail in Outbound Flight.
To be fair, in The Thrawn Trilogy, he's a Grand Admiral. He doesn't need to justify himself to anyone. In the Outbound Flight prequel, he has superiors who don't look too kindly on his rogue (by their standards) tactics.
Thrawn's The Watson, Gilad Pellaeon, graduates to this in Hand of Thrawn. While not a match for Thrawn's ability, he successfully deduces that a fleet of attackers supposedly led by Garm Bel Iblis cannot be, by using one of Bel Iblis` own tactics to defeat it.
Sort of used and subverted in Allegiance, where the pirate leader called the Commodore floats in a pool with his eyes covered, the better to focus on the voice of his guest. He believes that doing this, damping down all of his senses but hearing, makes him more able to tell if he's being lied to and pick out hidden things about the speaker. But he's trying to gauge Mara Jade, who is able to subtly stir the air and water to interfere with his senses without his knowing, and so he misses the fact that she's an Imperial agent sent to find connections between these pirates and corrupt officials.
Mace Windu does this all the time. His main Force power is to detect "shatterpoints"; where to hit things, including situations or people's minds, so they break. On several occasions, he has been without a visible shatterpoint and still managed to come out on top. Just before the climax of his feature novel (guess the name!), there's a scene of him "looking" at the shatterpoints for himself, the people around him, the mountain he's on, the war the planet is in, and possibly the entire Clone Wars. It's Matt Stover's way of saying "Hold onto yer butts."
The Demon Device, by Robert Saffron, has Albert Einstein using this method in a game of pool against Arthur Conan Doyle. Although Einstein has never played pool before he scores well, though it's not clear if he wins the game.
Professor Derek in The Gone-Away World by Nick Harkaway, who claims to be so incredibly smart that, despite being an enormous nerd, he's able to emulate normal human behavior patterns through pure analysis.
Kiriyama of Battle Royale might be the ultimate example of this, as he possesses a prodigious intelligence that is able to master virtually any field of knowledge from biology to martial arts and combine them to incredibly deadly effect. Oh, and he's also a completely amoral and emotionless sociopath, which makes tangling with him loads of fun.
Biddy from Great Expectations spends so much time watching Pip at his work that he pronounces her, "In theory ... as good a blacksmith as I was."
Lord Loss, the first book of Darren Shan's The Demonata series, features a subversion. The main character is playing chess against a Demon Lord in order to save the life of his brother. However, every move he makes is repelled and countered until he realises that the only way to win is to stop thinking and simply play randomly, taking risks and not showing fear or sorrow, which is what the demon master craves. In this way he denies the demon master what he wants, and beats him, although in doing so he makes himself a life-long enemy of the demon master. Uh oh.
The Mentats of Frank Herbert's Dune series may be the most fundamentally realistic example of this trope in literature, though their feats of deduction and analysis are labeled as necessarily superhuman even within the context of the books. Miles Teg's T-probe induced, calorie-intensive "faster than the eye can see" mode could be described as exceedingly advanced prana-bindu training coupled with a version of this ability above and beyond even other Mentats, especially considering Herbert specifically describes "Mentat mode" computation as being calorie-intensive to a lesser degree.
In the Vorkosigan Saga, Miles Vorkosigan seems to have the ability to almost unerringly analyze and predict people. He's also had military training and excels at pure tactics (although he finds them boring because they're so predictable,) but his greatest victories throughout the series have always been as a result of his ability to understand, persuade, inspire and predict the actions of other people.
Miles's clone brother Mark assumes he also inherited this talent for military analysis and is proven disastrously wrong. Later, however, he discovers his own genius level aptitude for economics. It appears that their shared analytical skill is genetic but the field of application is influenced by their upbringing (Miles on the warlike Barrayar, Mark on the mercenary Jackson's Whole).
In "Improbable" by Adam Fawer, David Caine is already so good at calculating probabilities in his head that his graduate professor nicknames him, "Rain Man." When Caine undergoes a last-resort experimental procedure to treat his epilepsy, his brain becomes able to access the collective unconscious. This lets him reach information on everything everywhere at any time, and (once he figures out what's happening to him) he can choose from among all the possible causes and effects to find the action most likely to make things go the way he wants.
One of the many things that makes the Archive so dangerous in The Dresden Files is her ability to rapidly analyze available data, being the living repository of all human knowledge. At one point, Luccio notes that the prevalence of mad, female oracles throughout history was simply the result of previous Archives making highly-accurate conclusions based on analysis of the knowledge they possessed instead of predicting the future.
Vin does this to defeat Zane in Mistborn. Having already run out of atium, a metal that gives the person using it the ability to see and react a few seconds into the future, Vin counters Zane's attack by clearing her mind and reacting solely on instinct. She then watches his movements as he prepares to block her attack and strikes from the complete opposite side.
This is the secret weapon of Inspector Spector: he sold his soul to Satan to be the world's greatest detective. (not THAT detective)
The title character of the Mediochre Q Seth Series has the ability to 'see' probabilities ever since a magical accident in his past. Therefore, to work out the most likely scenario in any given situation, he just needs to learn enough variables.
In Noob, Fantöm can beat bosses meant for a full Player Party due to figuring out their behaviour patterns and plannning for them no matter how complex they have been made.
Captain Horatio Hornblower R.N. uses this as his primary method of gambling, seamanship, and war. In one book, he makes an accurate judgment of a French captain's intellect and likely behavior by observing how he handles his ship and uses it to Batman-Gambit the Frenchie into putting his own ship in irons. This is also what makes Hornblower an excellent whist player.
Live Action TV
The Borg, in Star Trek: Deep Space Nine, Star Trek: The Next Generation, and Star Trek: Voyager. They analyze anything used against them and adapt to it, rendering the technique useless in short order. At their first encounter, Starfleet phasers killed a few drones, but the Borg quickly developed personal shields that were immune to those phaser frequencies. The only serious threats to them were Species 8472 and possibly the complex picture developed by Starfleet although the latter was never used.
Data of Star Trek: The Next Generation is MADE of this trope. He can take in information, and process and understand it, so fast that his primary limitation is that the computer interfaces he uses to do this are simply not able to go as fast as he can (being made for organics). One outstanding example occured wehen Starfleet was trying to reveal Romulan involvement in the Klingon civil war. When Picard's idea fell apart, Data conceived of a new method, researched it, implemented it, and use it to unmask the Romulan ships in the space of a few MINUTES, while dealing with a crew ready to mutiny while commanding a ship in battle.
In "Time's Arrow", whilst trapped in the past Data gains money by hustling poker players, which the implication that he did so by counting cards, something he intentionally doesn't do during ship poker nights. In "Cause and Effect", Worf and Riker speculate if Data truly is randomising the deck each time he's dealer. It turns out one of the clues that allowed them to finally break the time loop the Enterprise was caught in was Data subconsciously rigging the deck.
In the Star Trek: Enterprise episode "Carbon Creek," the Vulcans survive on Earth by making money hustling pool.
Tuvok tried the same thing on Star Trek: Voyager when playing pool on the holodeck. Unfortunately for him, he didn't account for the table being slightly off-balance.
This may have been influenced by Barbara Hambly's Star Trek: The Original Series novel Ishmael, wherein Spock, trapped on the 19th Century Earth, excels at pool without thinking about it, later commenting to a surprised onlooker that it is nothing but simple geometry and physics.
An episode of Quantum Leap showed a variation of this, where Al uses a holographic projection of ball trajectories imposed over a pool table to allow Sam to impersonate a skilled player.
In these cases it's completely justified. Professional pool players are so good due to Awesomeness By Analysis in the first place.
Avoided in NUMB3RS, wherein the super-brain Charlie Eppes tries, among other things, golf and sniping, and learns that knowing math simply isn't enough. It requires some kind of instinct or gut feeling to get it right. But the Aesop the whole way through the series is one of synthesizing maths with the everyday skills of the FBI... Or something.
Averted when Charlie and Larry become college basketball coaches. They only manage to get their team their first win in years when Larry hires professional basketball players as his graduate assistants.
Contrast with Monica Dawson in Season 2. She has the ability to automatically copy any physical action she sees without any analysis whatsoever.
In Season 3, Peter absorbs Sylar's ability in order to use it to understand the show's plot. No, really. He's trying to avert a future he visited but realizes he isn't smart enough to take all the factors into account especially since in the Heroes verse, the future has a way of putting itself back on track (sometimes).
Interestingly, Sylar's power appears to be hereditary. When he finds his real father, he finds out that the old man has the same core power as him. In fact, both of them have telekinesis, meaning his dad also found some poor schmuck with the power and cut it out of him. This is the first time a person got the same power as their parent, although Peter and Arthur came close.
Throughout her time on Buffy the Vampire Slayer, Cordelia was mainly a comic relief queen bee type, a role she also filled for a while after spinning off to Angel. After developing beyond simple comic relief, it was revealed that Cordelia was the best cheerleader in Sunnydale for a reason: she has exceptional muscle memory and coordination, allowing her to perform complex physical routines (such as a martial arts kata) at full speed with relatively small amounts of practice.
Avoided in an episode of The Pretender (mostly) when Jarod must learn how to beat a pool hustler at his own game. Being a super-genius he figures it'll be an easy task since it's just "simple physics" and initially does very poorly. Fortunately for him, he learns very quickly.
Used in about every third episode of Doctor Who, when the Doctor (or some other smart hero, usually a companion) will come up with a last minute, slightly MacGyverish, down to the wire, last ditch, just-crazy-enough-to-work scheme that, of course, works because he did something involving a lot of technobabble. One example was the realisation that the Empty Child in "The Empty Child"/"The Doctor Dances" were the type of nanogenes Jack used earlier, and all the sci-fi stuff the DoctorDonna spouts after becoming part Time Lord, which is also how she saves the day. In about a quarter of them, however this is subverted, with something that looks really planned out and life-saving happening, and the Doctor admitting that he made it up as he went along.
The Eleventh Doctor seems to have "instant replay" vision. Basically, he thinks so quickly, everything around him slows to a crawl while he analyzes the situation and works it to his advantage. The Ninth Doctor did the same, observing a giant propeller fan spinning incredibly fast.
The Time Lords have this as an innate trait, being one of the many Time-Sensitive species. This gives them the ability to essentially "see" and perceive the flow of time, "what was, what is, and what could be and what should not".
Rose: I can see everything. All that is, all that was, all that ever could be.
Doctor: That's what I see. All the time. And doesn't it drive you mad?
The Tenth Doctor still retains traces of this whilst temporarily rendered human in "Human Nature". In the middle of a conversation, he notices a piano about to fall across the square. Instinctively, he grabs a nearby cricket ball, lobbing it with perfect accuracy to set off a chain reaction of objects that ends with a milk churn falling in front of a baby carriage, preventing the woman and infant from being crushed by the piano when it falls where they would have been otherwise.
Subversion: In Engine Sentai Go-onger, the villain Hiramekimedes is all about calculation, analysis, and fighting via mathematics. Several of his attacks are even based around angles of triangles. However, the Go-ongers and Go-on Wings always decimate him, with Go-On Gold explaining that it's precisely because Hiramekimedes is so logical that it's easy to predict his attacks. This causes Hiramekimedes to go crazy and swing to the other extreme of Game Theory: the completely random player who attacks with random mathematical fallacies (like 4 divided by 189 is exactly 100). He beats the crap out of the logical Go-On Gold, but is defeated by Go-On Red because his attacks are not based on logic or randomness, but pure Hot-Blooded power.
Low-stakes example: In an episode of Step by Step when the nerdy (at the time) Mark plays a mean game of pool thanks to his mathematical prowess. One time, we see him preparing to shoot, and a mathematical formula circles his head.
Psych: Shawn Spencer. It doesn't matter how complicated your plan is, the minute that little glowy montage starts, you are going down.
In the first episode of The Big Bang Theory, Leonard and Sheldon try to move a sofa up two flights of stairs. Sheldon thinks that it's impossible because they have little physical strength, but Leonard says that they don't need strength, they're physicists. Unfortunately, it's not that easy.
Also subverted in an episode where Sheldon tries to learn swimming and rock climbing on the Internet. It doesn't work.
One of the transgenics in Dark Angel had a level of strategic planning that seemingly made him predict the future.
In a better example, Max is able to win thousands of dollars from a casino by using physics to predict where the ball will land in roulette. Also, she studies the shuffling deck in poker to figure out who has what cards.
Firefly's River: "Also, I can kill you with my brain."
And we see just how true this is in "War Stories," where River comes upon Kaylee, who is pinned down by gunfire from three separate enemies. River glances at their positions, does the math, takes Kaylee's pistol, and proceeds to headshot all three of them with her eyes closed. Later lampshaded by Kaylee during a discussion of the incident in "Objects in Space":
Kaylee: She just . . . did the math.
On the other hand, given that she's a psychic, this and her other combat skills may be the result of telepathically sensing where enemies are and what moves they're about to make.
"Tabula Rasa" — Hotchner, under cross examination in court, profiles the lawyer who is questioning him, and shuts him down: "...Your vice is horses. Your Blackberry's been buzzing on the table every twenty minutes, which happens to be the average time between posts from Colonial Downs. You're getting race results. And every time you do, it affects your mood in court, and you're not having a very good day. That's because you pick horses the same way you practice law...by always taking the long shot."
"Lessons Learned" — Interrogating a terrorist, Gideon has him figured out in the first two minutes and spends the rest of the episode out-psyching him into revealing the target of his next attack.
"Extreme Aggressor" (the pilot) has us meet Gideon for the first time giving a profile of a killer. At the end of the episode, he walks into a gas station, and the cashier happens to fit the profile. He might've been about to dismiss it as a coincidence, if the cashier hadn't pointed a gun at his head. In the following episode, "Compulsion", he tells a group of students about how he told the killer what he knew about him, including the reason he stuttered. The team spends the entire episode trying to figure that out. Subverted when it turns out Gideon was lying to the killer about that last part. Double Subverted because Gideon knew it would stall him long enough to make his move.
Averted once in Xena: Warrior Princess. One episode started with Gabrielle explaining to Xena that she had analyzed one of Xena's more complex somersaulting moves into separate stages. Gabrielle then attempted to duplicate the move by following those stages in sequence. She spent the rest of the episode limping with a sprained ankle.
And played straight in the Groundhog Day episode. Xena spends the penultimate day of the cycle ignoring all the events she has to stop to break the cycle in order to calculate angles, measure distances, and observe what the environment is doing. Then, when she wakes up (again), she's able to do everything in mere minutes with her carefully planned actions and well-aimed chakrum throws.
Kyle and Jesse from Kyle XY both have super advanced brains and can copy anything by watching or doing the math. A good example is when Kyle joins the basketball team at school and can make any shot just by measuring the angles or learning how to fight by watching martial arts movies(he also learned Chinese this way).
In one 3rd Rock from the Sun episode, Dick Solomon wins a racquetball match against a man who's been playing all his life after he realized that the game was about Newtonian physics. His abilities to instantly master almost anything just from thinking about it are shown every few episodes.
Another episode teaser shows the Solomons watching the lottery drawing, and hitting all the numbers. They then happily tear up the ticket (either not knowing or not caring about the money, they ARE aliens, after all), and make remarks about how easy the prediction was, since it's just physics.
In The District, the whole point of CompStat (Comparative Statistics) is apparently so Chief Mannion can demonstrate this trope to bring down Washington, DC's high crime rate.
Tracy, AKA Dice, in an episode of The Cape is a savant who perceives the world around her on a quantum level, allowing her to make extremely accurate predictions about the future and set events in motion by doing something seemingly innocuous. At one point, she drops a coin, which starts off a series of events that almost result in Peter Fleming's death. She is also able to walk right past any security by picking a moment when no one is looking.
For some reason, the protagonist is immune to her calculations, allowing him to screw up her careful planning.
Fleming's people have managed to analyze Tracy's brain and mapped it to a program that can be used to predict stocks with great accuracy.
This trope is why Ryan Stiles never played the host during a game of "Party Quirks" in Whose Line Is It Anyway?: he's able to figure out the quirk in thirty seconds.
The eponymous protagonist of Sherlock. Admittedly, this trait is par for the course with the character, but still worth mentioning.
Subverted on Red Dwarf, when a white hole was causing chaotic time jumps and needed to be plugged, Holly, whose IQ had been increased into the tens of thousands, calculated a trajectory to fire an explosive that would use one planet to knock another into the white hole. Lister looks at the plan, realizes she's playing pool with planets, and manufactures his own plan using only his mad pool skills, performs a trick shot using three planets and their solar orbits, sinking the last one. "Played for and got".
The titular character in the short-lived series John Doe has this as a superpower: he knows everything (except anything about his own past) and has the intelligence to apply that knowledge in whatever situation he's in. The show showed that despite this he wasn't infallible: some situations could have multiple explanations and he didn't always chose the right one, with a prime example being an episode where he was asked to help figure out how a thief had managed to sneak a rare gem out of a museum without being seen on the security cameras. Doe quickly demonstrated how knowledge of where the cameras were and their limitations, a convenient sculpture, and use of the environment could pull it off. When the guard who actually stole it finally confesses, it turns out he simply swallowed the gem and walked out the front door.
C.J from Tower Prep has this, in the power to analyze body language.
In Alphas,Kat's Alpha ability is her insane procedural memory, allowing her to learn and keep complex skills remarkably quickly. Unfortunately, this being Alphas, there is the inevitable trade off: her declarative memory (i.e. everything else) only lasts for about a month, max. she has no idea who she is, or what she's done in her life. This can result in weird situations where she knows that if she has done this before, she'll be able to do it now...but whether she's ever done it before is anyone's guess.
Dexter is a blood spatter analyst able to deduce and recreate a crime scene or a relevant incident within seconds. He finds a match in Lundy, a legendary FBI investigator who is not fooled by some of Dexter's tricks and reverses some of them to deduce the true nature of the suspect: "Law enforcement".
Scandal: Olivia gets quite a lot of information from analysis.
A villain-of-the-week in Fringe could predict events with great accuracy by analyzing everything around him. He used this to plan fatal accidents for his targets, starting the "domino effect" by innocuous actions (e.g. dropping a pencil). He fails to predict Olivia's actions, because that episode took place in the Red universe and since Olivia comes from the Blue universe her behaviour was subtly different to that of a native.
Will Graham in Hannibal, through a combination of his skills as a former homicide detective and his own unique "pure empathy", is able to work out a killer's method and motivation simply by analyzing the crime scene. While this makes him a skilled profiler, it also makes him unstable because he has trouble getting back out of the killer's heads once he's done analyzing them.
Inspector Morse once revealed to Sergeant Lewis that he seriously contemplated suicide as a teenager. Morse being Morse, he approached the issue of how to go about it as analytically as anything else: he wanted to spite his family and calculated how each method would affect each family member. He realised it would be a shame to waste such a brilliant mind.
Spirit Of The Century has the Theory in Practice stunt for exactly this purpose. It has strict limitations compared to similar stunts, but allows characters to use their Science skill in place of any other skill provided they can come up with some plausible sounding Technobabble for how their analysis helps. The rulebook quote:
Shooting a gun should be easy - it's just physics, right?
Dungeons & Dragons has an epic feat called Polyglot that allows you to learn languages - by hearing a few words.
Not exactly. The feat simply confers knowledge of all languages. Also, it requires superhuman intelligence and fluency in at least five languages.
The Smart Hero "Exploit weakness" talent from d20 Modern allows him to use his intelligence modifier instead of his dexterity or strength modifier, "as he finds way to outthink his opponent and find weaknesses in his opponent's fighting style" (paraphrased).
Ocelot from the Metal Gear Solid series. He's a talented enough shot that he can shoot people from ricocheting bullets within a second of studying and analyzing the angle. Later on Ocelot's able match Snake at CQC, a technique he and The Boss spent years perfecting, simply by watching Snake use the moves and then mimicking them.
Any RPG with Leaked Experience implies that the characters that don't partecipate in the battle still become stronger by merely watching the fights.
Final Fantasy has the Scan spell (Also known as Libra). Its effectiveness varies from game to game, but it's generally very useful to know your opponent's current hit points, immunities, and elemental weaknesses.
Useful enough that it's actually a common weapon ability in Final Fantasy X.
FFX even has an optional dungeon full of monsters immune to scanning.
Bartolls/Valtols from the OVA and Original Generation Gaiden. Attacks become useless on them after they've been used once, since they can dodge any future attempts of that attack pattern.
Unless you kill them in one blow, or use the Spirit Command 'Strike' the next time you try to attack them.
That's not eeeexactly true. Rather, Valtolles have +2 Morale on dodging an incoming attack, and their signature ability is "ODE System", which means that all of them have a Morale score equal to the Valtolle on the map with the highest Morale score. Since Morale affects your dodge rate, hit rate, damage given, and damage taken (and possibly critical rate), and since they also gain Morale when they hit you, odds are if you miss one Valtolle, you'll start missing a whole lot more. Fortunately it also means that if you beat them black and blue in one turn they'll suffer a horrible Morale drop, which makes them very easy to kill owing to their paperthin armor.
Welkin Gunther from Valkyria Chronicles achieved this in Operation Cloudburst. He drove his tank through a river, Oregon Trail-style, and all he had to do to make it happen was watch how the grass grew in the shallow parts and ask Isara to waterproof it. Being a nature lover sure comes in handy, and the surprise attack gave the imperial soldiers on watch a spooking.
The in-universe explanation for how the Vault Assisted Targetting System (V.A.T.S.) operates in Fallout 3. It creates a real-time tactical overlay that scans the threat, assesses various weak points and comes up with the statistical probability of whether the operator will successfully land any hits.
In Fallout: New Vegas, the appropriately named "Math Wrath" perk improves the efficiency of V.A.T.S. if the player's Science skill is high enough.
In the third Ryu Ga Gotoku (or Yakuza) game, Kazuma can get inspiration for new combat maneuvers by watching other people perform out of the ordinary stunts (i.e. a middle-aged woman flipping on her motor scooter as the basis for a jumping attack, or a girl fending off a drunken pervert to learn how to counter grappling moves).
This is part of Dark Chronicle's Invention process. Max, a First Person Snapshooter, can take pictures of ordinary (and not-so-ordinary) items, which give him ideas for creating new inventions. Some of them are easily missable, so you have to work quickly and think fast in order to get them all.
The Copy power (power, not ability) from Kirby Super Star. Once Kirby has this ability, he obtains an optical scanner that analyzes an opponent (complete with computer readouts and targeting reticule shown onscreen, no less) and replaces Copy with whatever ability the opponent has.
If the enemy you try this on has no copy-able ability you analyze them dead.
Minor original character Fracture from the second DC Universe Online trailer has this as a power. It briefly shows his vision, analyzing statistics, probability, and structural weak points to overcome a Brainiac drone in single combat. Apparently, it only works on threats he's aware of, since purported ally Luthor stabs him in the back moments later
If you choose the Dark Side Path in Knights of the Old Republic II, observe your character fight Jedi Masters in a one-on-one battle to the death and learn to perfectly copy the enemy's Lightsaber Fighting Style while taunting them and stomping them into the ground afterwards. Probably with their own moves.
The Pokémon ability Analytic can give any Pokemon this, giving it a boost to its attack power if it attacks last.
Similarly, the abilities Download (ups a stat based on opponent's defenses), Anticipation (shudders depending on the power of its foe's attacks), Trace (copies the foe's ability), Rivalry (raises Attack if the foe is of the same gender), and Imposter (transforms into an opponent in front) all involve reacting to the opponent in some way. And there is apparently very little involved. Telepathy takes this and applies it to ally Pokemon in Doubles. An inversion exists in Unaware which COMPLETELY IGNORES the foe's stat changes.
And finally, there are several moves that are used by analyzing the opponent. Detect requires the user to avoid the opponent completely by knowing what move they'll use next. Role Play allows you to copy the foe's ability just by pretending to be them. Mind Reader is said to do Exactly What It Says on the Tin. Predicting your opponent's moves is also a given for anyone wishing to compete in the higher levels of the metagame.
Emerl from the game Sonic Battle is a good example of this. He gains ALL powers of an opponent simply by watching them fight or being beaten up by them.
In the final battle, Emerl takes all of Sonic's abilities, powers them up to the point where some of them instantly KO you, and becomes a star killing machine by seeing Eggman's battle ship in action.
In Fire Emblem: The Sacred Stones, the Dancer Tethys is extremely perfecptive and good at catching details (Though this doesn't show in-story since she's a non-combatant.) In example, as a teenager she learned how to dance solely via mentally replaying a famous dancer's moves and practising them from memory. She also deduces that her friend Marisa only pretends to be a southpaw, when in reality she isn't; Marisa is very surprised, meaning that no one else had managed to see through her.
Somewhat surprisingly, Archer fits this trope. This is mostly surprising because he's Shirou's future self. While his physical strength and reflexes aren't much when compared to the other Servants, Archer is able to use his battle experience and cunning to come up strategies to counter and even overpower his more capable opponents and their strategies. The game calls this ability "Mind's Eye (True)":
"Capable of calm analysis of battle conditions even when in danger and deduce an appropriate course of action after considering all possibilities to escape from a predicament. So long there is even a 1% chance of a comeback, this ability greatly improves the chances of winning."
There's also another version of the skill dubbed "Mind's Eye (False)". While it confers similar abilities as the (True) version, it belongs to Servants who don't have battle experience or can't remember it. Two Servants in particular have this skill: Berserker (whose madness keeps him from remembering his experience in life) and Assassin (who as a fictional hero, never had the chance to earn experience in life).
In the Heaven's Feel route, Shirou mimics this skill, and uses it to defeat Dark Berserker in three seconds.
Both Archer and Shirou also apply this. They subconsciously scan any weapon when they see it, and analyse it down to its creation, its history, its previous usage and the wielder's skill. This allows for recreation of the weapon, complete with all that previous information, rendering the projection dozens of times better than any other magic-user can manage.
Not exactly as Analyzing as the previous examples, but Shirou in the beginning managed to survive multiple deathblows by Lancer this way. One example being choosing to swing his weapon back just after jumping out of the window to block one, even though he's moreorless guessing that Lancer would attack him right after, and a misjudgment in timing would result in death.
Also from the Nasuverse is Sion Atlasia, and the rest of the Atlas alchemists. Their particular brand of magic involves consciously partitioning their brains to increase "processing" ability, essentially turning each of them into human supercomputers. Sion usually fights by simulating her opponent's attack strategies and predicting every move they make before they make it.
Yume Miru Kusuri: During the climax of Aeka's route, Kouhei finds himself pinned down by two armed assailants, whilst Gaito attempts to rape Aeka. In a matter of seconds, Kouhei manages to analyze the situation, throw off his assailants and take a hostage to rescue Aeka.
Guthrie Carroll of Fans! once programmed a spaceship the size of a 2' cube to engage in evasive atmospheric entry, dodging all enemy fire on the way down, then taunted an otherwise invulnerable foe to walk directly under it just as it slammed into the earth (all while being just outside the blast radius).
This is Klaus's specialty in Girl Genius: he's not specifically capable of duplicating physical feats, but he's very very good at examining other Sparks' inventions and improving them. This also apparently extends to neurology, as his current goal is to find out what causes Mad Science behavior in Sparks to begin with...
It's implied that while all Sparks have specialties, Klaus's specialty is the Spark itself.
Tarvek Sturmvoraus is a more minor example. While he didn't necessarily improve on the design until he built the second head, the fact that he was able to reverse-engineer one of the Van Rijn muses without completely destroying the original is impressive, considering that Master Payne (who knows more about the Muses than most) made it clear that even master Sparks had tried and failed to discover any of the Muses' special capabilities, and most of the Muses had been lost in the process.
Later on when he's accidentally captured by Klaus's forces and being led to the dungeons, he happens to briefly glance at an abstract operations table and informs his captors that a unit had been subverted and was about to cripple the entire army. They're so impressed they allow him to keep coordinating the army (under heavy surveillance).
Diamonds Droog from the Intermission section of Homestuck.
And then he aims for the bullet holes in the walls that are already there due to time traveling shenanigans.
In Kevin & Kell, Danielle Kindle saw George Fennec knocked high and far into the air. After a glance, she calculated his trajectory in her head and got into the exact catching position well ahead of time. Because she's Good with Numbers.
Another Gaming Comic: Subverted when Joe tries to play Poker. He claims to have used his math skills to completely analyze the entire game minutes after first seeing the rules, but he still ends up taking last place.
Tech Infantry has Icarus Hicks, the smartest man in the galaxy, who despite being a middle-aged medical researcher with little military training (and that as The Medic), manages to hold his own against Space Marines in Powered Armor by combining the fine dexterity he developed as a surgeon with analysis of the weaknesses of their Powered Armor suits to think up a way to shut them down.
In the Global Guardians PBEM Universe, most super-intelligent individuals had this ability, making them much more dangerous than their otherwise (usually) geeky exteriors would suggest. Doctor Simian, an evil, hyper-intelligent chimpanzee generally considered one of the two smartest beings on earth, is notable for combining Awesomeness by Analysis and the ability to generate new technology almost at will in weapons tailored to take advantage of a hero's weaknesses.
In the Whateley Universe canon, Chaka has the ability to see how Ki Attacks work simply by watching them, and can immediately duplicate them on her own. Similarly, a character named Loophole can determine the trajectory of bullets, bodies, and the like... and 'jump into' anything mechanical or electronic to commune with it, understanding how it works in a matter of moments. Contrast this with Caitlin Bardue, who can understand any magical object/device without knowing how it works.
In The Gamer, the main character gains powers that turn his life into an RPG Mechanics Verse. He can see very one's levels and basic status. While it at first seems to be a lame power, he and everyone around him quickly learn that he can potentially become ungodly powerful in a short amount of time by exploiting the mechanics. He quickly figures out how to exploit grinding, and can even master powerful magic abilities by "reading" books that describe them. We mean that in the Skyrim sense, in that he need only select "read" from the menu that pops up. The book will then vanish and he'll suddenly be able to skillfully make use of the technique. One of the earliest techniques he unlocks is observation, which lets him see the strengths and weaknesses and the very detailed stats of his enemies in combat.
This is what Ranger is known as in Comic Fury Werewolf. He analyzes everyone's actions down to the last detail, trying to figure out the culprit. In his first game, he even went so far back as to read the first five games in-depth to figure out everyone's play styles.
He only stopped because it became incredibly time-consuming to do it, as the first time he accomplished the feat was an all-nighter effort on his part. With the addition of the later games to add into the mix...
In the superhero story Worm, the character of Lisa a.k.a. Tattletale has this as a superpower. When analyzing someone or something, she needs to have some information about the target to begin with, and her power fills in the gaps in her knowledge, allowing her to crack computer passwords, profile people around her, and make predictions about the most likely outcome of a given situation, among other things. She's very accurate, although not infallible. In the few instances where she makes mistakes, she messes up pretty big. Also, she can become mentally overloaded if she tries to take in and analyze too much information all at once.
A few times she goes up against someone else with similar talents (If not a power based on them) and has a truely awesomeinterrogation exchange with Cherish in which she responds to having chunks of her past outed by calmly reading her opponent for every single piece of information Cherish intended for use as leverage.
In Lovelace One Two, Andi, the protagonist and recent recipient of some kind of Super Intelligence power, does a number of these (e.g. teaching herself the guitar by ear in minutes).
Despite being by far the most feeble of the trio, Edd of Ed, Edd n Eddy can often perform amazing feats with just a few calculations and some Bamboo Technology.
Ed in The Movie when he defeats Eddy's Brother when he sees that when he's pulling Eddy, who clinging onto a door, Ed simply unhinges the bolts on the door to turn Eddy into a one-man slingshot and have the door slam him in the head and knock him out.
In Batman: The Animated Series, the villain The Clock King (who's a middle-aged civil servant) is able to go hand to hand with Batman simply from having studied Batman's tendencies in a fight. As a matter of fact, this is one of Batman himself's methods; he does this often when caught by surprise, allowing him to defeat his enemy or, should the situation become too great (it happens, but rarely), retreat to fight another day.
In an episode of Justice League, the nanotechnological android based on the comic character Amazo takes this ability to its logical exreme—being able to analyze things on the molecular level while being able to at the same time alter its own structure at the molecular level. In short, you are so screwed.
So screwed, in fact, that even a nanotech solution doesn't defeat him.
Justice League also subverts the trope in the person of The Question. A brilliant reinvention of the older DC hero, Vic Sage is genuinely strange. While sane, he honestly connects things that are completely unrelated, tending to sound like a total conspiracy nut. However, his actual reasoning works rather well when he tracks down actual connections, to the point he is reluctantly given credit for it by the rest of the League. Yes, by Batman as well.
Iroh figuring out how to redirect lightning with Waterbending principles applied to Firebending.
There was a bit character in Looney Tunes called Egghead, Jr. that Foghorn Leghorn would occasionally be saddled with. A mute chicken lad with a spherical head, beady eyes, and huge glasses, he would quickly jot down some very technical-looking mumbo-jumbo and succeed at whatever he was attempting at the time... like throwing a 90 MPH fastball or winning a game of croquet with one swing.
When playing hide and seek, Foghorn took a circuitous route and ended up in a dumpster, claiming "He'll have to use a slide rule to find me". Cut to Egghead using a slide rule. Humorously subverted in that he then turns around and digs a small hole, pulling Foghorn out of it. Foghorn is understandably confused and goes back to the dumpster, but decides against opening it. "I just MIGHT be in there!"
Tom of Tom and Jerry would occasionally attempt the same stunt, except that either interference from Jerry, or just plain old malignancy and Sod's Law, would cause it to turn on him whatever he intended it do to Jerry.
In the Action Man computer animated series, Mann was given the ability to calculate vectors and trajectories in a fraction of a second by his trainer. It turns into Cursed with Awesome when his ability turns him into the MacGuffin.
It's a little beyond vectors and trajectories. His brain runs a ridiculously complicated mathematical equation that sums up the world, and calculates it in such a way that he can predict the future in ways beyond just physics. Once he develops his "gift" it gets to the point where he starts to have brief flashes of future events completely at random. So he's essentially psychic. With MATH! (Stay in school, kids)
On Jimmy Two-Shoes, Heloise manages to ace skeet shooting thanks to this. After Beezy becomes smart, he repeats this process on a much grander scale.
Po from Kung Fu Panda is able to learn advanced martial-arts techniques by seeing them performed once and just a small amount of practice.
Taken Up to Eleven in the sequel, where he learns a seemingly-impossible technique that took Master Shifu years to master and uses it to defeat the Big Bad. Apparently, all he needed to do was calm down (which is, actually, pretty difficult for him).
Toddlers and young children are like this by default. This is what helps them learn how to learn. Disabilities like Down's Syndrome result in the child lacking this ability.
Visual learners, who learn things through watching techniques and looking at images, as opposed to kinesthetic learners and auditory learners.
From the reality show Survivor, contestant Yau-Man Chan, despite being a small man in his 50s, was able to excel in many of the physical reward challenges because he calculated things like arrow trajectories. Early in the game, he opened a supply crate that several younger men couldn't open—lift the crate over a rock, drop the crate corner first, and let gravity crack a weak spot.
According to this Sports Illustrated article, Raymond Berry pulled off some truly amazing stunts in American Football through sheer power of preparation and training. Unfortunately, he managed to not get his 1985 New England Patriots a Super Bowl ring in rather humiliating fashion...
When working on the swashbuckler parody The Court Jester, Danny Kaye was trained in fencing by co-star and skilled fencer Basil Rathbone. Thanks to his coordination, which aided him in physical comedy, Kaye was able to become as competent at doing the fencing routine as Rathbone with about a month's practice.
In real life, fencing has been described as "high speed chess", so fencing itself would fit this trope.
One of the contestants (Hironori Kuboki, Ninja Warrior 7) at Ninja Warrior failed in his first run at the Warped Wall obstacle. Defeated but not conquered, he took measurements and ran the trigonometry of the wall through its mathematical paces. Next year, he beat the wall, with math!
The astronomer Neil deGrasse Tyson tells a story in his autobiography about how, one time, he was on a bus going along the single narrow road connecting two towns on the coast of Italy. The road was blocked by a carelessly parked car whose owner was nowhere around. The bus came to a stop and everyone got out and wondered how they were going to get to their destination. Tyson realized he could move the car: he knew that the rear end of a car is much lighter than the front, and from experience wrestling, knew how to lift things using your leg muscles. He lifted up the rear bumper, rotated the car around its front tires, and pivoted it off the road. It looked really impressive but the secret wasn't abnormal strength so much as figuring out the right way to go about it.
Frederick Lindemann, 1st Viscount Cherwell, was Winston Churchill's numbers man during World War II; as Churchill was as backwards in math as he excelled at English, the Prof's charts and figures on every aspect of supplies, munitions and manpower cannot be underestimated. But the Prof's trueCrowning Moment of Awesome came when he studied aircraft tail spins. At a time when no one had survived one, Lindemann figured out a technique by doing the math, then took flying lessons for his solo license, took a plane up, then put it in a tail spin before recovering control with his technique, which is taught to this day.
Science. Through systematic investigation of the nature of the universe, this enterprise has made possible achievements which would be unimaginable in earlier ages, from the miracles of modern medicine to space exploration to TV Tropes.
Mostly averted in Real Life, because if you think too much about something you become unable to do it properly. Also, to use Physics (or at least Mechanics) to work out trajectories, and pointing things in exactly the right direction is damned hard, and all Physical equations are approximations anyway, or they would be far too complicated. To be fair, many of those approximations are very, very good. The point remains that measuring and calibrating everything involved by hand usually takes longer than you have.
If the other guy has rigged a computer to do his number crunching on the fly for him though, try not to get on his bad side.
It's also worth noting that if actually practiced, you're able to get over the Dilemma pretty quickly. Intentionally invoke it enough and you're able to use both parts of your brain.
There's also the whole issue with that mathematical calculation is only useful to the degree of precision of one's coordination, which is a large part of what practice develops in physical activities.
Another way to consider it is that this is what everyone who is any good at things does all the time. Practice doesn't lead one to have better intuition, whatever that is: it burns the math into one's unconscious so that the result is "just obvious", in the same way that nobody needs to do complex numeric calculations to coordinate the intricate computational nightmare that is their arms and legs. Having to do the math consciously is arguably being too slow.
Engineers of all fields tend to work this way, including the military variety, whose cold calculations are often the basis of various sadistic devices such as shells that split apart into a myriad submunitions to make sure that it is difficult to miss, biological agents which decimate entire populations indiscriminately, and incendiaries that burn flesh off bone, whether the target is dead or otherwise. Engineers tend to develop their new pieces of equipment over a period of years rather than on the spot calculations...
Similar to engineers, artillerymen, who use propellant and trigonometry to drop heavy explosive shells on targets miles away, often using information relayed to them by forward observers. It is worth noting that the word "Engineer" comes from the guys who operated siege engines such as Trebuchets and Catapults. It took the geeks of the day to figure out how to build a device to lob a cow at an enemy city.
Sniping tends to work this way. It's often described as 90% mathematics and 10% actual shooting. The snipers' spotters also have to be equally proficient, and carry calculation sheets with them as part of standard kit.
And one knows it is involved when one has to take the rotation of the earth into account along with one's own heart beat.
And slight precession from the spinning of the bullet. Snipers also often shoot from elevated positions which means that bullet drop becomes a much more complex and counter intuitive calculation.
Temperature, humidity, wind direction, lead time...it's not just the physicality that makes sniper training some of the toughest in the military.
Similar to snipers, many aircrew positions, including pilots, gunners, and loadmasters, require substantial skill and practice in math. The pilot has to be able to calculate wind drift, fuel consumption, and a myriad other factors to effectively fly his plane to the destination. The gunner has to be able to quickly do the mental math to have any hope to hit a fast moving enemy fighter from a fast-moving gunnery platform (aerial gunners in WWII were trained in skeet shooting as a primer), and loadmasters have to figure out how much weight can be loaded in which part of the plane along with fuel and passengers. Even a relatively small amount of weight loaded too far off the center of lift can cause a plane to become unflyable.
In World War II the US Army Air Forces established an Office of Statistical Control that studied the effect of aerial bombing missions and how to make them more efficient in weakening the adversary. Part of this effort included a study that indicated that using the B-29 strategic bomber in low level incendiary attacks would prove much more effective than bombing from high altitude for which it had been designed. General Curtis LeMay agreed and in the final 7 months of the war the change in tactics devastated the better part of 67 Japanese cities, killing as many as 500,000 and rendering some 5 million more homeless.
Another example from WWII was the analysis the RAF performed on aircraft returning from combat. They studied the battle damage sustained by their aircraft, made a graph of the various parts of the aircraft, and resolved to reinforce the areas that seemed be shot up the most. Then one bright fellow said they had it completely backwards. Since those areas were found the most on returning aircraft, it was deduced that they were actually the least critical. Areas that needed reinforcement were actually the areas that were lowest on the graph, as the aircraft receiving damage there did not make it home. This was followed and survivability increased.
Averted by many would-be (and some professional) game designers. Though one can beat a game with math, making a game fun purely on the math is generally unsuccessful.
Michael Larson, an ice-cream truck driver who won $110,237 on Press Your Luck, by analyzing and memorizing all the patterns and safe points, due to the computer not being truly random.
Similarly, an engineer named Joseph Jaggers in 1873 discovered a roulette wheel in Monte Carlo that was slightly unbalanced, causing some numbers to come up more often. It netted him a few hundred thousand dollars.
Richard Feynman told a story of his father reading a book on swimming, and then going in to the water and swimming successfully for the first time in his life. This was intended to demonstrate the power of book learning for his children. It worked.
In 1994, Canadian computer programmer Daniel Corriveau analysed the Keno drawn numbers of the Montreal Casino and found buried in the seemingly random results a pattern that allowed him to win 620,000$ with a single bet. After a few weeks of inquiry, the casino admitted he had beaten the system fair and square. They gave him a cheque for his winnings and hired him to fix the problem so no one else could pull off what he had just done.
Oakland Athletics general manager Billy Beane, according to the film and the book Moneyball, considered the usual methods of statistical analysis in baseball to be subjective, unreliable, and relics of a 19th century view, preferring to get use on-base percentage and slugging percentage, which are cheaper on the open market than the traditional indicators. How successful was it? "Moneyball" is now a slang term in baseball, and Beane is depicted in the movie by Brad Pitt.
The crew of HMS Venturer during WWII - Venturer is the only submarine ever to sink another submarine while both boats were submerged. Not so impressive in modern subs, which are designed to do this, and the only reason it hasn't happened again is because (thank God) a major war hasn't broken out yet. But in a WWII sub, having calculated (i.e, with paper and pencils) a firing solution in three dimensions, a feat previously thought impossible in combat conditions? Awesome.
This seems to be a very common ability amongst professional gamers. They become so adept at analysing all of the information that they see that they will predict exactly when and where an enemy will attack. Their sense of what the enemy is doing without any direct information can be pretty astonishing to casual players.
In something of a subversion, inexperienced players are usually more random and thus harder to predict. Depending on the game, this can be something of a problem for more experienced gamers.
In the field of poker, many of the top players can often tell what kind of hand an opponent has by analyzing their betting patterns. Thus, some can tell you what your hand is to the rank (sometimes even to the suit!) without you even giving them a classic tell.
According to most (including the man himself) this is what made Wayne Gretzky so great, despite having admittedly subpar (for an elite level player) physical gifts: he could figure out where the puck was heading on the fly, allowing him be in optimum position for shots on goal (and helping him avoid incoming defenders looking to clobber him).
Cracked did an article on how to win game shows that boils to this exactly this trope. Turned out that even beating Jeopardy! - allegedly a game completely based around knowing "obscure" trivia - is not a matter of memorizing every trivial fact ever, but rather, to know which parts of general knowledge trivia you are weak in... and do a bit of really casual reading on just those areas. The man who figured this out, Roger Craig, did so by feeding hundreds of hours' worth of Jeopardy! questions into a computer to put together statistics on the kind of questions you're likely to get asked, and then had it spit it out as a graph. Then he proved his theory was right by using said graph to study and subsequently win the game. Twice. Including beating the one-day record and then winning a quarter million dollars in the Tournament of Champions.
This partly how the US beat the feared Japanese Zero fighter. This happened when the US military found a nearly intact abandoned Zero fighter in the Aleutians, which was called the Akutan Zero. The US military analyzed every detail about the fighter class to discover its weaknesses and develop better tactics to take best advantage of them.