Vaccination Coverage

Vaccination Coverage

In the chart above, each dot represents a country. The size of the black outer circle represents the total population. The filled inner circle represents the population vaccinated (which received at least one dose), in absolute numbers.

The data source is Our World in Data. In this source, not all countries have data on the vaccinated population, only on the number of doses administered. In these cases, the population vaccinated with at least one dose and the population with complete vaccination are estimated using linear regression with the ratio of total vaccinations and population*. Data from the last available day for each country are used. Only countries with more than 1 million inhabitants are shown.

Charts posted daily on Twitter at @robertodepinho

Other graphics available at: Covid-19 graphics

* In earlier versions, the fully vaccinated were estimated based on the median of the ratio between applied doses and covered population observed in other countries. The vaccinated were estimated based on the assumption that it takes 2 doses to fully vaccinate a person. This second measure would thus be underestimated in those countries that use the Janssen vaccine.

Posted by Roberto de Pinho, 0 comments

Will Germany win the world cup?

In a previous post, I showed results from a model that gives a 23 percent change of victory for Germany in this year’s World Cup. It is the highest score. So, can I jump and say that Germany will win it, or worse yet, can I bet my savings that it will do so?

Short answer is: No.

As for a long answer, let me start reminding that I know nothing about football (soccer) and can’t even name a single player from Germany’s national team other that Bekenbauer, whose name I probably even can’t spell right. I am not even sure that he’s not a tennis player :-).

Keep also in mind that the model used for predicting winners for each match is very simple and that the main goal for this exercise, aside from being a learning experience for the intern, is to provide, at best, a common sense level understanding of how this Cup might play out.

This been said, the rule of thumb on making statistical predictions is to go back and see, whenever possible, how your model might have worked in the past for events that already have happened.

So, what would this model say before the last World Cup? I did not run it with data from the 2010 cup, nonetheless, it is safe to say that the winner, Spain,  would probably be no better evaluated at that time than it is now. In the current model, it has about 5% chance of winning and this is already impacted by the points Spain amassed in its winning campaign of 2010.

Thus, if, back in 2010, you took the country with the highest probability of winning and told everyone that it would certainly be the winner, you would have been wrong.

This is not to say that the model is or was absolutely wrong. The problem here is abusing it by using results beyond what they tell us. A 23% percent chance of winning, despite being the highest in the table, only says that out of 4 or 5 World Cups, Germany would win one of those. There are still 3 or 4 other potential World Cups where Germany does not win.

Going forward with this reasoning, an interesting thing to do is to contrast the model’s given probabilities with the list of actual winners of World Cups. The model has Brazil with a 22% chance of winning. This is a little over 4 out of the 19 past World Cups. The actual number is 5. For Argentina, the model hits the mark: a 13% chance of winning is equivalent of winning 2 of 19 past cups, what they actually have done.

Results being close is no surprise as the model is built on the past performance of teams in those 19 World Cups. On the other hand, their discrepancies can tell us a few things. First, we see that the model leaves some chance for the victory of teams that have never won before, which is a good thing.  Second, the fact it is based on points and not on wins is evident from what it says about Uruguay, predicting no victory for it. Despite having two wins, Uruguay has almost only half the number of points of Argentina, the other nation with two World Cup wins.

And lastly, it shows that this year, though we cannot say it will win for sure, Germany indeed seems to have a nicer path to victory than expected.

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 and Eduardo Viotti for questioning the model’s performance against the past.

Posted by Roberto de Pinho in English, the world, World Cup, 0 comments

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.


Posted by Roberto de Pinho in English, R, the world, World Cup, 0 comments