History Main / ArtisticLicenseStatistics

[[folder:Music]]
* This is how synchronization (most notoriously of ''Film/TheWizardOfOz'' with ''[[Music/PinkFloyd Dark Side of the Moon]]'') "works"; the brain notices the few dozen coincidences and goes "oh wow" at them, whilst ignoring the thousands of non-coincidences which surround them.
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* ''TabletopGame/WorldOfSynnibarr'' also does this.

* All ''VideoGame/FireEmblem'' games after the fifth display inaccurate hit/miss percentages. The game actually uses the average of two random numbers to determine a hit, so a 75% chance to hit is really 87.5%. This system is likely in place to make [[FragileSpeedster dodging-type]] units evade more (and thus more viable) and high-accuracy characters strike more and lessens the chance that such a character dies ([[AntiFrustrationFeatures Due to permanent death and limited saving, this means restarting the entire level in most games]]) against all 3 of the random mooks that has a 2% chance to hit each.

** ''VideoGame/XCOMEnemyUnknown'' ditches this in favor of telling player straight how likely he is to hit. However, many players insist that the game cheats in favor of aliens on higher difficulties and Classic mode. This eventually got so bad, that the [[http://www.schwanenlied.me/yawning/XCOM/XCOMPRNG.html RNG was taken apart for testing]] by the community... and found to be 100% correct. As it turns out, on the lower difficulties, the computer actually cheat for the ''player''. Thus, once the aid is removed on the higher difficulties, players feel cheated when their "sure" shots no longer hit all the time.

* ''TabletopGame/DungeonsAndDragons'' players often work under the rule of thumb that a character intelligence (INT) is equal to IQ/10. While this works well enough for the most part (the average human int is 10 and the average human IQ is 100, where as the highest IQ a [[BadassNormal real person]] can have seems to be around 210, and 20-20 is about the highest INT a human can have without magic or the like), the whole deal is a pretty big oversimplicifaction as, to name just one problem, there's more than one kind of IQ test while the INT score assumes there is some objective, universally agreed upon way to measure intelligence.)

[[folder:Films -- Live-Action]]
* ''Film/BowlingForColumbine'': Moore exaggerates the level of gun violence in the United States through spurious use of statistics, specifically comparing the amount of gun-related deaths in several western countries by citing gross figures for each country and not per capita stats. Even aside from that, the numbers he cites didn't match any known independent studies. Eventually, it was revealed that he took US Government crime statistics for gun homicides, and added uses of guns for self-defense and the use of guns by police.
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* One book on recreational mathematics described "the college bet", so-called because its inventor supposedly made enough money from it to put his son through college. If you select three card ranks randomly, and then draw a card from a fair 52-card deck, the chance that it will be one of your ranks is 3 in 13, right? Thus (the book claimed) if you draw three cards, the chance of at least one being one of your ranks is 9/13 (0.6923), and with four cards this rises to 12/13 (0.9231). If the author of the book had followed this "logic" a bit further, he would have seen that this gives the chance of one in five cards being one of yours as 15/13, or more than certain -- which is clearly nonsense. (In truth, if each card draw is independent of the others (that is, the card is replaced and the deck shuffled after each draw), the three-card probability is 47/85 (0.5529 -- substantially worse than the naïve calculation), the four-card probability is 2759/4165 (0.6624), and the five-card probability is 6221/8330 (0.7468); if the draws are with replacement the probabilities are 0.5448, 0.6499 and 0.7307 respectively.)

* One book on recreational mathematics described "the college bet", so-called because its inventor supposedly made enough money from it to put his son through college. If you select three card ranks randomly, and then draw a card from a fair 52-card deck, the chance that it will be one of your ranks is 3 in 13, right? Thus (the book claimed) if you draw three cards, the chance of at least one being one of your ranks is 9/13 (0.6923), and with four cards this rises to 12/13 (0.9231). If the author of the book had followed this "logic" a bit further, he would have seen that this gives the chance of one in five cards being one of yours as 15/13, or more than certain -- which is clearly nonsense. (In truth, if each card draw is independent of the others (that is, the card is replaced and the deck shuffled after each draw), the three-card probability is 2170/2197 (0.9877 -- substantially better than the naïve calculation), the four-card probability is 28480/28561 (0.9972), and the five-card probability is 371050/371293 (0.9993).)

*** Similarly, the "absolute guarantee" of the Master Ball catching a wild Pokémon is not; there is an incredibly small chance it will fail when used, but luckily hasn't happened yet.

* ''Discworld/TheScienceOfDiscworld'' books have an arguably accurate but somewhat twisted take on statistics: the chances of ''anything at all'' happening are so remote that it doesn't make sense to be surprised at ''specific'' unlikely things.

** To prevent SaveScumming abuse, the tenth game's (unlike the ninth's, which was completely random) bonus experience system [[note]]EXP that may be freely given to any unit between levels, helpful for raising MagikarpPower characters, getting that precious extra level of stats ups or helping the guy lagging behind[[/note]] will ''always'' increases a character's 3 stats with the highest growth rate (Has an x percent chance to raise this stats on every level up). This wound up making it ''more'' broken, as some units quickly hit the {{Cap}} on their main stats (Aran), causing stats that would other almost never grow to suddenly increase at insane rates.
*** It is less broken and more "different". Bonus experience in the game should never be spent levelling characters without maxed stats[[note]]nearly all characters who have not hit a cap will have an overall stat increase averaging over 300%, or ''more'' than 3 stats on average[[/note]], but instead should be used to level characters who have already hit the caps on their main stats, resulting in hoarding and struggling a bit to get through the levels, followed by a sudden rise in level to the maximum amount when they finally hit that point at which using bonus experience is optimal.

** The MaddenCurse works this way. Generally, the cover is awarded to some athlete who just had a phenomenal season. The next season, the player is often beset by the sorts of bad luck that befall all athletes (injuries, bad games, etc) except they receive more attention. In some cases, it may also be a SelfFulfillingProphecy if the player gets a big ego and skimps on workouts, or if other players are more motivated to play hard against him. But mostly it's just that any season of a player is likely to be average (for his or her capabilities) and any season which leads to feature a player in games or magazine stories is likely to be way above average, so it's just a good chance of a "dice roll" showing a lower number, just like the next number after you rolled a six on a normal die is likely to be lower than that. The technical name for this is [[http://en.wikipedia.org/wiki/Regression_toward_the_mean regression toward the mean]].

* ''VideoGame/JohnMaddenFootball'':

** A more direct example are the year-in, year-out complaints that either the stats or the on-field experience are unrealistic, by pointing to the raw numbers. Since ''VideoGame/MaddenNFL'' is a video game, the developers have to shorten the quarters because most gamers aren't willing to invest multiple hours on a single game. So ultimately this means that gamers are running between 50-70% as many plays as a real NFL contest. Yet many expect to produce as many points or exciting moments, while somehow maintaining realistic results on a per-play basis. This is mathematically impossible. EA chooses the former, heavily slanting the game in favor of the offense, which has caused somewhat of a BrokenBase amongst fans of the series.

* In the "Captain jerk" episode of ''Series/HenryDanger'' they set up a contest where people have to guess a random number to meet Captain Man and Kid Danger. The random number is four digits, but it takes a very long time (a few days) for the final winner to guess the number, especially as they show the entire city obsessively trying to guess the correct number.

* It's common for a naïve poker players to (correctly) fold a bad hand, such as flush draw with no other outs, to a large bet, only to lament their "mistake" when it turns out their hand would've improved on the turn or river. Especially naïve players may try to "correct" their mistake by calling the next time they find themselves in a similar situation, which more savvy players can exploit.

* ''Webcomic/AwkwardZombie'' addresses the matter [[http://www.awkwardzombie.com/index.php?comic=072312 here]].

->''"There are three kinds of lies: lies, damned lies, and statistics."''

** This kind of fallacious reasoning reached memetic proportions in the pre-expansion VideoGame/WorldOfWarcraft encounter "Onyxia's Lair." A player who'd run into a string of bad luck assumed that the developers had made the encounter harder, and loudly complained: "She deep breaths more!" (Not breathes, ''breaths''.) Today, "She deep breaths more" is the official name of an in-game achievement you can earn in Onyxia's Lair.

-->-- '''Benjamin Disraeli'''

* '''Projecting From a Small Sample Size''': Even a fair coin has a significant probability of coming up heads seven times in ten flips[[note]]11.7% for ''exactly'' 7 heads; 17.2% for ''at least'' seven heads[[/note]], 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). Obviously 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.

* '''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). Obviously 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.

* Wrestling commentators discussing multi-person matches frequently claim that the champion in a 4-way match only has a 25% chance of retaining his title, with no regard to comparative skill levels or possible alliances between the participants. Given the fact that the outcomes are always predetermined, however, neither skill nor chance really has anything to do with it.

-->''"Well, I see one of three things happening: she gets better, she gets worse, she stays the same, and we get strong evidence. Two out of three ain't bad."''
* Invoked in ''Series/{{Survivor}}'' - As the players in the game dwindle, Probst tells them that they have a "one in ''x'' shot at winning the million dollars." The way he mentions this, it sounds like the winner of challenges (and at the game ''period'') is chosen at random, when it actually isn't. You can argue that if you're in the final six with TheLoad and someone who the jury ''hates'', you would have a one in ''four'' shot since the jurors would not vote for them. Justified in that he [[FridgeBrilliance does this to motivate the players]] and it's part of his "character."

* 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.

** ''TabletopGame/WorldOfSynnibarr'' also does this.
* ''TabletopGame/{{Warhammer 40000}}'': Fears of "bad dice" abound. The previously mentioned lack of even distribution and the tendency of rolling methods to influence the result only adds fuel to the fire.
** Bad dice can be a real thing. Las Vegas maintains a very strict policy for evaluating the balance of dice BEFORE they go into a game, and replacing them at regular intervals. As most 40k players play with cheaper, mass produced dice, and will rarely replace them unless they have visually obvious defects, it is perfectly plausible for a player to be using biased dice.

* MMO players, almost without fail, will adhere to mindset two - they will notice the streak of resists/misses/landed enemy attacks/what have you that killed or almost killed them, but never notice the long, long, long string of hits that precede it. Any and all MMO forums will have a topic pop up fairly regularly asking whether (or sometimes screaming loudly even with no evidence to that effect other than they had a string of bad luck) the RNG is broken.

* ''{{VideoGame/XCOM}}'':

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[[folder:Webcomics]]

* [[Webcomic/FreeFall Sam Starfall]] uses statistics in artistic fashion to establish that [[http://freefall.purrsia.com/ff500/fv00438.htm riding the top of a moving train is safer than climbing a staircase]].

* This was parodied in ''WesternAnimation/LesShadoks''. The Shadoks' goal for Season 1 was to fail to launch their rocket 999,999 times, as they had calculated that it had a one-in-a-million chance to successfully launch. It doesn't work.

## If your original lost bet is one dollar and you follow this stratagem, an unlucky streak of ten consecutive losses (including the first) has you betting $1023 to chase after your original loss of a ''single dollar''. Even if you do win, all you get is your original dollar back. You were better off just betting one dollar at a time and hoping for a winning streak.

## If your original lost bet is one dollar and you follow this stratagem, an unlucky streak of ten consecutive losses has you betting $1024 to chase after your original loss of a ''single dollar''. Even if you do win, all you get is your original dollar back. You were better off just betting one dollar at a time and hoping for a winning streak.

* In a strange twist, ''VideoGame/CrisisCoreFinalFantasyVII'' 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.

* '''[[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 Law of Large Numbers.

* ''Film/BowlingForColumbine'': Moore exaggerates the level of gun violence in the United States through spurious use of statistics, specifically comparing the amount of gun-related deaths in several western countries by citing gross figures for each country and not per capita stats.

[[folder:Videogames]]