How the law of large numbers works.

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  • Edge
    27 posts Member
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    I feel a lot better now. Instead of feeling like I got screwed, now I feel like I am statistically predisposed to getting screwed.

    Best thing I’ve ever read here
  • Vohbo
    332 posts Member
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    Vohbo wrote: »
    Humans, especially untrained humans, are notoriously bad at statistics. Even a lot of scientists are bad at interpreting data and are prone to confirmation bias and a whole array of other logical fallacies.

    So Bob's observation is incorrect because people are often incorrect?

    Not entirely sure what you are trying to point out here. I never made such a claim, and you know that this is not about observation but about drawing poor conclusions from a given set of data.
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    Vohbo wrote: »
    Vohbo wrote: »
    Humans, especially untrained humans, are notoriously bad at statistics. Even a lot of scientists are bad at interpreting data and are prone to confirmation bias and a whole array of other logical fallacies.

    So Bob's observation is incorrect because people are often incorrect?

    Not entirely sure what you are trying to point out here. I never made such a claim, and you know that this is not about observation but about drawing poor conclusions from a given set of data.

    What is the poor conclusion?
  • Vohbo
    332 posts Member
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    That Onyxia deep breathes more, and all variants of this observation.
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    Many whelps, handle it.
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    Saying people don't understand how RNG works, doesn't mean that they're wrong....it simply means that they MIGHT be wrong. Which we all already know....

    The question is whether they still might be right even if they don't understand RNG.

    If for example, if the odds of a randomly generated event happening 5 consecutive times are so remote that it's unlikely to happen during the lifetime of the universe....you could reasonably say it's impossible....(although it's not).

    So when that event happens 20 times in a row, can you in good conscience say that RNG made it happen?

    Yes....RNG makes "nearly impossible" things possible. But it doesn't make "nearly impossible" things likely.....

    I'm not defending the RNG complainers....I think that given a decent amount of data, they could reasonably be assumed to be wrong (and I think that a 60 second look at the code could prove them wrong)....I'm just saying if you think that saying "you don't understand RNG" proves them wrong....then you're wrong too.

    Further....if you think that all you have to do is educate them about RNG....then you're not nearly as smart as you think you are.

    ttfn
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    I have been casually reading this over the last week... I don't have anything really to add... I found it interesting that while farming hard nodes that it more likely to get 0 shards in 5 sims than it is to get 5 shards in 5 sims. Much more in fact because a 30% chance of getting a shard 5X in a row is not a plausible as a 70% chance of not getting one 5X in a row. But since the addition of 5X simming, I always found it fascinating that I had never hit 5X shards. Soooo, maybe there is something going on here, but then... I got 5 shards in a 5x-sim.

    Not sure that means anything, but I'm still waiting to hit the 10M in a credit heist!
    https://swgoh.gg/u/speedokillz/

    December 2016 Arena Shard
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    I can't find the thread (yet again - and whenever this discussion comes up I try and find it -- kind of think it was deleted)

    Anyways someone put the results up of a really large sample, it was from both packs and then was from (at the time) mod drops.

    What it showed was, yes, random numbers, and yes, streakiness... but the streaks of win/loss were NOT really random, it was something like 60% bad drops and then 30 % good drops and a 10% middling range and then repeat.

    The reason it stuck with me is because that's what I see when I refresh and farm. good and bad streaks - on repeat.

    If it was really a random generator you'd certainly get streaks, but you'd get the other side too, just totally, utter ups and downs from one roll to the next, and we DON'T see that side.

    Like some basement trolls underwear... the game is way too streaky... and no one likes it.
    #AcolyteShootsTwice
  • crzydroid
    7383 posts Moderator
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    I have been casually reading this over the last week... I don't have anything really to add... I found it interesting that while farming hard nodes that it more likely to get 0 shards in 5 sims than it is to get 5 shards in 5 sims. Much more in fact because a 30% chance of getting a shard 5X in a row is not a plausible as a 70% chance of not getting one 5X in a row. But since the addition of 5X simming, I always found it fascinating that I had never hit 5X shards. Soooo, maybe there is something going on here, but then... I got 5 shards in a 5x-sim.

    Not sure that means anything, but I'm still waiting to hit the 10M in a credit heist!

    This is probably what you're saying, as yeah, a skewed distribution wil get you more results at one end. With a 33% drop rate, getting five 0s has a 13.5% chance, wheres going five for five has a four-tenths of a percent chance.
  • Viserys
    461 posts Member
    edited October 2017
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    Correct. When you are weighted towards not pulling something, there's a much greater likelihood you see a string of fails (0 / 20 on sims) than that you will see a huge string of successes ( 15 / 20 )

    So it psychologically appears that the game is more likely to cheat you than be nice to you, because you are failing to perceive a 9 / 20 as the game being nice to you.

  • Woodroward
    3749 posts Member
    edited October 2017
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    My biggest complaint about the law of large numbers is how people misapply it here.

    For example, they quote mixed together data that shows an overall 33% drop rate on character shards to say that it doesn't matter if you are just starting to farm for the next star or just finishing the current one, but the data doesn't actually say that.

    It absolutely confirms that there is an overall 33% drop rate, but in order to confirm that it doesn't vary by where you are in a character's farming, there would have to be large numbers of results at 1/65, 2/65, 3/65, etc.

    So no matter how many numbers are gathered, unless it is sorted by each shard per character farm it can NOT be used as data to say that drop rates are unaffected by where you are in a character's progression.

    That is what is called a conclusion unsupported by the facts in the scientific community.

    To do so is kind of like getting some Organic hamburger and mixing it to a perfect mixture with some cheap hamburger from a discount grocery store and then saying: "See! There's no noticeable difference between the meat!"

    ... well maybe there is and maybe there isn't, but if you don't keep it separate, there's really no way to tell.
  • Peer
    299 posts Member
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    NicWester wrote: »
    If a ship has a 44% dodge rate and you attack it 8 times, there is a 0.140482% chance of all eight attacks being dodged.

    (PS: My numbers are probably wrong because I'm very bad at math. But I get the general idea anyway.)

    No, there is a 0,0014% chance that a ship dodges 8 subsequent attacks. For 3 times the chance is 8,5% which is quite low. For this game all events would have to be treated as independent events - previous events do not influence probability of any current event.
    Maegor wrote: »
    It's just so "streaky".

    Ask any statistics professor to analyze lists created by human generated randomness vs computer generated randomness with the same p, and they will most likely be able to pick out the human generated list. Basically because humans avoid too much streakiness in probability, and when we see it in a computer generated event like this game, alarm bells go off, even if there isn't anything nefarious occurring.

    Currently there is no way to generate random numbers with any kind of computer because any machine needs a given type of distribution in order to produce numbers that fit this distribution. I think that CG/EA chose some very, let´s say: "unnatural", distribution types for drop rates. Something like the probability of being struck by a lightning calculated over all lightnings ever recorded. Even the ones that occurred in unpopulated areas.
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    Peer wrote: »
    NicWester wrote: »
    If a ship has a 44% dodge rate and you attack it 8 times, there is a 0.140482% chance of all eight attacks being dodged.

    (PS: My numbers are probably wrong because I'm very bad at math. But I get the general idea anyway.)

    No, there is a 0,0014% chance that a ship dodges 8 subsequent attacks. For 3 times the chance is 8,5% which is quite low. For this game all events would have to be treated as independent events - previous events do not influence probability of any current event.

    Incorrect, it's 0.14% as the OP suggested. I think you're mixing yourself up with the conversion of decimals to percentages. You are correct that it's 8.5% for 3 consecutive dodges

    Either way, there's a lot going on when someone says that the enemy TIE fighter dodged 8 times in a row, the first of which is that it probably did not -- the mind distorts observations pretty easily. If the TIE dodges 4 times in a row and that makes you mad, it suddenly grows in your mind as the number was "a lot, more than three. I dunno!". The human mind is particularly bad at recalling specifics beyond a pattern of three instances.

    As for the 33% drop rate mentioned above -- of course CG doesn't need to fudge probabilities and tilt them based on how many shards you still need, the natural way probabilities function works plenty well enough. There's no actual need to construct a convoluted system of tilting probabilities. The human mind is very bad at naturally interpreting them. You remember when the game 'cheated you' and as I noted in my previous post, most players see a 1/8 as the game cheating them, but don't see a 6/8 as getting equally lucky off the drop curve. Thus you see yourself getting cheated, and never getting lucky, and conclude that the statistics must be rigged especially now when I need them the most.

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    Viserys wrote: »
    Peer wrote: »
    NicWester wrote: »
    If a ship has a 44% dodge rate and you attack it 8 times, there is a 0.140482% chance of all eight attacks being dodged.

    (PS: My numbers are probably wrong because I'm very bad at math. But I get the general idea anyway.)

    No, there is a 0,0014% chance that a ship dodges 8 subsequent attacks. For 3 times the chance is 8,5% which is quite low. For this game all events would have to be treated as independent events - previous events do not influence probability of any current event.

    Incorrect, it's 0.14% as the OP suggested. I think you're mixing yourself up with the conversion of decimals to percentages. You are correct that it's 8.5% for 3 consecutive dodges

    Either way, there's a lot going on when someone says that the enemy TIE fighter dodged 8 times in a row, the first of which is that it probably did not -- the mind distorts observations pretty easily. If the TIE dodges 4 times in a row and that makes you mad, it suddenly grows in your mind as the number was "a lot, more than three. I dunno!". The human mind is particularly bad at recalling specifics beyond a pattern of three instances.

    As for the 33% drop rate mentioned above -- of course CG doesn't need to fudge probabilities and tilt them based on how many shards you still need, the natural way probabilities function works plenty well enough. There's no actual need to construct a convoluted system of tilting probabilities. The human mind is very bad at naturally interpreting them. You remember when the game 'cheated you' and as I noted in my previous post, most players see a 1/8 as the game cheating them, but don't see a 6/8 as getting equally lucky off the drop curve. Thus you see yourself getting cheated, and never getting lucky, and conclude that the statistics must be rigged especially now when I need them the most.

    You are misinterpreting my post. I am not saying that it is so. What I AM saying is that those who try and convince others it isn't true don't have any data to support saying so since it isn't constructed that way, and yes the data would have to be constructed as I have said for any data to be relevant.

    Basically I don't like people trying to use bologna to convince people they're wrong while calling it facts.

    As for dodging 8 times in a row, it's not a 0.14% chance of it happening (poor wording). The odds say that it WILL happen 0.14% of the time, which means that, on average, people should experience TFP dodging them 8 times in a row every 714 matches. If you do all 5 matches every day, that's 142 days. So about once every 5 months you should see a tfp with 44% dodge dodge 8 times in a row.
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    Viserys wrote: »
    As for the 33% drop rate mentioned above -- of course CG doesn't need to fudge probabilities and tilt them based on how many shards you still need, the natural way probabilities function works plenty well enough. There's no actual need to construct a convoluted system of tilting probabilities. The human mind is very bad at naturally interpreting them. You remember when the game 'cheated you' and as I noted in my previous post, most players see a 1/8 as the game cheating them, but don't see a 6/8 as getting equally lucky off the drop curve. Thus you see yourself getting cheated, and never getting lucky, and conclude that the statistics must be rigged especially now when I need them the most.



    You are misinterpreting my post. I am not saying that it is so. What I AM saying is that those who try and convince others it isn't true don't have any data to support saying so since the data isn't constructed that way, and yes the data would have to be constructed as I have said for any data to be relevant to whether or not they change drop rates based on where you are in your farm.

    Basically I don't like people trying to use bologna to convince people they're wrong while calling it facts.


    I am currently going to school for biotech... to work in a lab. Trust me, interpreting data is a large part of my daily life right now. There is 0 assumptions or confirmation bias involved in my analysis of the data people quote. I am examining it solely on its own merits, none of which include being able to use it to disprove that they change the drop rate.

    As for dodging 8 times in a row, it's not a 0.14% chance of it happening (poor wording). The odds say that it WILL happen 0.14% of the time on average, which means that, on average, people should experience TFP dodging them 8 times in a row every 714 matches. If you do all 5 matches every day, that's 142 days. So about once every 5 months you should see a tfp with 44% dodge dodge 8 times in a row.
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    60% of the time, it works every time
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    Woodroward wrote: »
    As for dodging 8 times in a row, it's not a 0.14% chance of it happening (poor wording). The odds say that it WILL happen 0.14% of the time on average, which means that, on average, people should experience TFP dodging them 8 times in a row every 714 matches. If you do all 5 matches every day, that's 142 days. So about once every 5 months you should see a tfp with 44% dodge dodge 8 times in a row.

    I don't think you and I are disagreeing at all. It would happen one in every 714 sets of 8 dodge attempts, but I'm gonna guess that the vast majority of matches don't include the TIE fighter being shot at 8 times in the first place. So practically, this will happen even less than one in every 714 matches. My whole point was that people aren't actually seeing this case. They're more likely seeing it dodge three times in a row and mentally assuming that it "dodged every single attack and I attacked it like, eight times!"

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    You guys... you forgot about the law of lazy programming. There's no way they went through the extra effort to add in exactly how many shards you have at the moment to impact the success factor of your draw. That would require unnecessary effort, and thus, based on the law of lazy programming, will not have been coded up.

    :D
  • crzydroid
    7383 posts Moderator
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    You guys... you forgot about the law of lazy programming. There's no way they went through the extra effort to add in exactly how many shards you have at the moment to impact the success factor of your draw. That would require unnecessary effort, and thus, based on the law of lazy programming, will not have been coded up.

    :D

    This is probably the most convincing argument on here.
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    crzydroid wrote: »
    You guys... you forgot about the law of lazy programming. There's no way they went through the extra effort to add in exactly how many shards you have at the moment to impact the success factor of your draw. That would require unnecessary effort, and thus, based on the law of lazy programming, will not have been coded up.

    :D

    This is probably the most convincing argument on here.

    Couldn’t agree with this more. RNG is the easiest to put in place.
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    You guys... you forgot about the law of lazy programming. There's no way they went through the extra effort to add in exactly how many shards you have at the moment to impact the success factor of your draw. That would require unnecessary effort, and thus, based on the law of lazy programming, will not have been coded up.

    :D

    Totally believe Occams Razor.
    But I also believe in the need to ensure 3rd quarter profits are up this year from last by 16%.
    #AcolyteShootsTwice
  • Vohbo
    332 posts Member
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    What I find funny about this conversation is that some people seem to think that EA/CG is messing with drop rates to increase profits in some sneaky way, and I simply don't believe that. Why not ? Well simply put: they openly do things with this game that the Hutt Cartels would frown upon just to squeeze money out of people, why would they go out of their way to hide some silly drop rate.
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    So, I actually *am* a professor of Statistics. For reals. AND I've worked in mobile gaming, running stats on purchasing behavior. Mainly I just wanna say that you guys are awesome and funny. Most of you are at least kind of right and some of you are very wrong, but I love that you guys are thinking along these lines.

    The bad news is that in the mobile-gaming company I worked for, they were always talking about using what's called "Dark UX" to manipulate players into spending. A horrible example that I do not know to be true (but might be): when you sim for a character shard or a piece of gear, and you need multiple shards to complete the character or set, the RNG is probably whatever it is. However, when you are only ONE shard away (say 49/50) they might indeed reduce the probability for that one, singular roll. Because nothing will make a person buy gems more than being balked that close to success and having to wait for their energy to replenish. I'll bet they literally get more gem purchases from people in that circumstance than almost any other, because it's not a thought-out purchase (like a pack of Chromiums), it's an angry, psychologically-induced spontaneous purchase.

    It's all conjecture, though. Some companies are not above this. But although I believe in my angry human heart sometimes that EA is messing with us, I actually believe in my statistical, intellectual head that they are not and that very small probabilities just look like impossibilities to human eyes.

    One more thing: the law of large numbers simply states that as your sample size approaches infinite, the mean of your sample will come to more closely approximate the true (population) mean. This may or may not be a good reference for what you're discussing. Maybe the central limit theorem (that as your sample size approaches infinite, your sampling distribution will come to more closely approximate the normal curve) is a better example. ; )

    Keep on keeping on!

    Samurai UX
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    I 100% believe this game is streaky. It's like they because it's designed to be. People are more likely to use crystals to sim more when they get a great sim (they feel "hot" and want to do it again) or when they have a horrible sim (they get frustrated and want to do it again to compensate for what they didn't get).

    They base many aspects of the game on the trillion dollar gambling industry. There's laws and regulations though with slots. Not saying even if they add variance it's bad, just that it's a rather naive stance to think that any company wouldn't do certain things when metrics show it's more profitable.

    Oh, I don’t blame them one bit. That’s part of my argument. Adding in streakiness increases profit, so it’s a safe bet they have done that. It doesn’t mean I like it.
  • Dretzle
    716 posts Member
    edited October 2017
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    So, I was thinking about this a bit. Are they adding in bad luck streaks and good luck streaks? How would we know? We love to talk about "significant sample size", but in reality there's no way to really tell without reading their code.

    But I could run an independent experiment using a Java pseudo-random number generator with no built in streakiness. What results would we get then?

    I ran a test of 200,000 sims (please let me know if you'd like me to test with a larger sample size). Here are the results. I also recorded the number of really bad streaks and the number of really good streaks. Percentage drop I set to 20% (we're simming for purple gear here). Bad streak size I set to 20 (Hey, I just simmed 20 battles and got nothin'!) Good streak size I set to 5 (Yes, I know you want more, but let's face it, at 20%, getting 5 in a row is a really good drop.)
    Total Sims: 200,000
    Drop Rate: 0.2
    Good Streak Size: 5
    Bad Streak Size: 20
    Results: 
    Total Score: 39,940
    Percentage Achieved: 0.20
    Number of really bad streaks: 362
    Largest Streak: 43
    Number of really good streaks: 362
    Largest Streak: 7
    

    I've run this several times and got very similar results, but let me know if you want me to change any more parameters or see more data.

    What this tells me is CG doesn't really need to code anything nefarious at all. Put in a bad enough percentage drop rate, and the RNG will handle giving you bad streaks all by itself.

    EDIT: For my own curiosity, I'll do one of these with dodge percentages, too.
    Post edited by Dretzle on
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    SamuraiUX wrote: »

    One more thing: the law of large numbers simply states that as your sample size approaches infinite, the mean of your sample will come to more closely approximate the true (population) mean. This may or may not be a good reference for what you're discussing. Maybe the central limit theorem (that as your sample size approaches infinite, your sampling distribution will come to more closely approximate the normal curve) is a better example. ; )

    Keep on keeping on!

    Samurai UX

    I'll see your law of large numbers and raise you the "law of infinite universes" ....which states that since there are an infinite amount of universes, not only is everything possible, everything has actually happened an infinite number of times and we are in one of those lucky universes.

    That sort of makes your entire field of study meaningless.....dunnit?

    Great worldview if you don't want to be bothered by those burdensome discussions of odds.
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    I’ll see your law of infinite multiverses and raise you a law of pseudo-intellectual bullroar.

    Folks are seriously overthinking all of this in the hopes that it impresses someone...
    Ceterum censeo Patientia esse meliat.
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    I raise you all theorem's by an exponent of Donny Darko...
    tumblr_m7ftt8KPq21rp26cno1_500.gif
    Oh, no... wait... I'm sorry... I can't change it... but, please, that "days" should be "months" and "When the world will end" should be "when you will have 7* MT" Sorry for the errors...
    #AcolyteShootsTwice
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    NicWester wrote: »
    I’ll see your law of infinite multiverses and raise you a law of pseudo-intellectual bullroar.

    Folks are seriously overthinking all of this in the hopes that it impresses someone...

    Or they just enjoy discussions on this level.
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    @OP is just making the point that RNG overall is not the same as that one particular instance where you get offense up on your best attacker, the target you WANT to hit is not being protected by another hero taunting and that target has no foresight or stealth on them either.

    Its also NOT the same as the enemy having offense up on there best attacker and a clear shot at your weakest link with no foresight or stealth or taunt to protect them.

    RNG is more, or it could be less than the average overall % of those things happening AND furthermore the combination of the AI and player commands...

    In other words... its saying that if you win the lotto your more likely to be struck by lighting and vice versa...

    And if lose the lotto your less likely to be struck by lightning...

    The thing about RNG and statistics is that you can bias your opinion off anything... if i have the ability to call any thread PINK if it has the keyword LUKE or CLS in it then i can say that over 50% of the threads in forum have the word PINK in them... now in reality its far far far less... so also factor in that theres some unique buffs/abilities that are unit specfic... and some that are shared by multiple heros... all of these little things add to the RNG of one thing over another. But if i keep repeating the whole pink thing again and again then more peeps are likely to belive it and somehow it becomes more accepted... or rather it happens more often... because more peeps belive it. Unless the community shoots it down and beats it like a dead horse, seperates the corpse and buries it in different corners of the universe and then kill themselves to hide the locations forever.

    So in recap...

    Basicly just because the drop rate is 33% doesn't mean its gonna be 33%...

    Just like the way obamas "hope & change" slogan didnt bring hope & change... or trumps "make america great again" slogan is not making america great again... or maybe they did/are... just depends on who ya ask... because its all relative to your experience.

    Just because it is, doesnt mean that it is.
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