What do you tell me about the world cup?

I do not care for football (soccer). So what do you do in order not to be totally alienated from the surrounding conversations in a world cup year?  More so when the cup is happening in your home country?

To me it involves running some R script to assess the chances for each team and who will be playing where.  It all began as an exercise to show the economics intern how to build a Monte Carlo simulation in the R software environment for statistical computing and graphics.

The script has two main parts: (i) the probability of victory for each team pairing, let’s say Brazil and Germany; (ii) using those probabilities, run simulated world cups, game by game, randomly drawing winners and moving on to the next game according to the previous random results.

I ran one million of those simulated world cups. That’s most likely well above what’s needed for many statistically significant uses. But this is not a computation intensive task and runs in not much time.

The simulation of games is quite neat and gives interesting results. For instance, if you run a batch where there’s only one favorite team and all the others have the same chances in head to head matches, those teams that cross the favorite’s path to victory are penalized and end up with the worst chances of winning the cup.

The other neat thing of the simulation is that you can have game-by-game odds, not only of who wins but also who will probably play each match. Of course, this comes from the fact that a game’s players are the winners of matches from the previous round. So, if you have a ticket for a game of the quarterfinals you can check what is the match that you will probably watch.

The other part of the script requires figuring out probabilities for each match. And here is where things are less solid in this exercise and where there is most room for improvement. Nonetheless, we still can say that end results are at least plausible, as we will see.

These probabilities are based on a list of points earned by each country in world cups. For each match, the probability of victory for a team is its share of points in the sum of points for the two teams in that particular match. So for a Brazil X France, Brazil had 216 points, France has 86 points, so Brazil’s chances are {216}\div{(216+86)} or 72%. Of course there are some much more complex and better models. Notice that no attempt is made to model the possibility of ties.

So what kind of things do we see in results? For example, we see that Portugal had about 10% of chance of being part of the semi finals. This is consistent with a friend’s assessment of Portugal as having “some chance” of doing so.

Now, if this model allows me to mimic the opinions of a football fan, then I would say it has accomplished its goals 😀

But what probably most people will be interested will be who will win the Cup. So, to get this out of the way, this is the table:

We can follow this information step by step, figuring out the distribution of victories among countries. That is what I try to show in the next chart, from the round of 16 (oitavas) until the final:

In this chart we follow the distribution of victories among countries as the final match approaches.

Another interesting thing to do with the model is to re-run or re-query it after each game, fixing whatever has already happened. This works up to the final, where the answer that we will get is the one given by our simple match winner model.

Somewhere in the future, hopefully before the world cup, I might be posting odds for each game.

You can download the file with the winners for all the 1 million simulations here. The R script is here.

I thank Andre Luchine, Beto Boullosa, Charles Queiroz, Fernando Varejão, Marcio Eduardo Bezerra and Neca Boullosa for their consulting on the inner workings of the World Cup.


The mean, the median and the GDP – part I

A version of this post was originally published in Portuguese as a guest post at Walter Hupsel’s blog On The Rocks @ Yahoo! Brasil.

For over 50 years we have had Huff’s “How to Lie with Statistics” telling us that we should know better. And yet, we still rely on the wrong average in one of our most important tools for evaluating the world and countries’ economies: the GDP per capita. We are still using a mean in places where a median would be the better choice.

Gross Domestic Product (GDP) per capita1 is a simple and effective indicator, coming from a straightforward division of GDP by the population, being used appropriately and elegantly in many instances. Nonetheless, the GDP per capita cannot escape the hard reality that it is a mean average. Thus, as Huff warns us, it has shortcomings and flaws: it fails to capture the effects of inequality in a given reality. From this, one could say that this “mean” average is mean in the sense that it’s cruel and unkind.

But… Can we do better now?

The GINI index has reached mainstream status and is now the de facto standard for measuring income inequality. It measures how much the distribution of income deviates from an even division. A value of 0 in GINI would then be found only in an absolutely egalitarian society where everyone earns exactly the same. In contrast, a value of 100 would imply the entire income earned by a single individual or household. In the real world, it ranges from the low 20s (better distribution) for countries like Denmark and Belarus, to over 60, in the case of such unequal societies as Namibia or Botswana. Brazil’s GINI is 552.

It is time to move on to the median GDP, derived from GDP and GINI. It is a fresh metric that may better reflect both the changes in the economy’s output and trends in income distribution, while accounting for population sizes. It is to the GDP per capita what the median is to the mean.

While the mean is the average of all values in a given set of values (the sum of all values divided by the set size), the median represents the value found in the middle of the set, dividing it in two equally sized halves. Means are affected by extreme values, whereas medians are not. As we can see in the classical “How to lie…” example, an increase in earning of the best paid employee would change mean pay, whereas the median would not move. To move the median requires a change of pay for those in the middle section of the population, those that are neither the wealthiest nor the poorest. This is to say that this median GDP would better reflect the reality of our imaginary average Sally or Joe.

Policies that target economic growth regardless of its [human] costs have support in GDP per capita, which rises even if only a few benefit from these policies. Median GDP would not be fooled or let us be fooled by that.

 to be followed with more detail and examples. I kindly thank  comments and suggestions received from Andre Luchine, Beto Boullosa, Camilo Telles, Eduardo Viotti, Emilia Spitz, Joniel da Silva, Leonardo Fialho, René Dvorak, Vini Pitta and Walter Hupsel.

1. The article could similarly discuss GNI per capita. GDP per capita is chosen due to its wider use;
2. Unless otherwise noted, all figures from World Development Indicators, access on December, 31st , 2013. Indicators: GDP per capita, PPP (constant 2005 international $): NY.GDP.PCAP.PP.KD; GINI:SI.POV.GINI, latest available year.