Is Scrabble more Equal than Belgium?

It is surprisingly simple to rank countries by their relative income inequality. Surprising, because income inequality within a country is not straightforward and the economies of different countries can vary drastically.  Simple, due to a hundred-year-old measure of income inequality called the Gini coefficient.

Gini Coefficient

The Gini coefficient is the most common way to measure a country’s inequality. It ranks equality on a scale from 0 (perfect equality, all values being the same) and 1 (perfect inequality, where one person has everything and the rest have nothing.) Income inequality  Gini coefficients for countries vary from about .237 (Slovenia) to .632 (Lesotho). (Sometimes, as in that link, the values range from 0 to 100 instead of 0-1, in this case the indicator is called the Gini Index.)

The Gini coefficient allows the complicated matter of inequality to be turned into a single number.These numbers allow inequality in different countries to be compared to each other and tracked over time.

There is an issue with this, I don’t have an intuitive sense of what these distributions look like. The United States has a Gini of 0.45, but it’s hard to get a grasp of what that might mean. I can tell it’s less equal than Japan and more equal than Brazil, but that’s about it. 0.45 is sort of in the middle of the 0-1 scale, does that mean this is a middle level of inequality.

How does it compare to something else, for example, the board game Scrabble.


Those who have had the misfortune to experience the game, will know that Scrabble largely consists of small squares with letters on them. Each piece is worth a certain number of points, common letters such as E are only worth one point, rarer letters, such as Q and Z, are worth 10.  The more common letters are also more prevalent than the high point letters, so there are a bunch of low point letters and a few high point letters. If a country had its income distributed the same way the points were distributed over the pieces in a scrabble set, how equal would it be.

Specifically, would it be more equal than Belgium.

A Diagonal Line

Throughout history, dreamers and visionaries have tried to imagine what a world of perfect equality might look like.  As It turns out, it looks like a diagonal line.


This is a line of equality which plots the cumulative share of the population vs. the cumulative share of income. In a world in which everyone has the same income, this results in a straight line.

Of course, we do not live in this linear world, we live in one that looks more like this:


This is a Lorenz Curve, showing the inequality between countries in per capita gdp (as a proxy for country wealth).  To create this, each country is put in order from the poorest to the wealthiest, then each country’s share of the total (per person) income is calculated. The cumulative share of income is added along the vertical axis and the cumulative share of countries are added along the horizontal axis.

In the line of perfect equality the poorest 60% of countries will have 60% of the total income. The real world is, being far from perfectly equal, the poorest 60% of countries only combine for about 20% of total per-person income. The closer the Lorenz Curve is to the line of perfect equality the more equal the society is, and the further away the less equal.

This is summarized in the Gini coefficient which is the ratio of: the area between the line of equality and the Lorenz curve, and the total area under the line of equality.

calculating GiniGini Coefficient = The dark gray area/(dark gray area + light gray area)

In this case the Gini coefficient is 0.52.


It is not difficult to calculate a Gini coefficient for things that are not countries. All that is needed is a distribution or a list of non-negative numbers.

One place that is a lot more equal than the world at large is major league sports. Sports and Numbers, calculated Gini Coefficients by revenue for Major Sports Leagues, as well as player income.

Team revenue in the major North American leagues is very equal:


This is much less true of the major European Soccer leagues:


While team revenues are equal, player salaries very much are not.


(For reasons as to these differences, along with the associated Lorenz Curves, I encourage you to check out the Original Blog Post at Sports and Numbers.)

MLB salaries are more unequal than nearly any other country in the world. Of course, every MLB player, even the ones who doom my fantasy team, makes hundreds of thousands of dollars a year, so it’s hard to feel too sorry for them.


An example of a non-income related inequality is Crime. Some places have high levels of crime, others do not.

Using the numbers from the Wikipedia page on crime rates by US cities, I calculated the following GINI indexes. These reflect how equally various sorts of crimes are distributed among US cities.


There is significant variation in crime rates, but this variation differs among different crimes. Murder is, perhaps not surprisingly, the most unequal. Arson is high, driven by very high values in Detroit and Cincinnati. Less serious crimes, such as theft and burglary tend to be more equally distributed, and property crime is more equally prevalent than violent crime is.

Other Things

Since I was already on Wikipedia, I did what anyone on Wikipedia does, I kept clicking on things. Before long I had found data on all sorts of different things.

These things run from the nearly equal (the number of days per month), to the wildly unequal (there are hundreds of airports with just a few thousand passengers, and a handful with many millions.)


While the views among the top YouTube Videos are fairly equal, if all YouTube Videos were included the inequality would likely be extremely high, as there are probably millions of videos with essentially no views. The same is almost certainly true about US towns and cities, if all towns and cities were included the inequality would likely be very high.

The Days spent in Office by US presidents gini is probably particularly high right now, as President Trump has only spent a few ( 54 when I pulled the data) days in office so far. That leaves two presidents, Trump and William Henry Harrison, who have served less than 100 days in office, with most of them serving over a thousand.  Since there aren’t that many presidents, these two make up about 4% of the total crop.  That matters in terms of the inequality of days in office, as can be seen from the Lorenz chart below.



Books and Belgium

This sizes of drinks at Starbucks, the length of books on my bookshelf, how long US presidents tend to be in office, are all things I have a sense of. Income inequality in the US is more unequal than these things. It is also more unequal than the points in a Scrabble set.  Personally, I’ve always thought that the distribution of letters in a Scrabble game was shockingly poorly distributed, as it consists entirely of letters that I didn’t want.

The question of inequality is, essentially, a question of what we want society to look like.




I am fortunate to have a bookshelf filled with quality books, largely worth re-reading. While there are fatter books and thinner books, nothing seems grossly out of proportion, even including the occasional stray textbook. I would be happy to live in a society where income was distributed like the pages in those books. The Gini coefficient of pages in the books on my shelf is 0.315. This is more equal than most countries, although Ireland is close with a Gini of 0.313.

Belgium, which is one of the most equal countries on earth, is more equal still at 0.259.

That makes it much more equal than a Scrabble set.

And isn’t that a good thing to know.


Related Articles:

Is Global Inequality Increasing?

How should inequality be measured?



Sources and Further Reading: 

Sports and Numbers

Country Gini coefficients

State Gini coefficients

How to Calculate Gini coefficients with R

Full data and data sources are here.


Gini coefficients were calculated in R using the ineq package.


How should global inequality be measured?


Earlier this month, Oxfam published their yearly headline grabbing inequality stat. The global anti-poverty organization reported that the 8 richest men have as much wealth as the poorest half of the world’s population. The bottom half of the population is a group of about 3.6 billion people. They are matched in wealth by a group of 8. Not 8 million, not 80,000, not even 8,000 or 800. Eight.  You could fit them all in a minivan if you made Bill Gates sit in the trunk[1].

This metric is very good at grabbing attention. Unfortunately, it’s has one really annoying problem.


Wealth Inequality

Wealth is an important aspect of inequality because it accumulates and persists over time. Due to this, wealth inequality is almost always much more pronounced than income inequality. The global wealth distribution is very concentrated in the hands of a small group of people. 73% of people have wealth under $10,000, accounting for 2.4% of global wealth. To be in the top half of the half of the world’s wealth distribution requires a net wealth of only $2,200. The top 1% (those with a net wealth of $744,000 or more) now own as much wealth as everyone else.


Many people have even less than little. The bottom decile is in debt and therefore has a negative wealth. Those in the second decile have pretty much no wealth at all. After that, wealth starts to accumulate, with each decile having a larger share than the one that preceded it.

How it treats debt is probably the most common criticism of this metric.[2] The people with the least wealth, per this report, are those who are indebted. Often though, those who are most in debt are often not particularly poor.  It takes a certain level of affluence, and functioning credit markets, to get a significant debt going.  The archetypical example is a recently graduated North American college student. They might have a lot of debt, but they are likely living a more comfortable lifestyle than many of the people who have no wealth. When calculating the total wealth owned by the poorest half, the negative value cancels out much of the wealth of the other deciles. This makes a noticeable difference on the final calculations. Leaving this out increases the wealth of the bottom half to $1.5 trillion (about 56 of the wealthiest people).

Volatility is Annoying

I am not too bothered about how the report treats debt. It seems like when measuring net wealth, debt should not be ignored.

The thing that bothers me about this number is how very volatile it is. Oxfam are kind enough to report it every year, In 2014 they said it was 85, In 2015 it was 62, and in 2016 it was 8. That’s a big change. So what happened? The world’s wealthy might have gotten richer in 2016, but surely, they didn’t get nearly 6.8 times richer. Did they? The world’s poor might have gotten poorer but surely, they didn’t lose that much?

The Data

What changed was the estimate for the poorest half of the population.

The data for the world’s wealthy are taken from Forbes’ list of stupendously wealthy people. There isn’t a great deal of ambiguity in this data, we pretty much know how much wealth each of these people has. The other part is much harder. Wealth is a complicated thing, and half of the world’s population is a huge amount of people.

The best source for this, and the one that Oxfam used, is the global wealth report that Swiss bank Credit Suisse puts out each year. From this, Oxfam determined the amount of wealth that the poorest half of the world’s population had, and then went down the list of wealthiest people until they had a roughly equivalent amount.


Between the 2015 and 2016 reports, Credit Suisse got new and better data sources which altered their estimates of how much wealth the poorest half had. The new data showed that there was less wealth in India and China and more debt in general.  The original 2015 estimate was 0.7% of global wealth. The 2016 figure with improved data was 0.2% of global wealth, recalculating this figure for 2015 results in an updated figure of 0.2%, which is equivalent to the 9 richest people[3].table.PNG

This is all fine. Using better data is good, so is revising estimates to more accurately reflect the world.


Rich people are not a Unit

The impact of this change on the headline figure is not proportional to the underlying change in the poor’s share of global wealth. The original estimates for 2015 were that the poorest half had 0.7% of all the world’s wealth, under they improved methodology that figure changes to 0.2%.

Measured in the fortunes of the wealthy, this change is from 62 to 9 which makes the revision look more dramatic than it actually was. The change is dramatic because wealthiest people are not a consistent unit. Bill Gates is the wealthiest person in the world, with a total wealth of $85.9 Billion. The 48th wealthiest person, Ray Dalio has, a frankly pitiful, $15.6 Billion[4]. Not only must this be disappointing for Mr. Dalio, it is a problem for anyone wanting to interpret changes in Oxfam’s stat. The further down the list of wealthy people, the less wealth each wealthy person has.  Going from the top eight wealthiest people to the top nine is a change of $42.1B, much more substantial than going from 45 to 46 ($15.6B).


This depicts the amount that each additional billionaire contributes to the total. Since there are ties, some of the numbers in the x-axis repeat. For example, going from the 9th richest person to the other 9th richest person still adds another $40 Billion. Data is here.

Not only does it make it difficult to interpret changes when revisions occur, it makes it difficult to interpret changes over time. A good metric should let its audience know if things are getting better or worse, and by about how much. This doesn’t do that very well.

Mental Images

Despite the difficulty of interpreting the magnitude of changes, this is a very clever metric. It is designed to grab headlines and get people talking about global inequality. It clearly succeeds.

Abstract wealth can be a hard thing to grasp. It’s easy to imagine some of the trappings of wealth: private Jets, mansions in Aspen, Ferraris, and the like.  These mental images fall short when trying to conceptualize, for example, the fifteen-billion-dollar difference in wealth between Bill Gates and Warren Buffet.

If it’s hard to grasp the differences between Billionaires, getting an intuitive sense of global inequality is even more difficult. Partially, this is the fault of the scale of the numbers involved. Total global wealth is about $256 trillion, and there are about seven billion people on earth. These are not numbers our brains are good at handling. We hear these numbers and think something like “golly, that sounds like a whole lot”.

Of course, there are other ways to measure inequality that are easier to interpret, but they don’t offer as clear a mental picture. Saying the least wealthy half of the world’s population have just 0.2% of the world’s net wealth, is a more easily interpreted metric, but it doesn’t have the same sort of immediacy.

This stat is clever because it turns something we can’t easily imagine-global inequality, into something that we can-a minivan full of wealthy people, with Bill Gates in the trunk. It’s tricky for the exact same reason.




[1] Bill seems like a chill dude, I suspect he’d be cool with it.

[2] For example: here, here, and here.  Some other common criticisms include susceptibility to exchange rate fluctuations, and the decline in absolute poverty.

[3] I couldn’t find any explicit mentions of it but I’m going to assume that the reason .2% is equal to 9 billionaires one year, and 8 the next, is due to changes in billionaire wealth, rounding, or both.

[4] Based on this data





Credit Suisse Wealth Report

Oxfam Report Methodology

Oxfam Press Release