Greedy Goblin

Thursday, May 13, 2010

It's not a normal distribution!

Please look at the picture and tell me which graph is the odd one out. I'm sure you will pick it without seeing any titles or numbers:
While they are all different from each other, the bottom right is qualitatively different, not just numerically. What are these graphs and why are they important?

All four answer the question "how much X does the bottom, second, third, fourth and top 20%" has?" In the first three, X is simply a number without meaning, and the distribution is normal (Gaussian). The variances of the normal distributions differ, so the sizes of 20% bars differ too. But - due to the characteristics of normal distribution - the middle 20% is exactly halfway between the second and the fourth, and also in the exact halfway of the top and the bottom.

The bottom right chart s absolutely different. Without having a slightest idea what X is, we can say that its distribution is far-far from normal. Are you curious what the bottom right graph displays?

I could say it displays WoW skill. The top 20% is much-much more skilled than the next 20% which is pretty close to the third, fourth and fifth. I could say the top 20% shows all the people who downed anything in ICC so has proven that they are able to prepare, read, follow tactics. Then comes a big gap to those who pull their weight in easy heroic AoE fests. These people are closely followed by those who do less damage, and less, finally reaching the bottom 20%. How many times have you seen damage meter looking exactly like this graph, one guy doing double-triple of the others, who follow each other closely? I believe this explanation is true, despite I couldn't prove it.

The bottom-right graph is not about WoW. It's the income distribution in the USA. The top 20% has 60% of all income in 2003, the last year when I could dig up such data. While you are most probably not shocked by this graph, it completely destroys a common belief that most people - most probably you too - share: that the skills of people are distributed normally. Most people are average guys (with average salary), there are some below (McJob) and above (doctor, engineer), and there are a few CEOs and hobos on the two extremes of the spectra.

It is completely not true. The distribution of income cannot be described by normal distribution. Since we know for sure that IQ is normal distribution, also the psychological factors of employment like tolerance for monotony. The "luck" is by definition normally distributed in a large population. So there must be some mysterious and not normally distributed factor. This factor is more or less binary. If you have it, you belong to the top group. If you don't, you belong to one of the bottom groups.

Of course each group is normally distributed itself. Among the top people there are some who are really dumb and mess up deals, lose their top job just to find another one in months with top-beginner salary, and there are CEOs making 7 figures. In the bottom people there are really intelligent and really-really hard working guys making close to $100K by studying and working day and night, and there are punks who starve on the street. Just like there bigger and smaller mules and bigger and smaller sheep. The distribution of height among sheep is normal, so is among mules. But in the group containing both sheep and mules, the distribution will be anything but normal.

I purposefully don't try to explain this mysterious quality. Obviously I have an idea, but that's irrelevant at this point. We can make interesting and true conclusions about such sheep-mule mixture without knowing the difference between sheep and mules.


Ablimoth said...

Well, yes. The luck is standardly distributed. But is luck correlated with income? If it is, then do high levels of luck have an exponential impact on income? Thereby you are measuring the impact of luck on income, not the mysterious variable...

I actually disagree that you're measuring the impact of luck on income, but you haven't sufficiently explained that that is not what you are measuring... not that it matters.

Azzur said...

I don't think you understand what a normal distribution is. EVERYTHING with a large sample size can be approximated as a normal distribution.

The income distribution you observed has a large standard deviation.

Olga said...

The income distribution is not about skill. Money flow is far from fast. When you are a heir of a very rich family, you will not became poor even if your skill is not as good as your father's. If you would dig into the history of people who are in those 20%, you will not find a lot of people whose parents were not in that 20%, and even whose grandparents weren't.

Samus said...

Perhaps your country works this way, because your country is only recently (historically) capitalist. Not too long ago, everyone started at the same place. I can definitely see where you live, the smartest, most skilled businessmen rose to the top, and the failures failed.

That is not how America works. There is a saying here that "who you know is more important that what you know." The top is a buddy system. You need to read Warren Buffet's views on executive compensation. He is not some bitter poor man, he is the second richest man in the world, and he thinks our compensation system is essentially broken.

People are not especially skilled at the top here, they are simply connected.

Klepsacovic said...

That doesn't at all say anything about skills. Do not mix up income and skill, and when you do, keep in mind the magnifying effects of the 'pyramid'. Imagine a manage who makes those directly under him 10% better. Give him 10 employees and he is just as good as one of them. Give him 20 and he's worth twice as much. Now put a manager above him who also makes people 10% better and give him 20 managed to manage. With just three levels we have a 4x increase in apparent worth. Add another and you're at 8x, and so on.

The most money is in managing, whether it is people or accounts, not in doing. Very few people get rich from doing because they aren't the ones directing flows of money.

I'll use the example of my brother. He's working as a contractor, small scale home stuff, and he does good work. He's better than most. But his income won't go up very far as long as he's doing the actual work, since he has only so many hours he can work. So he's working on a PhD and eventually may have people under him. Through him he can work effectively unlimited hours, just by having more people.

Workers have incomes limited by time while managers have incomes limited by employees under them. That's going to cause a huge income gap even with only small differences in ability, intelligence, motivation, etc.

Sven said...


Normally distributed outcomes do not automatically follow from normally distributed inputs. What matters here is the function that maps "ability" (however that is defined) to reward. Only if that is linear does normally distributed ability result in normally distributed reward.

To explain, imagine a simplified company with 1 boss and 99 workers and assume that we define ability as "whatever it takes to make you the boss". Now the boss may only be slightly more capable than the next most able employee, but because there is only one boss job, the second guy will have the same income as the bottom 10% in the company. A highly non-normal outcome from normally distributed inputs.

The non-normality of income isn't caused by a mysterious X factor that some people lack, it's caused by the structure of the economy. The ability->reward function is non-linear.

Spinks said...

The mysterious quality is to do with structural inequities in society. Which is why some people start out in life with the best education, trust funds, connections, et al. If you start with a lot, it's easier to end up with a lot.

Some people break the convention but very few, relatively speaking.

Andru said...

I believe that the form of the graph comes from 'living costs'. The lower segment spends most of their income on living costs, with little left for investment, while the top has much more income which they can invest.

Or at least if this is not an explanation, is a factor at least.

Xaxziminrax the Second said...

Of course you're hinting at your previous doomsday post, which was very interesting in its own right, but which your new 'wow only' rules cuts out.

So how is THIS post applicable to WoW?

Jeanie said...

Hmm I'm not sure if that was just me, but the post looks just like a restatement of the pareto principle (20% of the population keeps 80% of the wealth), albeit slightly different number and some really confusing example. Especially the second to last paragraph, reading it the third times and I still don't get what you imply.

In the bottom people there are really intelligent and really-really hard working guys making close to $100K by studying and working day and night, and there are punks who starve on the street.

Aren't you using salary as a mean to sort people into different groups ? If that's the case, then there is no "100k salary guy" that could belong to the
bottom group: he has to belong to the top group. Also how are your examples proved that each group is normally ? I can't seem to get the connection.

IQ is normal distribution doesn't mean that skill would be normal distribution too. Say for example if the society in a country can only support 20% of the kids to be educated, then the skill of that generation would be anything but normal distribution. I'm not explicitly saying that it's in the case in the USA, just that it's a possibility and there is no way we could know.

Also, one last thing is that wealth may not scale linearly with one skill, it could scale exponentially (which i believe is just the better explanation than your "binary factor" of skill), how about graphing a graph with smaller bar size, 1% 5% ?.

French Guy said...

Unfortunately, Gevlon, you mix up many different concepts like salary (or is it income? ...which is slightly different especially for the top people) and skill. And your post does not enter into the complex mechanisms of "why" such differences happen.

An over-simplified explanation is that people who have money or power can use their money to support/preserve/increase their power and reciprocally... As explained in Rousseau's (French philosopher) "discourse on the origin of inequalities amongst people", the powerful ones own something (money or power) which they don't want to lose and have an interest into building alliances that warrant them keeping the lead on the masses. The powerful unite against the weak and advance their own benefit in an "unfair" way (for future generations) : their offspring have better chances to access higher education thanks to money for tuition fees or better environments/material for studying, better jobs (through connections and opportunities), etc. This explains why the wealth is not a normal distribution.

As for the amplitude of this unfair/non-normal distribution, there are some interesting statistics like the ratio between CAC40 CEO's salaries and the standard worker's salary. In France (my country, which is the one i know more about), this ratio used to be around 40 in the post-WWII glorious 30 years of "full employment". This ratio is considered by some economists (source: France-Info) as "fair" or "reasonable". In the recent years, This ratio has increased to a shocking 250. The past 25 years have also seen a shift of around 15% on how benefits are distributed among employees and shareholders... which is one of the causes behind the subprime crisis as households' debt has kept increasing to support the countries' growth (in France as well as USA) while the shareholders (typically richer than the average) were cashing in some big fat dollars... Until some households could not pay back their debt anymore.

The way wealth is spread in capitalistic organisations is therefore pretty unfair or based on criteria which do not match my idea of "skill". That's why i'm posting this disagreement to the terms you use.

The Gnome of Zurich said...

What you see in picture 4 is what happens when you take a normal distribution and apply it to a base that is logarithmic. In pictures 1-3, you've essentially assumed a linear model. IQ points are linear relative to the normal distribution because they've been *defined* that way. IQ's of 67 and 133 are defined to be exactly 2 standard deviations from the mean.

In the real world, pretty much anything that involves growth of any kind (including money or any kind of economic activity) is logarithmically which, when over a normal distribution, gives a graph somewhat like your graph #4.

This is the mathematics behind behind Pareto's law: 20% of your X, account for 80% of your Y, for many different values of X and Y.

Income isn't fully normally distributed, but your graph doesn't really show where the normal distribution differs from reality, because it's largely confined to the top .1%. The graph you show is fully consistent with a normal distribution over a power law resource.

Campitor said...


The top 20% in America stay in the top 20% because they have a good network and regulary meet to strategize on how they can stay in the top 20%. It can be easily compared to the top 20% of raiding guilds. They are in the top 20% because they spend a lot of time theory crafting and crunching numbers to get the "optimal" raid composition and execution which in turn allows them to conquer content that would otherwise thwart the average idiot who thinks he can walk into a hardmode fight without doing any research.

Rich people put in the time and research to get into the top 20% - its never really "luck". Sure you can hit the lottery but the top 20% in America create wealth that last generations and are not a "flash in the pan". And just like the fire standing monkeys, if you are the real life equivalent and start costing the top 20% money, they will soon kick you out of the "inner" circle.

The biggest myth ever perpetrated is that the top 20% wealthy attained their money on luck or by brute force (such as working 120hours a week). They keep their wealth via research, planning, and actively lobbying the government to ensure only the most beneficial of business and tax laws are passed that favor them. They only associate with people who can help them keep or earn more money and rapidly denounce and kick out anyone who will cost them money.

Everyone complains about the top 20% but no one wants to put in the brain time and discipline required to get there which really isn't that hard. Find out what services or goods people want or find someone rich and show them how you can save or earn them money. Don't spend money needlessly (its not what you earn -its what you save), and do your research - you will be surprised how much in demand you will be in from the top 20% (gaming or RL). And the top 20% pay well =).

Big said...

Great post Gevlon. Where did you get the data?


Ulrik said...

How big a percentage of the earnings of the top 20% goes to CEOs? And how much of that is due to them being "more skilled" and how much is due to them simply being skilled at making sure the top dollars go to them?

Some skills are also more in demand than others, the skills to become a top CEO most noticably. I highly doubt that expertise in any other fields pay anywhere close in the US, even though those skills (doctors, engineers) are also vital for wealth generation.

Monkfish said...

I'm not sure that it's wholly reasonable to take the step from distribution of income to distribution of skill, unless you insist on a definition of skill along the lines of "actualized ability to achieve a certain income level" or some other such circular thing.
I'll wait and see what you define as the "mysterious factor."

The Gnome of Zurich said...

Azzur, the income distribution is a normal distribution times a power law distribution (what you get when you normally distribute ability+luck to acquire a power law resource).

Basically if you use log[income] (as you should, since all economic numbers follow pareto/benford laws etc.), the graph for income would look just like the other graphs.

Anonymous said...

An alternative explanation is that skills are distributed normally, but that the top actors (companies) realize that hiring the top people will require more than a linear increase in salary. It is similar in pro sports, a player that is 1-5% better often gets paid 10-20 times as much. Is ARod (320 million dollar contract) ten times better then someone with a 32 million dollar contract? No, he's just a little bit better, same as most of his extremely well played teammates thus allowing the Yankees to win more games on average. This is not my original idea.

The advantage to this explanation (which there have been a few studies exploring the actual skill gap) is that it doesn't require two or more classes of people, the pay scale naturally develops from the bell curve of the IQ.

Does this work for WoW? The top 20 percent, as mentioned in your post, often do 2x the damage or more than the people below them. But is that true or is that an artifact of small sample size? At any given time we only have 25 people in a raid and this sample size is not enough to say yes or no to curve shape. There are two approaches to answering my question, we can take many 25 person samples and merge them together or we can go online and look at the data aggregate servers that mine the open logs to rank players.

The dps curve, while appearing blocky, is actually quite smooth (at least as far down as those websites go). IE if the raid had 25000 players in it instead of 25 it would most likely have a smooth curve. I say nothing about the shape of that curve, it might still be better modeled by an exponential. To my mind it would be a linear increase until right at the very end, but that's just an opinion and we could argue about why all day.

@azzur: No, everything with a large sample size cannot be modeled as a normal distribution. Or rather you could do so but it would tell you less information than looking at a raw graph. Every data set has 2-3 ways of looking at it and while one of them is frequently turning it into a normal that's not always true.

Gevlon said...

@Azzur: absolutely NOT. Every RANDOM large sample can be described by normal distribution. The example (sheep + mule) was inserted exactly to prove this. No matter if you collect billions of sheep and mules, their "strength distribution" will have TWO peaks, one at the "average sheep", one at the "average mule". The large variance is nonsense. No matter how large the variance is, the bars must form an even staircase. With large distribution, the steps are larger, but still evenly paced.

@Olga: this is luck issue, therefore should form a normal distribution. I completely agree that having rich parents is important to be rich. However I doubt if it's the inherited money that matter. Just read about lottery winners. They got huge sum, and most of them were poor in 5 years.

@Samus: My country is much more corrupted than the USA according to all agencies (for example Transparency International). The "who you know matter more" is much more true here. And - just like it's with Olga - I'm not even saying you are wrong.

@Klepsacovic: you are actually PROOVING my point. You just claim that the "management skill". Read Sven's comment.

@Sven: you are right, however you'd have to explain why the "second best manager" simply quit his job and starts his own company. Since manager must oversee employees, the work becomes harder with the amount of workers. So the best boss will make worse job over 99 employees than the second best over 10, simply because his job is 10 times easier.

@Spinks: if you'd be true, we'd still be living in the medieval age. In the French revolution the sons of middle-poor man overcame the sons of barons. If "powerful man's son is powerful" is the rule with only a few exception, than the noble class would have 99% powerful man (and 1% exception), while the innoble would have only 1% powerful and 99% sheep.

@Andru: if you mean "survival cost" that would explain poverty lock. But the second 20% is far from poverty. The "living cost" is largely class-dependent, and for rich people it often contains outrageous spendings like heated pool.

@Xaxziminrax: have you actually read the post? I wrote that the bottom right looks exactly like a damage meter. Since the underlying quality is not RL ECONOMIC but RL HUMAN, it affects WoW equally.

@Jeannie: I'm saying that in the top 20% there are two kind of people a few "very strong sheep" and most of the "mules".

@French Guy: your comment does NOT oppose mine. You simply claim that "power" is the mystical skill.

@The gnome of Zurich: then the question is that why income obeys to power law instead of linear, despite common sense suggest linear. I mean if I work two times more hours, I get two times more salary

@Campitor: your example is flawed exactly because nothing would stop a fire-standing monkey to start research. What is the mystical quality that make them stand in the fire.

@Ulrik: I can dig you up this data.

Chirs said...

Most discussions like this come down to one thing - personal accountability.

Is it easier to become rich if you come from a rich family? Sure, of course it is. But America is full of stories of immigrants or the less-fortunate starting with nothing, and becoming rich.

Was it harder for them than it was for the trust-funded Northeasterner? Of course, but at the end of the day, all their hard work put them into a rich position. And then, their future generations can reap the rewards of having a trust-fund.

Iiene of Kul Tiras said...

Wow! You guys are a bunch of socialists. Being born into money, CEOs who only succeed because of connections... these are a TINT TINY percentage of the top 20%. A tiny percentage so small it's negligible.

People get rich in this country every day because of innovation, invention, and the management of the labor of others. That takes bravery, a willingness to risk security, and a decent plan (Not always a well thought out plan.. innovation is a process, not a preset plan).

You show me a broke person in America, and I'll show you someone who has defeated themselves through their misguided beliefs in the 'privilege', 'connectedness', or 'luck', of others.

I would say that the single greatest common factor in broke assed, whining about how the system is 'stacked' against them people is this:

They have no knowledge about how money works and how to manage it. In fact, they treat money as 'evil' and unconsciously sabotage their own ability to save or invest it. (The WoW equivalent of blowing all your gold on a Mammoth or a Motorcycle).

If you give a kid a paper route at age 12 and teach him about accounting, money management, and effective budgeting.... in 30 years he or she will be a millionaire.

Jeanie said...

@Gevlon: what I was asking is that: why is there mule in the top 20%? There should only be strong sheep there, if there is a mule that is doing better than a supposedly strong sheep, then essentially the mule is the strong sheep, and the strong sheep is the mule! Or are you using two different criteria there: one to classify them into group of 20%, and another one to classify whether they are sheep or mule. In that case it doesn't make sense.
As a side note, our current society has put too much emphasize on economic, which indirectly makes everyone to think that being economically skillful is the ONLY skill, or rather the only that matter, it's not true. The other skill, which are in the scientific or technical fields are just as important, if not more important (and they takes longer to master than economic skill to, imho). To me it's mostly a flaw of the current system: top scientists, inventors etc should be at least some where near top CEOs, not neccessary surpass them, but not a thousand time poorer either.
P/S: can we use lion and mule instead? Cause sheep and mule both looks weak to me, and actually confuse me during my post >.<.

Jeanie said...

Just to make myself cleared, what I meant in my reply is that: supposedly there is one VERY dumb people that is lucky to get a top position, then eventually he will fail, and getting back into his real group: the bottom 20%, just like there will be VERY intelligent people who will mess up thing one in a while. In the end, momentary success or failure doesn't make you better or worse, you have to judge one on his lifetime's work/accomplishment. So in the end, there can't be "a few strong lions and most of the mules" in top group: mules will fail, lions will raise to their rightful positions, there will always be lions in the top group.

Sven said...


You're right that "Mr second best" could simply start his own company. But that would leave him with two options: start a rival organisation in the same business or start again in a new market. In the first case, he is not only not quite as good as manager #1, but will also suffer under the disadvantages of start-up costs, lack of established routes to market, trained staff etc. Not a good route to wealth. If he tries again in a different market, he'll have the start-up costs, plus needing to learn a new business, which puts him at a further disadvantage.

In any event, there's no reason to believe that the outcome will follow that that linear ability->reward relationship that your post posits.

Part of the reason for this is competition. A competitive market magnifies small differences in price/quality because market share has many advantages in terms of efficient production, customer relationships etc, which causes a positive feedback loop - an initial small advantage leads to a greater one next year.

Think back to what happened when you were king of the AH and others who weren't as skilled as you tried to join in. Who won? I doubt you were really 10x cleverer than your rivals, but I wouldn't be surprised if you made 10x as much money as them. Small advantages can turn into large differences in income over time.

Anonymous said...

Many posts for something so obvious, USA is a place where a bunch of dominant people controls all the others. It's called Oligarchy/Ολιγαρχία(ολίγοι αρχούν, few rule) and it's a social by-product of the most savage ideal of all until now: Capitalism

That's why 20% of america's people got 60% of the wealth,
no luck, skill or any other "secret" quality does explain that, because obviously it does NOT derive from those. It derives straight from the abyssal greediness of some powerful Bankers and "Big" guys in general who managed to pass the Federal Reserver Act at 1913, and thus forging the slavery of all U.S. citizens as well their own goverment, due to the Eternal Debt*

* The Federal Reserve System is controlling 3 things:
Central Bank, which produces the $
Interest Rates

The Central Bank loans the $ needed to your goverment. That essentially means, for every $ produced, your goverment must return to the central bank 1 $+ a fraction of it (interest). So your goverment must find money to pay the interest back too.
But, with Central Bank being the only legal producer of $(monopoly on producing the national currency), it is obvious you gov. can't ever payback as they owe more money than the sum of the produced dollars.
So, one thing's being created from the day 1 of this system: DEBT.

But, eventually, our days will come.

The Gnome of Zurich said...

Gevlon, it has to do with investment of social and human capital.

Thinking that linear is common sense because at a wage-earning job working twice as long results in twice the pay is marxist thinking (i.e. "labor is the source of all value").

OTOH, when you invest money, you normally expect a percentage return, invest more money, you get a greater percentage return, and experience logarithmic growth.

Well human and social capital works like money, the more you have, the more you can get, there is logarithmic growth.

Income data (and all real economic data) obeys Benford's law (that there are more '1' digits than '2' digits than '3' digits etc. -- the technique can be used to spot fake data in audits). If income were a linear phenomenon, or some other non-power-law phenomenon it would not. Benford's law is based on the numbers in a logarithmic distribution. Do a google search, it's a fascinating subject.

Sometimes common sense is not sense.

Kristine Ask said...

@Iene of Kul Tiras

It doesn't matter if you are a socialist or capitalist. The vast majority of social studies over the last 200 years have shown us that differences are reproduced. That the person coming from a low income and educational background, is less likely to grow up rich and welleducated.

All the reasons mentioned so far: lack of knowledge, lack of contacts, lack of access to finances, poor luck etc etc are all factors that are keeping this reproduction of wealth and poverty stabile. I dont think anyone here is arguing that it's how we want it, but it's how it is.

How we can change this and create greater socioeconomical mobility is the political issue.

You say yourself "They have no knowledge about how money works and how to manage it." And I agree. But, being a socialist I believe in creating an educational system and workplace that will ensure that provides this, instead of letting the "forces" of the market be the teacher.

Klepsacovic said...

I must have missed it, what was your point? You showed a few graphs, said one is different, made references to WoW, and then rambled off asking why the graph isn't a normal distribution, ending with a mysterious "I'm not going to tell you why."

@Iiene of Kul Tiras: Labeling is always the way to go. Yes.

CEOs do succeed because of connections. That doesn't mean corruption or oligarchy, just that networks of people tend to be much more productive than isolated individuals. Since they are social, they will tend to work with their friends and less with outsiders, strengthening their networks.

Of course there are exceptions, the lone inventor and the guy who got in at just the right time, but only so many people can be rich, since it is a relative description. Of course if we look back we'll all look rich, seeing as the majority of us rarely starve to death or wind up homeless. This isn't due to us being better than the previous generation, just that the previous generation build up a great system for us.

Andru said...

I'll just take a stab in the dark.

Is the 'mystery quantity' education?

French Guy said...

Gevlon said : @French Guy: your comment does NOT oppose mine. You simply claim that "power" is the mystical skill.

As stated in conclusion, my comment was not meant to "oppose" yours but to disagree on the terms used. Indeed, "power" (whatever its form) is the magical... variable (i prefer this word). It is just misleading as well as frustrating to refer to it as "skill", since it does not need to be acquired... due to social pre-determination, this is mostly inherited depending on you being born in the right family or not.

Lujanera said...

Gevlon claims:

"The bottom-right graph is not about WoW. It's the income distribution in the USA. The top 20% has 60% of all income in 2003, the last year when I could dig up such data. While you are most probably not shocked by this graph, it completely destroys a common belief that most people - most probably you too - share: that the skills of people are distributed normally."

Gevlon is conflating "skill" and "income", which is bad for a variety of reasons. I illustrate two of them below.

First and obviously, some people's income is not earned (eg, inheritance, the lottery), meaning that it is not the result of skill.

Second, a distribution of income that is not normal does not imply that skill does not have a normal distribution. As an example, consider running speed versus olympic gold medals won. Running speed is (roughly) normally distributed, but gold medal distribution is extremely non-normal in distribution (see graph: Most people can run 25% the speed of an olympic sprinter, but there is no chance of getting 25% of a gold medal for that achievement. In other words, the rewards of skill do not scale linearly with skill.

Anonymous said...

Gevlon states:

"Every RANDOM large sample can be described by normal distribution."

For anybody foolish enough to believe the above statement, I recommend reading a little more on the subject of mathematical distributions and/or reality. The truth is that a great variety of natural phenomena do NOT fit a normal distribution.

As a starting point, I suggest "Some Misconceptions about the Normal Distribution" (

(Note: for anybody trying to weasel out of this by appealing to 'RANDOM', I should note that almost nothing in life is truly random. Distribution of skill certainly isn't, given the various selection pressures that exist within the world.)

Campitor said...

Gevlon said: @Campitor: your example is flawed exactly because nothing would stop a fire-standing monkey to start research. What is the mystical quality that make them stand in the fire.

Not all fire standing monkeys start off that way. The dps meter and their quest for dps meter leetness causes them to develop tunnel vision. I have often observed players who never were fire standing monkeys, but suddenly find themselves with the gear/spec/rotation that allows them to put out more dps than before - they get greedy, start playing to the meters, and suddenly become those monkeys will all hate.

Rich people are like that too - they suddenly reach a plateau where they have so much money they develop tunnel vision and forget that money gained can also be lost. You've never heard of a rich person going poor? Donald Trump almost went bankrupt because he over extended himself and almost lost it all... he became a fire standing monkey but he wised up.

All of us have the potential to be fire standing monkeys even if its only for a little while:

And every fire standing monkey has the chance to get better if he wants to. Getting rich in america isn't all that hard. If you earn 80k or more a year you are already making more than the lower 70% of the population. The median income for most households is 34k a year.

Wealth is attainable if you work at it. But most of those I see complaining about how hard it is to get ahead don't really put the effort or sacrifice to get wealth. To get wealth requires discipline, thrift, industry, and research.

Anonymous said...

I'll just leave this here...

Tobold said...

The distribution of talent is a normal distribution, the distribution of income gained with that talent is exponential. That is the reason why your curve is different, you multiplied your gaussian distribution with an exponential function.

In other words: A person with a median income, in the exact middle of the curve, doesn't earn all that much more than the person at the poverty level, I'd estimate about 4 times that. But the CEO earns 400 times the income of the median income guy. That is what screws your curve, and the economy.

Valkyrie said...


Interesting post. If you haven't already, I suggest you pick up a copy of "The Black Swan" by Nassim Nicholas Taleb. A large part of the book deals with sectors of society that are not subject to the traditional, Gaussian, bell curve.

Michael said...

Actually the income distribution is much more severe at the top. E.g. 20+% of income is 1% of population. 10% is 0.1%.

Super-Rich people use hacks and exploits!!!

Also the outcome you see in chart 4 occurs when you take a parameter and it has a non-linear impact. e.g. IQ increases you ability to earn money and also increases your ability to invest well.

In the same way PVP skill lets you get the best PVP gear. Therefore the difference between average and good PVPers is multiplication of the gear gap and skill gap.

Anonymous said...

For things like income, it matters where you are talking about mean or median.

I also would not expect normal distribution; I am used to the "80/20" rule. Very roughly, 80% of your sales come from the 20% largest customers. 80% of your oil discoveries/sales/inventions come for your top 20% employes. etc.

It is why [top performers claim that] top performers are worth much more than average performers.

There is also only one axis here. It is a personal preference who you consider the most successful: a stay-at-home Mom with 0 income, a 40 hour per week happily married parent who earns $75k or a twice-divorced, childless CEO making $15 million.

There is also "satisficing." I want the medical team who operates on my brain tumor, or vasectomy, to be the best regardless of their personality. But there are certainly skilled players who are obnoxious enough that I would rather never see the LK than to raid with them. Except Bliz has made it so virtually anyone can see the non-hard LK a couple of months after the top tier. So I want to be with good people; but I am not so insecure that I really am driven to prove something in a video game. Certainly what little "success" there is in a game is not worth putting up with some people. But neither is being around true M&S. It is a balancing act.

The Gnome of Zurich said...

"Donald Trump almost went bankrupt because he over extended himself and almost lost it all... he became a fire standing monkey but he wised up."

This is a classic example of wealth begetting more wealth. Trump wised up to an extent, but his wising up came after he went broke. For most people that would mean he'd end up a working stiff, and maybe 10-20 years down the road be very well off again if he is smart and a bit lucky.

Donald trump *did* go insolvent (broke) in financial terms (I don't remember whether he was forced to declare bankruptcy), but once you have made enough money to be *famous* for it, that represents social capital that doesn't go away just because you go broke in $.

DT used that social capital (celebrity status) to get a TV show, not something your typical middle-class small business owner who goes bust could realistically do.

Anonymous said...

You should check for Poisson distribution for the 'luck' factor imo...

Anonymous said...

Realize this is old and few people if any will see it, but all those pointing to Pareto distributions and exponential functions have some explaining to do.

There's no reason to think wealth accumulation should not be a normal distribution. As I cite here it is for most of us:
"They found that while the income distribution among the super-wealthy - about 3% of the population - does follow Pareto's law, incomes for the remaining 97% fitted a different curve - one that also describes the spread of energies of atoms in a gas (see graphic)."

It's only the super rich that are actually reflecting a different type of function, so it still doesn't explain the graph we end up with, which can probably be accounted for because wealth accumulation is skewed unfairly.