The World Cup was recently over. Along with the competition, the sticker album also arises, it’s a quite big tradition, but I’ve never joined it. I got interested in the statistics behind it and asked myself how many stickers you must buy to fill the album completely.
My approach is a statistical simulation, modeling each package, until the album is complete. The same procedure is repeated for a large number of runs to get an estimated distribution of the total number of packages/stickers that are necessary to complete the album. First, I tested the convergence of the routine, initially based on 2 unanimous assumptions: the distribution of the stickers is uniform (that means, you have an equal chance to get any of the stickers) and that there are no repeated stickers for each pack (this one is maintained for all the tests here). Secondly, I tested what are the advantages of buying the missing stickers (from 1 to 50). Finally, two cases where the distribution is not uniform are evaluated: for a selected nation, the stickers are more abundant (from +10% to +50%) or rarer (from -10% to -50%) than the others.
This analysis can be performed for any album, being the number of stickers in the album and the number of stickers in a pack the necessary variables. So, for this case, the values for the Panini World Cup sticker book are selected:
681 stickers in the album;
5 stickers per pack.
Also, the possibility to buy missing stickers directly from them (maximum of 50) is also considered in this work.
As a part of my PhD, I’ve re-taken classes of statistics recently. Somewhere in the process, I realized that pie charts are called camembert, a type of cheese, in France. After a couple of seconds until I realized that those are pie charts, I recalled that they are also called differently in Brazil: pizza charts. Since then I’ve been thinking of what circle charts are called in different countries/languages.
To fulfill my curiosity, I’ve looked at Wikipedia articles on circle charts in several languages (full list on the Wikidata page). I’ve also stumbled across this french course on circle charts by J. R. Lobry of the University of Lyon that took me to the ISI (International Statistics Institute) glossary.
To see what the graph nicknames are, I used Google translate, always from the original language to English. The process started from the “Also known as” column on the Wikidata page, and later on the article itself if necessary, where I looked for expressions that looked like “something diagram” or “something chart” and occasionally I translated the full article. A total of 38 languages were analyzed, mostly indo-european (26).
The results are presented in the following graph: pie (36.8%) stands for languages where circle graphs are called pie charts, or some regional recipe that Wikipedia told me that it was a type of pie; cake (15.8%), pizza (2.6%) and cheese (2.6%) respect the same idea; pie/cake (13.2%) are either cases where the two versions were presented, such as for german, Kuchen-oder Tortendiagramm, or the translated word resulted in the two terms; and none (28.9%) represents cases where I could not recognize any related food analogy in the articles. In most of those cases only different terminologies related to circle or sectors were found.
Although the pie chart is not really a good choice for representing any type of data, I considered it a must for the analysis of pie charts. Data treatment and plotting is done with Excel 2016, with a little help of Inkscape to prepare the images. The raw data is available here.
My results are obviously limited to my not so extensive sources, that don’t account for regionalisms (such as the use of different terms in countries that speak the same language). Also, there is a strong chance that mistakes were made in translation, what is really a problem when similar foods, such as cake and pie, may be called by the same word and vary by the situation. Certainly, such type of nuances are neglected by Google translate when no context is given (or even when it is supplied!). Finally, I miss the proper knowledge to technically distinguish a pie and a cake, so the “cake” and “cake/pie” categories must be considered with care.
Surprisingly, the only outliers (highlighted in the figure) are the ones that I have personally encountered in my academic life, according to my results. That explains why I have not found any type of analysis like this over the Internet.
If you find this slight interesting, please comment!