Tuesday, November 25, 2014

The Bell Curve of Crazy: A Statistical Approach to Understanding Fandom Metrics

I've been meaning to write an article for Anti Kpop-Fangirl that somehow incorporated my areas of expertise, aka the bullshit I studied for 4 years of my life at college. I see how you all like it when Kpopalypse talks about his industry skillz, so I figured why not give it a shot.

And thus we come to my groundbreaking model for the wide range of... "behavior" we see in KPop fandoms today. Without further ado, I present to you, THE BELL CURVE OF CRAZY.

As presented by Fei.
If there's anything I've learned from Kpopalypse, it's that people will pay more attention
if hot people are used to present the information.


  • mean (μ, lowercase Greek mu- a measure of the central tendency of a probability distribution, this value is simply the the sum of all possible values divided by the total population
  • standard deviation (σ, lowercase Greek sigma) - a measure of the average amount of variation from the mean, hence STANDARD deviation. The calculation for this is a little complicated, so it's not as important for you to know it for the purposes of this article. A HIGH standard deviation means that you have a set of data that is spread out over a large range of values. A LOW standard deviation means you have a set of data that tends to cluster around the mean.
  • outlier - a data point that is very distant from other data points. An example of this would be a set like [41, 43, 39, 37, 40, 100], where most of the data points are clustered around 40 except the 100 data point.

The most important analysis tool we'll be using is the normal distribution. This is a function that tells the probability that any real observation will fall between any two real limits or real numbers, as the curve approaches zero on either side. In layman's terms, the normal distribution is a bell-shaped curve that models the statistical likelihood of obtaining/observing a specific data point based on its relationship to the mean via standard deviation. Remember that the standard deviation measures the average variance of a set of data points to the mean, so we use standard deviation to measure this probability.

As you can gather from the picture, the big three probabilities to keep in mind are 68%, 95%, and 99.7%. On its own, this tells us nothing without a concrete model for us to use.  With that in mind, I've created an arbitrary scale that seeks to objectively quantify the ranges of fangirl behavior.


We'll be using a 0-100 scale for fangirl behavior, with 50 as the effective mean value. As we know, the ends of the bell curve approach infinity on either end which means there is no finite cap on fangirl behavior in any direction. The closer you get to 0 or 100, the more extreme you are.

On one end of the spectrum, we have extreme hate. These are the types of people that:
  • start fanwars over the slightest provocation
  • form anti-fan cafes to rage about how rude/ugly/stupid/plastic an idol is
  • send hateful tweets at idols
  • photoshop or otherwise fabricate "evidence" of wrong-doing
  • think T-ara is the epitome of evil
  • give enemy oppas water bottles laced with super glue to drink from
These people are consumed with loathing and antagonism to the point where it becomes their new raison d'etre. The closer you get to 0, the more sociopathic you get in your single-minded pursuit of petty hatred.

Ready to SASAENG
On the other end of the spectrum, we have excessive love. These are the types of people that:
  • refer to their faves as oppas despite neither being Korean and/or younger than the idols in question
  • break into oppa's apartment to steal underwear and/or stray pubes
  • buy oppa and unnie expensive brand name accessories
  • bulk buy albums and minis to boost sales for their oppas and unnies
  • insist oppa/unnie did nothing wrong
  • write mpreg fanfics about their oppas
  • furiously defame their unnies' main rivals on social media
  • wave album sales and concert ticket numbers as proof of superiority
These people just love their Korean idols so much, it becomes their sole reason for existing. The closer you get to 100, the more delusional and out-of-touch with reality you get in your pursuit of oppa's seed.

True Neutral??
Of course, there exists a happy medium for all of this behavior. These are the kinds of people that:
  • realize Kpop is just as manufactured and derivative as the pop music you can find in any country
  • like to wait for all the facts before passing judgment
  • illegally download singles or single tracks that they like off albums and minis
  • can hardly keep up with who the fuck is debuting these days unless they have a nice track and hot members, and even then can barely keep all the names straight
  • are Team Schadenfreude
  • eagerly await the next scandal to break out in order to laugh at both delusional sides that inevitably form 
These people are (mostly) sane and rational, and their level of involvement in Kpop varies. But the one thing that remains constant in all of them is that they can divorce the idol from the music. Lets take a page from Kpopalypse's book and go with a hypothetical situation.

Person A recently stumbles across Group B, a 5 member group of cute girls who have debuted for around 3 years now to average success. Group B have mostly kept their noses as clean as their idol image, not really making any waves one way or another aside from the odd fanaccount praising them for their down-to-earth humility and bright smiles for fan and staffer alike. Person A gives their entire discography a listen and downloads a mini album or two, but ends up deleting most of the tracks save a couple of gems in the sea of balladey-filler trash and the promotional singles. Person A figures they'll just buy the group's first full album to make up for it, whenever the hell that one comes out. Maybe it'll come with a poster and a photocard of that Idol C that's caught their eye because she's the hottest, got a fine ass to match, and an outgoing personality that makes them smile at her antics on her occasional variety show appearance.
One day, Idol C is caught up in a dating scandal and it is revealed she has been dating Idol D (the hottest guy from a senior group with over 5 years of experience under their belts) for months now. Person A doesn't give a shit, and is happy for Idol C, privately wishing her and Idol D a happy relationship.
That pretty much sums up the people hovering around the 50 mark, give or take 7 points one way or the other. Like I said, some may be a little more cynical than others and some may be a little more prone to the odd bias than others, but these people generally keep it together.

So how does all this data and statistical stuff matter in a case like this? Let's say that 50 is our mean (μ) and we observe a standard deviation (σ) of about 15 in our overall population. Keep in mind that standard deviation is the measure of the average deviation of the population's scores from the mean, so a standard deviation of about 15 is fairly generous in terms of spread. I've gone ahead and labeled a nice graph for you to better visualize this concept.

68% of the population lies between 35 and 65.
99.7% of the population (mostly everyone) lies between 5 and 95.
From this data, we use a z-score estimate to get real numbers we can understand. For the purposes of this article, you don't need to know how the values are calculated but you can use nifty online calculators to do the bulk of the work for you. Personally, I just used this one

Using our estimate of usual sanity (43 to 57), only about 36% of the population can be considered sane. Personally, I would consider anyone below/above two standard deviations (so either lower than 20 or higher than 80) to be batshit insane, which covers about 5% of the population in either direction. Meaning about 2.5% crazy haters, 2.5% crazy devotees to be clear.

So how does this apply to real-world Kpop populations? Using the girl group fancafe numbers for October 2014, we can make estimates for the insane people in each fandom. If 236,384 people are in SNSD's fancafe, we can assume that they're all SONEs and thus lie above at least 43 on the scale. If we use a score of 65 (one full standard deviation) as the baseline for insane devotion, about 15.8% of the population will be in this range. 15.8% of 236,384 equals 37,349 people in the FANCAFE ALONE who are crazy bitches that do shit like endlessly circlejerking the Power of 9 on everything you can see. In comparison, Rania (COMEBACK WHEN?)'s 3821 fancafe members means only about 603 insane crazies instead. And that's just covering the number of people in the fancafe on Daum. If we apply this principle for a theoretical total population of SONEs, it's no small wonder why people get so annoyed by their usual antics -- they're more prevalent than you realize!

AND it gets worse! That's just the number of people we assume to actually LIKE SNSD. If we consider the total population of Kpop fans who have encountered SNSD and hate them, we could theoretically double the number of crazies by including the people who care enough to form groups like STAND. 

Therefore we can see that my initial assumption makes sense: the more popular a group gets, the more likely it is that you'll run into a crazy bitch on the internet that either hates them or loves them WAY too much. It's a simple matter of statistics that probably is common sense, and probably didn't need any of this bullshit for you to realize, but oh well. If  you learned a little bit more about stats, then I've done a good job.

Thanks for reading. l0l


  1. tl;dr

    Moar pics of Fei, plox

  2. Fei or not, math is still unbearable.

  3. Doesn't everyone have to take statistics for their degree? At my uni, every business major had to take stats and that's when I met AKF for the first time.

    1. I didn't need them for my music degree. But then someone would argue that that's not a degree but a bit of paper to wrap up fish and chips with.

    2. Music degree is about as useful as an Art degree. Or Literature. God help you poor souls

  4. What if I think T-ara is the epitome of evil yet still furiously defame their main rivals on social media?

    1. If anyone wants some Boram underwear, I got the hookup on that, too. Just tell me what color and in what state of used you'd prefer.

    2. I just hope Kpopalypse doesn't find out about this.....

    3. I'm not into underwear. Underwear is for removing.

  5. I think your curve vastly overestimates the amount of sane people.

  6. I think you vastly overestimates the amount of fucks would be given with maths as the theme.

    1. Are you the yoloswag for this post?

    2. https://justinschwab.files.wordpress.com/2011/06/unicorn-man.jpg

  7. There certainly are plenty of deranged oppalogists out there.

  8. So, what's the bell curve for the amount of people who'll ask kpopalypse about this post on ask.fm instead of zaku?

  9. I've been running with the general principal that Big Group A has a huge amount of fans
    Nugu B has barely any
    But both have the same % of crazies
    But because A has more fans even their % of crazies is bigger than B's entire fandom so it makes them look worse

    as a theory for a while

    But I feel your bell curve is missing a key variation in the form of herd mentality.

    The bigger the number of crazies, the more accepted the extreme behaviour becomes, the more people join in cause others in the fandom are doing it so I can too.

    I call this the Exo rule

  10. I dont knwo what's happening in this page so I'll just say some smart things.


  11. This is a cool post. This is the first article I've read from your blog and it's nice to see you educating people on basic statistics (everyone should know some stats!). I just have a couple of points: first, your central message of "each group probably has roughly the same percentage of crazy fans which implies that if there are more Group A fans, there are proportionately more crazy Group A fans" probably didn't need the rest of the exposition and second, and this is a really minor thing, the real numbers are complete so real limits are real numbers. Thanks and keep up the good work!


Note: Only a member of this blog may post a comment.