History Main / ArtisticLicenseStatistics

* '''Projecting From a Small Sample Size''': Even a fair coin has a significant probability of coming up heads seven times in ten flips, so you can't project from such a trial that the coin has a 70% probability of coming up heads. Although there is no real "minimum sample size" to speak of, most accept the arbitrary magic number of anywhere between 20-50 (most notably 30). Obvious a higher sample size will grant better results, even though it might not be cost effective. In academia this isn't a problem as long as the sample size is shown, so the readers can decide for themselves whether the sample size is good enough. But your everyday layman will not notice this detail, and thus are prone to erroneous conclusion from scientific statistical research.

* '''[[GamblersFallacy The Gambler's fallacy]]''': All probabilities should somehow "even out" while you're playing. For example, if the computer has a hit chance of 50%, and hits, that's okay. However, if it then scores another hit right away, TheComputerIsACheatingBastard. In truth, it just happened to be the way the "dice" fell. As is often stated, "dice have no memory." In situations where extreme good/bad luck streaks are undesirable, the Gambler fallacy can be invoked, chiefly in the form of pseudo-random distribution (or PRD). Under PRD, consistent misses will slowly increase the chance of a hit, and vice versa. Many video games uses this variant of "random" without being noticed, because "pseudo-random" feels more random than real random. Note that there's a nugget of truth in the idea that odds should even out eventually, the operative word here being '''eventually'''; this is known as the Central Limit Theorem.

** Similarily, German card game ''Skat'' has rules in place, that if one player in a tournament has to use a shuffling machine (e.g. due to a disability), everybody has to, because hand shuffled decks are less random and favor the player after the dealer compared to the better randomization of a machine.

** That might not have helped. People are ''horrible'' at generating random numbers, so even if she picked equal (or near-equal) numbers of black and white cards, a more sophisticated analysis of her picks would reveal what she was doing, most likely by identifying a lack of runs of a single color (see fallacy #2 above). It might ''delay'' the recognition of her ability, though...and unless it were ''blatantly'' obvious what she was doing, it might leave enough doubt to prevent others from being certain.
** The ''best'' way for her to deceive the examiner would be to not even bother to ''use'' her ability during the session, but merely pretend to concentrate while drawing the cards blindly.

* The {{Series/Mythbusters}} have tackled several things that touched on statistical misconceptions, but probably their most direct assault on this trope was the "[[https://en.wikipedia.org/wiki/Monty_Hall_problem Monty Hall problem]]". In a nutshell, this is when you choose one of three doors that may hold a prize. The host (who knows the truth) opens a ''different'' door, showing no prize, and asks you to keep your original choice or choose the remaining door. The hasty assumption is that this second choice is 50-50, and people will tend to stay with their first door, but the reality is that changing your choice has twice the probability of success. The Mythbusters demonstrated that much experimentally, with one hundred trials (fifty each way). When they tested the other half of the myth, the psychology of it, twenty out of twenty of their test subjects stayed with their original choice, many claiming that it was because of the supposed 50% chance.
* In OnlyFoolsAndHorses, Boycie refused to bet on a coin toss against Del because, having beaten Del in the previous few tosses, the "Laws of averages" dictated that he would likely lose this one. When Del suggested that Boycie challenged Rodney instead, he agreed!

* The Creator/FoxNewsChannel's fondness for flashy graphics to engage the viewer's attention occasionally lends itself to a few mistakes. Such as [[http://pics.blameitonthevoices.com/112009/fox_news_math_fail.jpg a pie chart where the total breakdowns add up to 193%]], or [[http://www.mathfail.com/scientists-poll.jpg this poll with a breakdown that adds up to 120%]]. Either with the pressure of the rush to get on-screen information ready by showtime, those responsible have little time to double-check their work; or they care more about making a quick impression on the viewer than ensuring accurate information.[[note]]If the people polled can pick more than one option, poll results can easily add up to more than 100%. The first poll might be such a case, but a pie chart is a poor choice for showing that kind of data. The second poll suggests someone was stupid, whether the people who made the graphic, the people who calculated the numbers, or the people who voted for more than one mutually exclusive option.[[/note]]

* Players themselves sometimes fall afoul of the gambler's fallacy.

* In a strange twist, ''Final Fantasy VII: Crisis Core'' had the DMW, a slot-machine of various character faces that spins during combat, creating different effects. The only way to level-up is for three "7"s to align. Isn't that awful?!? Leveling based on total randomness?!? Except...it isn't. The manual ''lies''. The DMW is actually controlled by an ''insanely complicated'' mathematical formula that, in-game, manifests itself as the strange impression that chance always ''just so happens'' to work out exactly the way natural progression should. In essence, one in a million chances succeed nine times out of ten. Furthermore, while it's not shown anywhere in the game, enemies actually do give experience when killed, increasing the odds of hitting the combination that gives Zack a level up. As can be expected, this means that getting 2 or more level-ups in a row or shortly one after another can only happen if you've been under the effects of Curse status which disables DMW for an extended perioid of time and killed a ton of enemies during that time and if you kill enough enemies, you're eventuallly guaranteed to get the combination that gives you a level up.

## To be guaranteed a win, you'd need an infinite amount of money and time. If you had infinite money, you wouldn't need to bet. :)

* '''Decision-Making and Probability''': When a reasonable decision was made according to the odds, where the odds are calculatable, a measured risk is always taken. If this somehow backfired, calling this a ''wrong'' decision is fallacious because that would imply clairvoyance is presumed; Conversely, when all data and signs are ignored, thus a silly decision was made. Even if that worked out in the end that doesn't make the decision any less ill, as that's just literal dumb luck. For example, if two gamblers agree to roll a fair die, betting 1:1 where Gambler A wins on a 1, and Gambler B wins on a everything else, Gambler A is making an irrational decision to bet -- the outcome of the dice roll has no bearing on said irrationality. ''If it's stupid and it works, it's still stupid and you're lucky''

* '''[[GamblersFallacy The Gambler's fallacy]]''': All probabilities should somehow "even out" while you're playing. For example, if the computer has a hit chance of 50%, and hits, that's okay. However, if it then scores another hit right away, TheComputerIsACheatingBastard. In truth, it just happened to be the way the "dice" fell. As is often stated, "dice have no memory." In situations where extreme good/bad luck streaks are undesirable, the Gambler fallacy can be invoked, chiefly in the form of pseudo-random distribution (or PRD). Under PRD, consistent misses will slowly increase the chance of a hit, and vice versa. Many video games uses this variant of "random" without being noticed, because, "pseudo-random" feels more random than real random. Note that there's a nugget of truth in the idea that odds should even out eventually, the operative word here being '''eventually''', this is known as the Central Limit Theorem.

** Ask anyone who's played ''VideoGame/{{Civilization}} IV'' (''especially'' those who play mods like ''VideoGame/FallFromHeaven'') and they will tell you that any combat with less than 80% odds is suicidal and should be avoided at all costs [[note]]though this isn't purely for the chance weighting, as it affects how much your unit gets damaged; combined with the AI favoring large stacks of weak units, this means your unit will likely die next turn[[/note]], unless the odds are 1% or worse, in which case victory is surprisingly possible (see Spearman v. Tank).

** This is really a matter of game theory, not statistics. In general, you can't afford a policy of entering battles with an 80% chance of winning, because the cost to the player of losing each battle is so much greater than the benefit of winning.

* [[http://jalopnik.com/hey-idiots-stop-saying-americans-won-t-buy-diesel-manu-1563050028 This]] Jalopnik article advocates bringing more diesels to the US market by showing how big of the VW Jetta sales chunk is diesels. This means next to nothing, since most Jetta buyers buy them for the TDI engine.

* ''WorldEndEconomica'' has the protagonist, who is a little full of himself, apply the Gambler's Fallacy to trading on the stock market.

* The Creator/FoxNewsChannel's fondness for flashy graphics to engage the viewer's attention occasionally lends itself to a few mistakes. Such as [[http://pics.blameitonthevoices.com/112009/fox_news_math_fail.jpg a pie chart where the total breakdowns add up to 193%]], or [[http://www.mathfail.com/scientists-poll.jpg this poll with a breakdown that adds up to 120%]]. Either with the pressure of the rush to get on-screen information ready by showtime, those responsible have little time to double-check their work; or [[TheyJustDidntCare they care more about making a quick impression on the viewer than ensuring accurate information]].[[note]]If the people polled can pick more than one option, poll results can easily add up to more than 100%. The first poll might be such a case, but a pie chart is a poor choice for showing that kind of data. The second poll suggests someone was stupid, whether the people who made the graphic, the people who calculated the numbers, or the people who voted for more than one mutually exclusive option.[[/note]]

* ''[[{{VideoGame/XCOM}} X-COM]]:

* ''VideoGame/XCom'':
** ''{{X-COM}}'''s accuracy reports during combat aren't exactly blatant lies, but they're not exactly accurate, either. What ''X-COM'' does for a hit check is up to two rolls. The first is done against the accuracy check, and if it passes, you automatically get a dead-on shot. The other roll, if the first fails, is the deviation from where you're aiming, which may also end up being nil, resulting in a dead-on shot. So that 75% Accuracy the game reports? More like 77% to hit the target you're aiming at, and up to around 20% to hit someone else, resulting in somewhere around a 86% (on average) chance of someone getting hit by any given shot in a heated battle. Oh, and 100% accuracy reportedly doesn't exist.

* DaveBarry once joked that he always flew on the airline with the most recent crash, on the assumption that it wouldn't be "due" for another one.[[note]]This could have some validity if you assume that the airline with the most recent crash would be under the most scrutiny and thus have the most reason to tighten up their safety standards, but it's not valid for the reason he (jokingly) gives.[[/note]]
* MarkTwain's ''Life on the Mississippi'' contained the following proof of what you can do with statistics:

* '''[[GamblersFallacy The Gambler's fallacy]]''': All probabilities should somehow "even out" while you're playing. For example, if the computer has a hit chance of 50%, and hits, that's okay. However, if it then scores another hit right away, TheComputerIsACheatingBastard. In truth, it just happened to be the way the "dice" fell. As is often stated, "dice have no memory." In situations where extreme good/bad luck streaks are undesirable, the Gambler fallacy can be invoked, chiefly in the form of pseudo-random distribution (or PRD). Under PRD, consistent misses will slowly increase the chance of a hit, and vice versa. Many video games uses this variant of "random" without being noticed, because, "pseudo-random" feels more random than real random.

* There is an optional "Event Deck" for the board game ''TabletopGame/SettlersOfCatan''. Using it instead of the dice makes probabilities "even out" somewhat (going through most of the deck before reshuffling guarantees that each number will come up about as often as it "should").

* Discussed and defied in one ending of ''VideoGame/StoriesThePathOfDestinies''. After discovering that the [[DismantledMacguffin completed]] [[LostSuperweapon Skyripper]] could potentially [[spoiler: [[TheEndOfTheWorldAsWeKnowIt destroy the universe]]]] if fired, he discusses the matter further with the sage Calaveras, who narrows it down to a 1 in 128 chance. Reynardo decides this is no big deal; when confronting [[DatingCatwoman Zenobia]], he even explains the 1 in 128 chance in terms of the Gambler's Fallacy (i.e. that the risk will increase the more he fires the weapon, but the first shot should be perfectly safe), which an exasperated Zenobia points out is ''not'' how odds work at all. Needless to say, he fires it, and [[spoiler: it destroys the universe.]]

* '''Naïve Combination of Probabilities''': Given the probabilities of two events, people will often simply either add them or multiply them. Generally speaking, calculating the combined probability is much more complicated. For example, suppose you roll a die twice. The probability of a six is 1/6 each time, so the probability of at least one six in two rolls must be 1/3, right?[[note]]It's actually 11/36, or about 31%. This is because of all the 36 possible options (1-1, 1-2, 1-3 etc...) Only 11 contain the number 6. These are (1-6,2-6,3-6,4-6,5-6, their inverses and 6-6 which only counts once and not twoce, which is why the odds aren't 1/3 but instead 11/36. [[/note]]

* '''Naïve Combination of Probabilities''': Given the probabilities of two events, people will often simply either add them or multiply them. Generally speaking, calculating the combined probability is much more complicated. For example, suppose you roll a die twice. The probability of a six is 1/6 each time, so the probability of at least one six in two rolls must be 1/3, right?[[note]]It's actually 11/36, or about 31%.[[/note]]