Artistic License Statistics: Difference between revisions

Line 7:

It has been generally demonstrated that, because human brains are wired toward pattern detection, we are lousy at intuitively interpreting statistics; this is the main reason why casinos are viable businesses. Trying to do anything to curb this problem often results in the worship of the [[Random Number God]], or beliefs like:

* '''The hit/miss belief''': "A hit ratio below 25% is hopeless and a hit ratio above 75% is guaranteed. Everything else is a crapshoot."~~<br /><br />Not so much. There are four groups of 25% in 100%. Go ahead and count them. We'll wait. <br /><br />There is a 1 in 4 chance of hitting any one of them.~~

* '''The hit/miss belief''': "A hit ratio below 25% is hopeless and a hit ratio above 75% is guaranteed. Everything else is a crapshoot."

Not so much. There are four groups of 25% in 100%. Go ahead and count them. We'll wait.

There is a 1 in 4 chance of hitting any one of them.

* '''[[Gambler's Fallacy|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, [[The Computer Is a Cheating Bastard]]. In truth, it just happened to be the way the "dice" fell. As is often stated, "dice have no memory."

* '''Naive 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, if someone accused a group of 100 people of taking drugs, each person would be 1%. Accusing 4% of adults, and 4% of children, if the group is half of each, would be 4 people, not 8.

Line 27:

Line 31:

** Anyone playing roulette for anything other than costly entertainment.

* Many [[Bridge]] players feel that the computer-generated hands used for many duplicate games are more unusual (i.e. favor more unlikely distribution of cards) than human-shuffled hands. They're right, but in a backwards way: The computer-generated hands are ''more likely to be completely random'' than hands dealt from a human-shuffled deck. Even the best human-shuffled deck will retain a few cards in the same relative order as they were played in the last hand; computer-generated hands don't (except at the frequency you'd expect from random chance).

* Many players of the online version of ''[[Magic: The Gathering]]'' are convinced that the algorithm used to shuffle players' decks is flawed and is biased. (Some say the bias is towards "mana flood", where you get too many mana-producing cards (and not enough spells to actually use that mana with), while others say towards "mana screw", which is ''the exact opposite'' ~~-- not~~ getting enough.) In reality, the algorithm is completely incapable of either, since it does not consider what type any given card is when performing the shuffle. The reason for the dissonance between physical and online play (when there is one at ~~all -- mana~~ screw and mana flood are common on cardboard too) is that having to physically shuffle a deck enough to provide a truly random distribution every time would be ''incredibly annoying'', particularly given the number of times some decks end up being shuffled in a single game. Most people just take their land cards, which end up all in one pile at the end of a game and put them into the deck at fairly even intervals to avoid there being giant clumps of nothing but land. For practical reasons, even in tournaments it's accepted that the deck doesn't have to be truly randomly ~~distributed -- it~~ just needs to be random enough that a player can't predict what comes next.

* Many players of the online version of ''[[Magic: The Gathering]]'' are convinced that the algorithm used to shuffle players' decks is flawed and is biased. (Some say the bias is towards "mana flood", where you get too many mana-producing cards (and not enough spells to actually use that mana with), while others say towards "mana screw", which is ''the exact opposite''—not getting enough.) In reality, the algorithm is completely incapable of either, since it does not consider what type any given card is when performing the shuffle. The reason for the dissonance between physical and online play (when there is one at all—mana screw and mana flood are common on cardboard too) is that having to physically shuffle a deck enough to provide a truly random distribution every time would be ''incredibly annoying'', particularly given the number of times some decks end up being shuffled in a single game. Most people just take their land cards, which end up all in one pile at the end of a game and put them into the deck at fairly even intervals to avoid there being giant clumps of nothing but land. For practical reasons, even in tournaments it's accepted that the deck doesn't have to be truly randomly distributed—it just needs to be random enough that a player can't predict what comes next.

** This one-land-per-two-cards sorting prior to the deck shuffling is accepted practice in tournaments, provided that they are spread blindly vis-a-vis the remaining cards. Any further stacking of the cards is usually frowned upon, such as placing a Dark Ritual right next to each one of your Hypnotic Specters.

* Go to any online [[Poker]] forum and look in the General Discussion forum. More often then not, you'll find a sticky about the game not being rigged, and an explanation of why it may seem that it is. Of course, most forums will also have a 'Bad Beats' section for whining about said 'rigged' play screwing the loser... (never mind that they were chasing a flush draw and getting really poor pot odds on the call...)

Line 76:

Line 80:

** Starting with the 10th, if a character does not get at least one stats increased during a level up, the game rerolls (unless a character has hit the cap on everything). Starting with the 11th game, a characters growth rates will be boosted or dropped if they are behind or ahead of the "average" stats. Like the main example, this helps deal with the ''very'' annoying chance that a character gets "RNG Screwed", except this is enough to force a restart on an entire ''file'' in some cases.

* [[Word of God]] to the contrary, most players of ''[[Puzzle Quest]]: Challenge Of The Warlords'' believe that the game "nudges" all sort of random stats in its own favor. As many people complain about the computer's habit of chaining together 4/5 gem combos and extra turns, it's even more blatant in Spell Resistance, where an opponent with 2% resistance across the board will block approximately 15% of spells. The player, with the same stats, will be lucky to block one spell in hundreds.

* This trope is often brought up in [[MMORPG~~|MMORPGs~~]], where many players believe that item drop rates can be mathematically calculated to determine how many monsters you must kill until you "should" find said item, by assuming that a 1% drop rate means that after you've killed a hundred, something's wrong if you haven't gotten one.

* This trope is often brought up in [[MMORPG]]s, where many players believe that item drop rates can be mathematically calculated to determine how many monsters you must kill until you "should" find said item, by assuming that a 1% drop rate means that after you've killed a hundred, something's wrong if you haven't gotten one.

** Because of players complaining about this, the drop rate formula in ''[[World of Warcraft]]'' was changed to ''increase'' the drop percentage every time the quest item required ''doesn't'' drop and reset it after one ''does'' drop. Of course, this is also to avoid the wild variation in time a quest can take when it's truly random.

** Indeed, while the mean number of kills is 100, the actual number will be greater than 100 37% of the time. Of course, this also means that 50% of the time it will require fewer than 70 kills.

* Speaking of ''[[World of Warcraft]]'', during the famous "[[Leeroy Jenkins]]" video, someone is asked to do a number crunch to calculate their odds of finishing an encounter. [[Poe's Law|It's actually not as simple as that - it was done to make fun of guilds]] as well as [[Straw Vulcan~~|Straw Vulcans~~]] who may often rely on statistical fallacies.

* Speaking of ''[[World of Warcraft]]'', during the famous "[[Leeroy Jenkins]]" video, someone is asked to do a number crunch to calculate their odds of finishing an encounter. [[Poe's Law|It's actually not as simple as that - it was done to make fun of guilds]] as well as [[Straw Vulcan]]s who may often rely on statistical fallacies.

* ''[[City of Heroes]]'' actually has a mechanic that behaves like the second part, called the "streakbreaker". For a given base percentage chance to hit, if a player or mob misses a certain number of times in a row, the next hit is guaranteed. For a hit chance below 20% you have to miss something like 100 times in a row, but for hit chances above 90%, it only takes one miss to get a guaranteed hit on the next attack. If you were paying REALLY close attention, you could use this to ensure that a key attack doesn't miss.

* [[Dungeon Fighter Online]] has a dice roller that is perfectly random for the first instance of every sequence (first upgrade attempt, or random item pickup, or something similar), but then often produces identical results for the next several sets (Failing an identical upgrade five times in a row, the same player getting every single item in a dungeon). It often "corrects" itself and skews the other way until results are even. The hit/miss ratio is the same, either producing a lot of hits or a lot of misses in a row, only rarely looking like the actual statistic.

Line 85:

Line 89:

** Prior to that, the ''[[Tetris the Grand Master]]'' series also had an algorithm to make the gambler's fallacy come true: The game rolls 6 times (4 in the first TGM) and takes the first result that isn't identical to any of the four most recent pieces dealt. It's still possible for this to "fail" and give you the same pieces over and over again since the game only rolls a fixed number of times; it's just much less likely than with a simple RNG approach.

*** The Tetris piece-picking algorithms are many and varied. One, the appropriately named Bastet system, [[Spiteful AI|picks the worst piece possible for your current situation with an 85% accuracy.]]

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

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

** Alleviated somewhat in the sequel, which is kind enough to give you all of the information BEFORE you attack and provides a rough estimate of where the forces will end up in strength after the round of combat. It was actually criticized heavily for its near-perfect accuracy in prediction! Later patches actually made it a bit more random.

* This trope is hugely responsible for the ''[[Pokémon]]'' entries on [[The Computer Is a Cheating Bastard]], and is the number 1 thing the game's professional players complain about to similar levels of usage.

Line 114:

Line 118:

== [[Tabletop Games]] ==

* Among its [[So Bad It's Horrible|many flaws]], ''[[FATAL]]'' says that to determine the probability of an event, you roll two percentile dice<ref>That's a 100-sided dice, or more commonly two 10-siders with one representing the tens digit, for non-gamers</ref>, and if the second one is equal to or greater than the first, you succeed. That means that everything has a flat 50.5% chance of happening. And yes, you're supposed to do this for '''anything'''.

* Among its [[So Bad It's Horrible|many flaws]], ''[[FATAL]]'' says that to determine the probability of an event, you roll two percentile dice,<ref>That's a 100-sided dice, or more commonly two 10-siders with one representing the tens digit, for non-gamers</ref> and if the second one is equal to or greater than the first, you succeed. That means that everything has a flat 50.5% chance of happening. And yes, you're supposed to do this for '''anything'''.

== [[Web Comics]] ==