[This post and its associated comments were originally published on Cohost.]

Note to stats nerds: I too have read Clauset, et al., and am well aware that many things claimed to follow a power law actually do not. (For example, this appears to be true for Patreon earnings.) But “I fought the log-normal distribution and the log-normal distribution won” doesn’t have quite the same ring to it.

If you happen to listen to “Discover Weekly” on Spotify (as I do), or regularly check out musicians on Bandcamp (as I also do) then from time to time you may have thought to yourself, “Wow, this is really good! Why haven’t I ever heard of them?” Apparently there are more musicians with real talent than there are popular and successful musicians, and sometimes the most talented are not necessarily the most successful.

This experience is not confined to music, but applies to other areas as well. For example, I suspect that hidden in the lower half of Patreon projects by number of patrons there are writers and artists whose work is as worthy as that of those who occupy the top 100 places.

Why should this be? That’s the key question for today’s post. It’s a very political question, in that proposed answers are often used to justify existing distributions of fame and wealth, or alternately to deny those justifications. I’m still exploring this general topic, so you can consider this just one take on the subject, with others possibly to follow in future posts. (WARNING: This will be a bit long.)

The proposed answer I’m going to present in this post is adapted from Sornette, et al., “The fair reward problem: the illusion of success and how to solve it.” The general idea is that when we look at things like the number of views on YouTube, the number of listens on Spotify, or the distribution of Patreon earnings, we’re seeing the effects of 1) individual talents influenced by lots of little things that add up (and hence result in a normal distribution), which then 2) combine through multiplication to produce a log-normal distribution of overall skill at artistic (or other) endeavors, and are then 3) supplemented by luck to produce a power law distribution (at least at the high end, and possibly at the low end as well).

It all adds up

Let’s start with a specific talent, for example, having a good singing voice. I’m no anatomist or vocal coach, but I can think of lots of little things that might influence this: size, structure, and health of the vocal cords, size and structure of the mouth, throat, nasal passages, and sinuses; size, shape, and motility of the tongue, lung capacity and diaphragm strength; the ability to control one’s voice (e.g., to accurately hit certain pitches); and so on.¹

Some of these things might be determined at conception (genetic heritage), some in utero (by random acts of development), and some after birth (e.g., being able to get a music education and afford voice lessons). The relative importance of these can be and is debated, but my point here is simply that most of these influences act relatively independently of each other, and together they add up to determine the overall quality of a person’s singing voice.

If multiple independent things do add up together to determine vocal quality, the result when we look at voice quality across the population as a whole should be a so-called Gaussian or “normal”² distribution, with a hump in the middle representing people with average singing voices, a tail at the left representing people with below-average singing voices, and a similar tail at the right representing people with above-average singing voices.

Why should this be? Think of having a really excellent singing voice as being the equivalent of flipping a coin and having it come up heads (say) 95 or more times out of 100 times, and having a really bad singing voice as having it come up up tails 95 or more times out of 100 times. There are relatively few ways that you can have a coin flip come up heads (or tails) 95% of the time, but many (many) more ways that you can have a coin flip come up roughly half heads and half tails. So, in practice most people would end up in the middle, not at the tails—thus the central hump.

Go forth and multiply

Suppose a person has an excellent, or at least well above average, singing voice. Does that mean they’ll have success as, say, a singer-songwriter? No, because a singer-songwriter by definition also needs to be able to write songs; more specifically, they need to write both melodies and lyrics. So there are now three things that they should ideally be well above average in, and those things are relatively independent: there are people who can sing well but not write catchy melodies, people who can write catchy melodies but not write good lyrics, and so on.³

To pull some numbers out of the air, let’s say that 20% of the population can sing pretty well, but only 5% can write catchy melodies and only 10% can write reasonably good lyrics. Then out of 100 million people we’d expect 20 million (20% of 100 million) to be able to sing well, 1 million to be able to sing well and write catchy melodies (5% of 20 million), and 100,000 (10% of 1 million) to be able to do all three. So in this example only 1 in 1,000 (100,000 out of 100 million) people have what it takes to be a singer-songwriter.

But it doesn’t end there. A potential singer-songwriter who wants to be successful also has to have the drive and conscientiousness to write and record lots of songs, the energy to tour, the ability to connect with audiences, the savvy to navigate the music business, and so on. Each of these requirements further reduces the potential talent pool, so that it may be that in a population of 100 million people there’s only about one in a million people who have what it takes to be a successful singer-songwriter.⁴

You can apply a similar analysis to any creative endeavor: writing novels, drawing comics, filming movies, making interesting podcasts or entertaining game run-throughs, and so on. In all of these cases many relatively independent factors will multiply together to determine overall skill-based success. The result will be a log-normal distribution: instead of most people clustering around an average level of success, with smaller tails to the left and right (as in a normal distribution), almost all people will have little or no success, and will thus form a very large cluster to the left. There will then be a very long right tail, with only a very few people in the extreme right of the tail having great success.

So, to sum up thus far: individual talents are hypothesized to be due to the additive effects of many independent factors, and thus to be normally distributed. However, having an overall skill set conducive to success in a given field of endeavor is hypothesized to be depend on the multiplicative effects of many different and relatively independent talents, and thus to follow a log-normal distribution.⁵

Luck and pluck

However, having an individual talent or even an overall set of talents is not necessarily sufficient to achieve success; often a fair amount of luck contributes to success, artistic and otherwise. We are used to attributing people’s success to talent and hard work—and of course people who are themselves successful are often the most extreme proponents of this. (After all, who wants to think that their own success is partly—let alone mostly—a matter of chance?)

This habit is so pervasive that we often attribute success wholly to merit even when it’s explicitly made clear that that’s not the case. For example, when people think of the 19th century novels by Horatio Alger, Jr. (when they think of them at all), they think of them as portraying the rewards that come from hard work. But if you actually read some of them (as I did), it’s clear that they are really stories of “pluck” and “luck”, with the latter typically given pride of place.

For example, in Alger’s first two novels, “Ragged Dick”, a homeless shoe-shine boy, is hard-working, honest, and open to new opportunities. But he becomes the successful businessman “Richard Hunter” only through a series of circumstances that combine mundane good fortune with incredibly implausible coincidences.

So, how might the effects of luck be modeled? Sornette, et al., treat it as an random additive component on top of what they call “overall skill.” They assume that overall skill is log-normally distributed (as discussed above) and acts to increase one’s already-achieved success by some percentage during each time period, with the exact percentage depending on the overall skill. Luck then acts to randomly enhance or counteract this effect of overall skill in each time period.

However good or bad luck does not affect everyone equally, but rather depends on a person’s appetite for risk: those who take more risks may benefit more than others from a given event of good luck, or may suffer more than others from an event of bad luck.

We see this, for example, in the Horatio Alger novels discussed above: the luckiest event of Dick’s young life occurs when he rashly leaps from a ferry to save a young boy who’s fallen overboard. The boy turns out to be the son of a business owner, who rewards Dick with a job in his establishment; the boy’s mother subsequently gives Dick a thousand dollars as a token of her own gratitude.⁶ But of course, in real life Dick’s selfless act might have brought no reward at all, or even resulted in his own death.

Modeling the effects of luck

As with overall skill, Sornette, et al., model the degree of risk taking using a log-normal distribution, presumably because, as with skill, it arises from several factors multiplied together: personality, social and economic situation, and so on. Thus some people would have an order of magnitude or more appetite for risk than others, and would be disproportionately rewarded (or punished) for their good (or bad) luck. Based on their simulation exercises they come to two conclusions:

First, they claim that the effects of luck may combine with the effects of overall skill to convert the distribution of overall success from a log-normal distribution to a power law distribution (as shown in the right hand graph above): at the top end would be people who benefited from extraordinary good luck and a taste for risk, beyond what their overall skills might justify, and likewise at the bottom end could be people with relatively high overall skills who have suffered bad luck of various kinds.

Second, they point out that in the short term it may be difficult to impossible to separate the effects of talent vs. luck. Only after a few years or even decades will it likely become apparent who has real staying power based on true talent and whose success was simply a matter of being in the right place at the right time, and little more than that.

Sornette, et al., give the example of success in investing in this context, but we also see this in artistic fields such as music. For example, think of all the acts who had #1 hits in their day but have had no lasting impact whatsoever. Think also of those acts who never achieved success due to bad luck of various kinds—internal conflicts, label troubles, financial problems, ill health or the death of a band member, or simply being out of step with contemporary trends—but who were rediscovered years later and acknowledged as exceptional artists. (Of course, in the meantime they lost out on the cumulative rewards of the success that eluded them.)

Conclusion

Sornette, et al., present one view of the interaction between talent, luck, and the society that rewards them both. As I mentioned above, there are other possible models as well, some putting more stress on the importance of luck, some putting more stress on talent, and others highlighting different factors, like the initial circumstances from which artists emerge.

But the overall picture is fairly clear: almost all would-be artists will be unsuccessful in both relative and absolute terms, and only a few artists will be truly successful. The question then becomes, what, if anything, should society do in terms of changing this picture? In particular, what stance should we take in terms of supporting current artists, or encouraging more people to become artists?

This is an especially pertinent question given the fear (or hope, as some might say) that we will be overwhelmed with a flood of AI-generated art (or “art,” in quotes, as some might say). Should we just accept that this is the way things are, and that it’s pointless to try to change it? I don’t personally believe that, but my thoughts on the matter are not yet fully-formed enough to summarize here. I’ll try to do that in a future post.

Royal Assassin (@RoyalAssassin) - 2023-02-26 16:42

Imagine being lucky enough to be born with a predisposition for having a good work ethic. Alas.

Frank Hecker (@hecker) - 2023-02-26 17:58

Yep, there are a lot of predispositions I wish I was born with :-(

Mightfo (@Mightfo) - 2023-02-26 16:46

Great post. Im also reminded of the quote by Gould “I am, somehow, less interested in the weight and convolutions of Einstein’s brain than in the near certainty that people of equal talent have lived and died in cotton fields and sweatshops.“

Even if you exclude economic factors, the vector of “did they pursue something they had talent for?” is a big factor imo. What are the chances of discovering different talents? Of pursuing those talents over other careers or other ways to spend time? Different cultures reward different talents and highlight different talents. Preexisting industries can be key to cultivate talents, like how voice acting in Japan is a lot more developed than most elsewhere. Audience size and language are also a major intersection- i think Finnish and Romanian are particularly beautiful languages, but they dont have the same audience to provide reverberating support for music and so on as English, Chinese, Spanish, etc.

Ill try to think more later about an idea of how things should be in this regard and maybe share those thoughts.

Frank Hecker (@hecker) - 2023-02-26 18:03

Your comments on place and time are very much on point. One of the papers I didn’t highlight was about how succeeding in the contemporary art world (i.e,, the sorts of art featured in, say, ArtForum) is highly influenced by the prestige level of the institutions an artist is associated with very early in their careers: art schools, galleries, etc. A great artist who comes from the middle of nowhere is going to find it difficult to impossible to achieve success.

I’d love to hear your thoughts on “how things should be”. (As I said, my own are still half-baked.)

[This post and its associated comments were originally published on Cohost.]

If you’re like me, you probably contribute to a project on Patreon. You may have even started a project on Patreon yourself, or are considering doing so.

Patreon boasts about its success: “8 million+ monthly active patrons … 250,000+ creators on Patreon … $3.5 billion paid out to creators.” Other sites run articles like “How Much Money Can You Make on Patreon?” and “25 Patreon Statistics You Need to Know.” There’s even a Patreon project devoted to collecting and publishing such statistics on an ongoing basis.

Occasionally you’ll find someone injecting a note of caution, as in a relatively in-depth analysis from five years ago. But the one set of statistics I could never find was about exactly how Patreon earnings were distributed across the whole set of projects, including what typical Patreon projects could expect to earn, and whether there was a straightforward way to characterize that distribution of earnings. So I decided to try doing that myself.

If you’re interested in the gory details, see “Distribution of Earnings Among Patreon Projects Charging by the Month.” The document is CC0-licensed, as is the R code used to create it. However the actual dataset I used (from Graphtreon) is not publicly available; if you want to replicate my work you’ll need to pay for the data yourself. (For what it’s worth, I don’t have a problem with Graphtreon charging for this; it took work to collect this data, and it has commercial value.)

One way to think about Patreon is to think of it as its own country (or state, or province), one with a population of over a hundred thousand. More specifically, Patreon had about 220,000 projects that reported their number of patrons as of December 2022, but only about 130,000 of them reported nonzero earnings from monthly charges. (About 80,000 projects didn’t report their earnings publicly at all, a few thousand charge by the podcast or video, not by the month, and a few hundred reported zero earnings.) Those are the projects I looked at in my analysis.

If Patreon were a country (“Patreonia”) then it would be by far the most unequal country on earth. As you can see in the left graph above, project earnings drop off extremely fast once you go past the top-ranked projects. In fact, the drop-off is so extreme that it’s better visualized using a so-called “log-log” plot, like the right graph above. While the top projects on Patreon earn hundreds of thousands of dollars a month, the median project (half earn more, half earn less) earns $25 a month, or less than a dollar a day.

This level of inequality is greater than in any country in the world; if you’re familiar with Gini coefficients, the coefficient for “Patreonia” is 0.84, while the country with the highest level of inequality is apparently South Africa, with a coefficient of 0.63. (A Gini value of 0 means income is equally shared, while a value of 1 indicates “perfect inequality” — one person gets all the income, everyone else gets nothing.)

I find it helpful to consider “Patreonia” as consisting of four separate groups of projects, each ten times larger than the last; together these four subsets account for almost all of the projects that I had valid data for. You can think of them as communities of different sizes and economic circumstances.

Patreon Heights

The first group, the “0.1%” of “Patreonia,” consists of the top 100 projects with nonzero earnings from monthly charges. The median project in “Patreon Heights” had almost 3,900 patrons and a monthly income in December 2022 of almost $25,000, or about $300,000 a year. This corresponds to an especially affluent neighborhood in an especially affluent county in the US, like Loudoun County, Virginia, which has a median household income of around $150,000, the highest of any US county.

Patreon Grove

The second group, the “1%” of “Patreonia,” consists of the next 1,000 projects with nonzero earnings from monthly charges. The median project in “Patreon Grove” had almost 800 patrons and a monthly income in December 2022 of about $4,200, or about $50,400 a year. This is well under the current median household income in the US, which is about $70,000. A US county with a comparable median household income and population is Crockett County, Texas, a rural county in the western part of the state.

Patreonville

The third group consists of the next 10,000 projects with nonzero earnings from monthly charges. The median project in “Patreonville” had just over 100 patrons and a monthly income in December 2022 of about $650, or about $7,800 a year. This is well below the US Federal poverty line of $12,880 for a single-person household, and is lower than the median household income for any county in the US, even lower than that for Adjuntas, Puerto Rico, the poorest jurisdiction for which the US Census Bureau has data. (The median household income for Adjuntas is around $12,000 a year.)

The rest of Patreonia

The fourth and final group consists of the next 100,000 projects with nonzero earnings from monthly charges. The median project in the rest of “Patreonia” had 5 patrons and a monthly income in December 2022 of about $28, or about $340 a year. This is comparable to incomes in the poorest countries on Earth, places like Somalia, Uzbekistan, or the Democratic Republic of Congo.

Patreon and the “creator economy”

At this point you might say to me, “Frank, these are really stupid comparisons. You can’t compare someone running a side gig on Patreon to a person eking out a meager living in the world’s poorest countries.” And you’re right, but: Patreon, Substack, OnlyFans, and similar services are pitched to “creators” as a way to earn at least a partial living by “monetizing” their “content.”

Not a month goes by without another blog post, news story, or website heralding the “creator economy.” It’s attracting the attention of venture capitalists, who’ve funded a host of startups, all eager to help you realize your dreams as an artist, writer, musician, filmmaker, game designer, or “influencer,” in return for just a few percent off the top.

But the reality? Not so rosy. What I’ve tried to do is to put some more numbers behind that assertion.

P.S. to math-savvy web developers: If you’d like to put together a different kind of “how much money can you make on Patreon?” calculator, it’s pretty easy to calculate the odds of a project earning more than a given amount of money on Patreon. Patreon earnings for the month I analyzed were best fit by a log-normal distribution with μ of 3.33 and σ of 1.84. So to estimate the probability of earning more than x dollars, you can plug x into the formula for the log-normal cumulative distribution function (you’ll need the erf() function for this), and then subtract the result from 1. For example, the probability of earning more than $100 a month is 0.24, or about 1 in 4, while the probability of earning more than $1,000 a month is 0.026, or less than 3 percent.

@Janet (@Janet) - 2023-01-21 11:05

messed up.

but you dont even have to go online. same goes for GEMA in germany. thats the state org handling musical rights, only a few percent of artists (mostly song writers and producers) earn anything at all. if you are a tiny band, there is no way you will ever get money from GEMA, yet any music made will automatically be handled by GEMA, except in case you find another org, but GEMA had a monopoly so you were sool. Some years ago another such org was founded just so you wouldnt have to deal with GEMA anymore… ah but im not really in the know, i only read about it when the new org C3S was founded

Frank Hecker (@hecker) - 2023-01-21 12:38

Thanks for stopping by to comment! I believe the US has the same system for music, a duopoly between ASCAP and BMI.

june (@junelinked) - 2023-01-22 05:54

a little different; ASCAP/BMI are performance rights only (and do have some small, private, for-profit competitors - notably SESAC) whereas GEMA is an integrated CMO (mechanical + performance), and actually has more restrictive assignment provisions at least in part since ASCAP/BMI are under consent decrees. the market dynamics end up similar though, small writers are lucky to make enough to hit the payout threshold

Frank Hecker (@hecker) - 2023-01-22 11:52

Thank you for correcting me!

jeroknite (@jeroknite) - 2023-01-21 13:46

… Of course the poorest place in the US is in Puerto Rico :c

Frank Hecker (@hecker) - 2023-01-21 14:15

Thanks for the comment! I was curious about this, and checked the median household income statistics on Wikipedia. The 40 poorest jurisdictions in the US and its territories are in Puerto Rico, as are 58 of the 60 poorest.

Maynard (@Quelklef) - 2023-01-21 14:20

is there large variance in the size of patreon projects (≈ number of people involved)? If we account for this by, say, dividing earnings by number of people, do the graphs seriously change?

(My first reaction to the graph was that ”this makes sense; the large projects get the most funding but also have to pay out to more people”. But actually I have no clue what the distribution of project sizes on patreon looks like, nor if size correlates with earnings)

Maynard (@Quelklef) - 2023-01-21 14:32

Say we very generously assume that all Patreon Heights projects are run by 100 people, Patreon Grove projects by 10, Patreonville projects by 1, and that the rest of Patreonia consist of abandoned projects that people forgot to unsubscribe from.

Then in Patreon Heights we have median income per person per month of $250; in Patreon Grove we get $420; and in Patreonville we get $650

Frank Hecker (@hecker) - 2023-01-21 15:53

You can find a list of the highest-earning Patreon projects at https://graphtreon.com/top-patreon-earners. You can check them out yourself (I haven’t), I suspect that the highest-earning projects aren’t run by anywhere near 100 people.

Maynard (@Quelklef) - 2023-01-21 22:07

Hmm, yeah. Looks like at least the top few are mostly podcasts featuring a handful of people. Presumably they employ editors and publicizers, etc, but I would be shocked if any number was approaching 100

Maynard (@Quelklef) - 2023-01-21 22:19

A four-host podcast making almost $200k a MONTH is absolutely bonkers; holy shit

Frank Hecker (@hecker) - 2023-01-21 15:49

Thanks for commenting! I cover some of this in the detailed document I linked to, in the section ”How are earnings and the number of patrons related?”; I’m not sure if you’ve had the chance to look at that or not. The short answer is that mean earnings per patron was $6.83 (with a standard deviation of $12.01), and the median earnings per patron was $4.50. Only 15% of projects have earnings per patron over $10, and very few have earnings per patron over $20.

Maynard (@Quelklef) - 2023-01-21 22:18

Ah, I had missed that link; sorry! (That is a very nice analysis)

I think I phrased my question poorly. I’m not interested in earnings versus number of patreons, but versus number of creators. Looking at Graphtreon, seems like this data isn’t available? I guess if it’s not something Patreon asks for people to self-report on, then it’s not really possible to generate in bulk.

Frank Hecker (@hecker) - 2023-01-22 00:30

To my knowledge there’s no source of data on the number of people per Patreon project. That’s why I was careful to refer to ”projects” not ”creators”.

Mightfo (@Mightfo) - 2023-01-21 21:44

Im not sure how related this is, but this reminds me of an experiment a music site did where they released two beta versions: One where you could see the number of views a song got, and one where you couldnt. The one where you could see the views, completely random songs would get a snowball effect of views and people would be really into them, but those songs were not significant at all on the other.

I feel like that sort of ”attention economy snowballing” is a key part of disproportionate success dynamics like this.

Frank Hecker (@hecker) - 2023-01-22 00:32

A very good comment, thank you for foreshadowing some of what I hope to be able to write about in future.

㋬Zen1th (@zenith391) - 2023-01-23 16:16

That’s very true, and it’s also why I like cohost. You can’t see like counts or follow numbers which brings us closer to the version where ’we can’t see the number of views’. I might be following complete nobodies or the most popular account here, I can’t tell the difference.

Pat (@tekgo) - 2023-01-23 16:29

As you noted in the caveats a number of projects with high patron counts don’t report earnings. Looking at the Graphtreon top projects list only 14 of 50 report their earnings. I’m curious if you graph all the projects by number of patrons(that report that data) does it have a similar distribution to the earnings rank graphs?

Frank Hecker (@hecker) - 2023-01-23 16:59

Thanks for commenting! Yes, the distribution of number of patrons per project has a similar sharp drop-off once you get past the top 100, 1000, etc. I actually did an analysis of this as well, but the analysis document was getting really long and I decided to focus primarily on earnings. I may do a separate document discussing the number of patrons vs. rank in number of patrons. I’m going to guess that it follows a log-normal distribution too.

exodrifter (@exodrifter) - 2023-01-24 02:35

I have a lot of complicated feelings about the ”creator economy” and this is part of it. Many of the people I know that participate only do it on the side for fun and use the extra income to afford a few things relevant to the creative pursuit they are doing for fun. And although we are small, we also like to support each other, but every time money changes hands, the platform takes a cut…

Meanwhile, I would like to work full time on my creative pursuits, but it’s hard to imagine how that would work given the slim odds. I don’t really think I’m trying to say anything in particular here, it’s just difficult for me to think about.

Frank Hecker (@hecker) - 2023-01-24 19:28

Thanks for commenting! To repeat what I wrote earlier, I am not trying to discourage people who want to supplement their income via Patreon or similar services. My main target was/is VCs and startups that are pushing services like this as the answer for people who want to support themselves full-time (or nearly so) as artists.

Censa (@censa) - 2023-01-29 23:23

huh this was really interesting. Thank you for sharing your findings!

Let’s go back to the tables I included in my previous post, repeated here for convenience. First, here’s Howard County vs. nearby counties and other jurisdictions:

and then Maryland vs. other high-income states and the United States as a whole:

Note the third column of the above tables, the Gini coefficient. The Gini coefficient (or Gini index, as the Census Bureau refers to it) measures the distribution of income, as opposed to the level of income. Its calculation is a bit more complicated than that for median household income; rather than discuss it here I’ll just refer you to my previous explanation.

For present purposes you just need to know that the Gini index has values between 0 and 1 (or 0% and 100%, depending on the source), that a value of 0 corresponds to a completely equal distribution of income (all households’ income is the same) and a value of 1 (or 100%) corresponds to a completely unequal distribution of income (one household receives all income, all other households have none). In practice almost all societies have Gini index values somewhere between 0.30 and 0.60. Also note that the Gini coefficient can be computed based on before-tax income or after-tax income; the Census Bureau figures are computed using before-tax income.

Recall again that the Gini index measures distribution of income, not the level of income. So, for example, for 2012 Howard County had a Gini index of 0.3909. Since this was below the overall US value of 0.4757, distribution of income in Howard County was somewhat more equal than in the US as a whole. Catoosa County in Georgia had a Gini index of 0.3904, almost identical to that of Howard County, but its median household income was only $42,251, almost as low as that of Baltimore city. Howard County is a place where everyone is (relatively) equally rich, Catoosa County is a place where everyone is (relatively) equally poor.

This point also applies to places of relative income inequality as measured by the Gini index: For example, Fairfield County in Connecticut (mentioned in the previous post) has one of the highest Gini index values in the United States at 0.5459, along with a median household income of $79,841 (ranked 43 in the United States), while Richmond, Virginia, has almost the same Gini index (0.5347) but very low household income ($38,926, less than Baltimore City). Fairfield County is rich and unequal, Richmond poor and unequal.

Why is income inequality lower in Howard County—not to mention Loudoun County, which ranked 5th in the US in 2012 in terms of income equality? It’s simply that the economies in both counties are heavily driven by Federal spending, with many people in the counties working for either the government or a government contractor. At the low end government jobs pay better than equivalent private sector jobs, while at the high end they pay worse.

This is true of contractor jobs as well: For example, a skilled programmer will be paid well if they work for a government contract, especially if they have a security clearance, but not as well as if they worked for an investment bank or hedge fund. It’s true also of entrepreneurs: Most people can name several tech billionaires (for example, Steve Jobs, Jeff Bezos, Mark Zuckerberg, Larry Page and Sergey Brin) but would be hard-pressed to name any billionaires who made their fortunes through government contracting. (Ross Perot is the only one I can think of at the moment.)

The net effect is that the spread of incomes in Howard, Loudoun, and other suburban Maryland and Virginia counties is compressed relative to other places: fewer really poor people, and fewer really rich people, but lots of people making good incomes.

So is relative income equality only a function of a government-dominated economy? Not necessarily; for example, per Wikipedia Switzerland, a country in the top 5 of the Heritage Foundation Economic Freedom Index, has a Gini coefficient of 0.409, just a tad above Howard County’s, while South Korea, a country with a thriving export economy, has a Gini coefficient of 0.344, below Loudoun County’s and identical to that of Sherburne County, Minnesota, the US county with the least income inequality in 2012.¹ (Again, note that these figures, like the US figures, are pre-tax; many countries have after-tax Gini coefficients below 0.3 due to very progressive tax structures and extensive social insurance programs.)

The conclusion, I think, is that income inequality is not simply driven by pure market forces but reflects cultural attitudes as well: social norms about what constitutes an adequate minimum wage (or indeed whether there should be a minimum wage at all), subjective judgements about how much CEOs and other senior managers contribute to a firm’s productivity compared to the typical employee, political decisions about how much government fiscal, monetary, and other policies should promote the interests of those who hold stock and other capital assets vs. those who do not, and so on. In 1993 the entire United States had a Gini coefficient of 0.389, comparable to that of Howard County today.² Thus in one sense Howard County is not an outlier that doesn’t reflect the rest of America; it just reflects the America of twenty years ago rather than that of today.

UPDATE: Added Charles County, Calvert County, and St Marys County.

The top-line news (which you’ll no doubt read soon enough in mainstream news outlets) is that we’re number 2: at $108,844 Howard County had the second-highest median household income of any US county in 2012, topped only by Loudoun County, Virginia, at $117,876. (Incidentally, what is it with Howard County always coming in second? This time it was Loudoun County, last time it was Eden Prairie MN. When do we get to be first?)

This is a major jump up from 2011, in which Howard County was in fifth place (at $98,953). Loudoun County was also first in 2011 at $119,134, but unlike Howard its median household income has decreased since then. Note that you can’t directly compare the 2011 and 2012 figures, because they’re not adjusted for inflation, but the relative rankings would still be the same.

So much for the headlines; now for the rest of the story.

Here’s a comparison of how Howard County fared in 2012 relative to its neighboring counties in Maryland, the counties of Northern Virginia, and the two closest major cities (I’ll come back to the Gini coefficient in the fourth column later):

Here’s the top ten states for 2012, plus the figures for the US as a whole:

Now let’s talk about what these numbers mean. First, where do they come from, and how accurate are they? The figures above are from the Census Bureau’s American Community Survey (ACS), and are taken from tables B19013, “Median household income in the past 12 months (in 2012 inflation-adjusted dollars),” and B19083, “Gini index of income inequality,” respectively of the ACS 2012 1-year estimates. (“Gini index” is an alternate term for “Gini coefficient.” I’m using the latter term for consistency with my earlier posts.)

These are statistical estimates based on a limited sample, and have a substantial margin of error (plus or minus $2,972 in the case of the Howard County estimate). Thus the more accurate statement would be that the Howard County median household income for 2012 was somewhere in the range of $105,000–113,000, pretty much the same as Fairfax County.¹

The next point is that we need to distinguish between income and wealth: income is what enables you to pay your mortgage, while wealth is what enables you to not need a mortgage in the first place. Headlines to the effect that Howard County is the second-wealthiest county in the US are misleading; it may be that there are other counties in the US where median household wealth (as opposed to income) is higher. For example, places like Fairfield County, Connecticut, home of hedge fund billionaires, almost surely have higher average household wealth than Howard County, and their median household wealth may be higher as well.

Other points: Household income is typically used as a measure instead of per capita income because households are the basic economic unit in most cases, and particularly with respect to major purchases like housing. All other things being equal, places where there are lots of two-earner families will have higher median household income than places where there are a lot of singles or one-earner families.²

The median household income is that income such that half of all households make more and half of all households make less. This is a better measure than average household income because average income can be misleadingly skewed upward by the presence of a few extremely high-income households: If a billionaire moved onto your street the average income of you and your neighbors would skyrocket, but the income of the typical neighbor (one who’s in the middle of the list of all neighbors ranked by income) would not be affected. The median household income is thus best thought of as a measure of what it means to be “middle class” in a particular locality, at least in terms of income.

This is an important point and worth expanding on, especially in looking the major jump in Howard County median household income from 2011 to 2012. There are at multiple ways in which median household income could grow:

Households across the board could include more people earning income, due to a higher rate of people living together instead of alone and/or to non-working spouses entering the labor force. Households across the board could also have higher income due to wage increases or other boosts to income (for example, selling stock that had appreciated).

Alternatively, the relative mix of households might change. For example, it might be that the high cost of living drives lower-income families (those below the current median household income) to move out of a particular area, while at the same time the perceived quality of life (schools, parks, libraries, etc.) influences higher-income families (those above the current median household income) to move into the area.

Any or all of these effects could be behind the jump in Howard County median household income from 2011 to 2012; teasing out the real story would require a more in-depth analysis the Census data (one I’m not prepared to take on at this time).

A final point about median household income: It gives a reasonably good picture of how a “middle income” household is doing, but it doesn’t tell us anything about how income is distributed among the various households. For example, suppose that the bottom 10% or 20% of households (by income) had their incomes cut in half, while the top 10% or 20% of households had their incomes doubled. This would not change the median household income at all, since half of all households would still be below the previous median value, and half still above.

So how do we measure the relative distribution of income across households, and how does Howard County stand on this measure? That’s the topic of my next post.

UPDATE: Added Charles County, Calvert County, and St Marys County to the list.

Chris Jackman (cjackman@hotmail.com) - 2013-09-23 12:36

You left Calvert County, MD ($87,449) off your list.

hecker - 2013-09-24 12:36

You’re right, I left Calvert County off the list; in my defense, I was focusing on the counties immediately neighboring Howard, and forgot about Calvert, Charles and St Marys County. Incidentally, at $87,449 Calvert County is 19th on the list of highest-income counties; Charles County is 15th at $90,880 and St Marys is 21st at $86,358. (Their Gini coefficients are 0.409, 0.3937, and 0.3779 respectively.)

Chris Jackman (cjackman@hotmail.com) - 2013-09-24 12:43

I just thought that you may want to include them since you posted several VA counties that are also in the Washington-Baltimore CSA.

hecker - 2013-09-25 03:15

You’re right. I updated the post to include them.

I previously discussed use of the Gini coefficient as a way to measure income inequality (or equality, as the case may be), and promised to discuss why Howard County is noteworthy in this regard. In brief, Howard County is one of only seven counties in the US (out of 800 counties and other geographic areas) that rank in the top 5% (positions 1-40) for both median household income and income equality (as measured by the Gini coefficient):

(By way of comparison, the estimated Gini coefficient for the entire US in 2007 is 0.467, while the estimated US median household income in 2007 is $50,740.)

All of these counties share similar characteristics: They are formerly rural counties, relatively small in population (ranging from roughly 100,000 to 400,000), that are close enough to major cities to benefit from their economic growth but far enough away to exclude urban concentrations of poverty. Except for Douglas County (a suburb of Denver) and Scott County (a suburb of Minneapolis-St Paul), all are located near Washington DC. This points up the role of the Federal government as the economic engine of the region, providing lots of well-paying government and contractor jobs but at the same time not fostering an entrepreneurial culture that might produce more truly wealthy people.¹

Although people disagree on the exact causes, there’s general agreement that income inequality has been generally growing over the past few decades, both in the US as a whole and within Maryland specifically. Howard County has been no exception, but even so its current level of inequality, although higher than it was in former years, is apparently no greater than that for the US as a whole in 1967, the year Columbia was founded.²

Howard County’s high median household income and low Gini coefficient could be interpreted as an endorsement of the “Columbia vision”: Columbia and Howard County have achieved 21st century-leading prosperity accompanied by 1960s-level equality. But does the Columbia vision really have anything to with this?

As noted above, while its situation is special in the US as a whole, Howard County is joined in its relative good fortune by several other Maryland and Virginia counties, all standard garden-variety suburbs with no Jim Rouse-like figures present at the creation (as it were). Rouse was certainly an enlightened developer, but first and foremost he was a canny developer, and the fundamental reason for Columbia’s success was Rouse’s foresight in seeing over forty years ago that Howard County’s “location, location, location” positioned it for future prosperity.

Despite that, I think the (lingering) vision of what Columbia should be does influence public attitudes toward income inequality in Howard County, and may help account for some of the special characteristics of the debates over Columbia’s future. For example, I’m sure that many opponents of the WCI Plaza Residences were sincerely concerned about the architectural compatibility of a 22-story tower with Columbia Town Center as it is and (in their minds) should be. However I also think some of the opposition was due to unease as to what it meant for the Columbia vision to have rich people in $2M condos looming over the split-levels, townhouses, and apartments of the surrounding villages.

Having the truly wealthy and their luxurious dwellings sprinkled through western Howard is one thing, having them occupy the symbolic heart of Columbia would be quite another, and I can understand why some older Columbians may have been troubled at the thought of it. I think a similar unease may lie behind the concern expressed that future housing in Columbia Town Center would be monopolized by the “wealthy few.”

In my previous post I mentioned Fairfield County, Connecticut. As Jay Hancock wrote in a blog post a while back, though it has a high median household income Howard County isn’t really rich in the sense that other areas are. On the other hand Fairfield County (or, to be more precise, Greenwich and other towns within Fairfield County) is indeed rich, with a vengeance. (Or at least it was, before the recent financial crisis; I don’t know how it’s doing now.) Home to a number of hedge fund billionaires and other people who made their fortunes in financial services, in 2007 Fairfield County had a mean household income of over $130,000, ranked in the top 5% for median household income ($80,241), and in the bottom 5% for income equality (with a Gini coefficient of 0.534).

Fairfield County is in a sense Howard County as it might have been in an alternative world, if DC were like New York. (In this regard it’s also worth noting that in 2007 New York City surpassed DC in both median household income, $64,217 vs. $54,317, and income inequality, with a Gini coefficient of 0.603 vs. 0.542.) That Howard County isn’t Fairfield County in this world might be seen as an unalloyed blessing: We live in a more fair and equal society, and are more insulated from the vicissitudes of global capitalism.

However it can also be argued that Columbia and Howard County are giving up something in return, and that (within limits) they might benefit from an increased influx of true wealth and the inequality that accompanies it. That’s a subject I hope to address in a future post.

JessieX - 2008-11-17 05:22

Frank, From day one, your perspective and thinking has made me more curious and thoughtful. Thanks again for sharing how you look at things. And thanks for this interesting, albeit a bit nerdy, post. ;-) See you at the BlogTale party Thursday, http://www.socializr.com/event/738244444 ~jessiex

Frank Hecker - 2008-11-18 03:32

Jessie, thanks for stopping by. Sorry for the nerdiness, it’s just that sometimes having the numbers and understanding the concepts is important – otherwise it’s all just opinions!

In a previous post I discussed the concept of median income and how it avoids certain distortions inherent in mean (average) income. However median income by itself is not adequate to characterize the economic status of households in Howard County (or anywhere else for that matter). In particular, the median income just provides the “midpoint” for income, i.e., the income value for which 50% of the households make more and 50% make less; it does not address the question of how income is actually distributed among the various households.

For example, let’s go back to our simple 10-household example from the last post:

I’ve added two new columns of data, but otherwise the situation is as I described it previously: the ten households have an average income of $118,900 but a median income of $101,500, very similar to the actual numbers for Howard County.¹ Now let’s look at a second 10-household example:

As it happens, these ten households have exactly the same average income ($118,900, $1,189,000 divided by 10) and exactly the same median income ($101,500, halfway between $43,000 and $160,000) as in the first example. However the distribution of income looks very different; in its division of households between rich and poor it looks much more like Baltimore city or Washington, DC, than it does Howard County. Clearly this difference in income inequality is not captured by the median or mean income, or even by related measures like the difference between the mean and the median. How can we quantify this difference?

One commonly-used measure of income inequality is the so-called Gini coefficient or Gini index. The computation of the Gini coefficient is more complicated than that for mean or median income, but it’s still relatively straightforward and comprehensible. The key is to look at the numbers in the last two columns of the tables above, and especially the last column, cumulative share of household income.

The third column simply gives the share of household income going to that particular household. For example, in the first table household #1 has income of $16,000 against a total of $1,189,000 for all households, or 1.35% of all income; similarly household #10 has a 26.66% share of all income ($317,000 divided by $1,189,900), and so on for the other households. The fourth column then uses these figures to compute the share of income going to the poorest n% households. For example, household #1 has a 1.35% share of total income and household #2 has a 3.11% share, so the poorest 20% of households (i.e., households #1 and #2 out of 10 total households) have 4.46% of all income (1.35% plus 3.11%). Similarly we can add the income share figures for households #1 through #9 to determine that the poorest 90% of households have 73.34% of all income, with the remaining 10% of households (i.e., household #10) having 26.66% as noted above.

The cumulative share of income can be graphed as shown in the figure below. The red points show the values from the fourth column of the table above, with the red lines then connecting the dots to approximate a curve; if there were more households there would be more points and a correspondingly smoother curve.

Now let’s look at the graph for our second example from above:

Again the red points represent the values for cumulative share of income from the fourth column of the second table, with the red lines connecting the dots. What about the blue dots in both graphs? Those represent the ideal case where all the household incomes are equal, or nearly so. In that case the poorest 10% of households will have (almost) 10% of total household income, the poorest 20% will have (almost) 20% of income, and so on. The corresponding curve will then be a straight (or nearly straight) line, here shown in blue.

Note that as household income becomes more unequal, the curve of cumulative income share (the red curve) moves further and further away from the blue line representing perfect (or nearly perfect) income equality. This gives us a straightforward way to define the Gini coefficient: It’s the size of the blue-shaded area between the blue line and the red curve, expressed as a fraction (or percentage) of the total area under the blue line. For nearly equal income distributions the red curve will be very close to the blue line, and the Gini coefficient will be close to zero, while for very unequal income distributions the red curve will be far away from the blue line, and the Gini coefficient will approach one (or 100%).

In the first example the Gini coefficient is 0.38, nearly the same as the Gini coefficient of 0.379 for Howard County (see the Census ACS table 19083).² In the second example the Gini coefficient is 0.53. This is comparable to the Gini coefficient for the District of Columbia, which is 0.542. More interestingly for our purposes, it’s nearly the same as 0.534, the Gini coefficient for Fairfield County, Connecticut, a suburban county in the New York City metropolitan area that’s home to many hedge-fund managers and other wealthy financial services professionals.

Unlike DC, Fairfield County is a pretty affluent area overall; it has a median household income of $80,241 (somewhat lower than Howard County’s) and a mean household income of $130,397 (somewhat higher than Howard County’s).³

The following 10-household example roughly mirrors the Fairfield County household income breakdown:

The corresponding Gini coefficient diagram is as follows:

What makes Howard County special with respect to income inequality, and Fairfield County particularly interesting as a comparison? The answers to those questions will be the subject of part 2 of this two-part post.

johntindale - 2008-11-21 02:26

This is a very interesting, informative, and well documented site about income disparity in HoCo. Thank you for all the hard work, research, and analysis,

Flug - 2008-12-01 15:13

I really love your stats and your interpretation of the datas. Great work, as usual. I bet I would have had higher marks in statistic, if have found your blog earlier:)