wm18:rankings

 Here we compare four popular rankings for the teams of #WorldCup 2018. All rankings are collected right before start of the tournament: Goalimpact (GI) Transfermarkt.de (TMW) FIFA World-Ranking (FIFA) Football Elo Rating (ELO) Soccer Power Index (SPI) The first two rankings are based on an individual player-strength averaged over the whole team, the last two are calculated on a team base by comparison of games against each other over the period of one year. The graphic on the right shows all four rankings in a linear scale, such that for each ranking Y = GI, TMW, FIFA, ELO and SPI, the lowest rank is located at 0 and the highest at 1. Naturally all ratings are more or less correlated. The cross correlation are shown in the following table. The highest correlation is given between ELO and SPI, the lowest between Goalimpact and FIFA. Altogether Goalimpact has the lowest correlation with the other ones.

#### Z-score comparison

Another way to compare completely different scales of ratings is given by Z-score-normalization. This is a normalization in terms of expectation value $E(Y)$ and standard deviation $\sigma(Y)$, defined as: $$Z(Y) := \frac{Y-E(Y)}{\sigma(Y)}.$$ So everything is expressed in units of $\sigma$ and centered around zero. The widest spread is given by Goalimpact, which means it mostly distinguishes between the teams. Furthermore, TMW is the most unequal and narrowest distribution. The reason is the non-linearity of TMW. It is a kind of exponential behaviour and indeed, taking the logarithm smoothes the distribution.

Altogether, one would expect that Goalimpact is the most meaningful soccer-ranking, followed by SPI. But due to the more widespread ELO rating, we use for the comparison against other rankings ELO instead of SPI.

 Let us compare correlations between rankings in more detail and start with the highest correlation between FIFA and ELO. This is shown in the graphic on the right side. The horizontal and vertical gray lines represent the corresponding mean values. The high correlation is immediately visible, but with some larger deviations for Saudi-Arabia, Tunisia with overestimated FIFA values and slightly underestimated FIFA values for Russia, Spain and Brazil. Overall the correlation is high and it should be noted that FIFA has revised the old ranking in favor of a new ELO based ranking system. Next let us compare the more interesting rankings and compare Goalimpact (GI) with market value (TMW) and ELO, shown below. There are some remarkable deviations. On the one hand, the two lowest valued teams of Panama and Saudi-Arabia are under- and overestimated by GI. The reason might be related to too few comparison games in case of Saudi-Arabia. On the other hand, at least England, France and Brazil are overrated by TMWs, due to players with crazy TMW-values above 120 Mio €. The correlation of GI and ELO is a bit smaller, with two really large deviations. Again Saudi-Arabia is highly overestimated by GI, for the same reason as before. In contrast, Peru is either much underestimated by GI or overestimated by ELO. If we replace those players by the mean of team, all point shift down, as indicated by the corresponding smaller flags.

We only compare the population and global domestic product with collected from Statistisches Bundesamt. The most suitable ranking to asses the player-strength of a country is of course the Goalimpact ranking, which is by construction an individual player-strength rating system.

#### Population

Let us start the comparison with the population and use the male population aged between 16-35 years, the typical age of players. There is no direct correlation or pattern visible. For example Brazil and Belgium have similar GIs, but a huge difference in population and Spain and Peru have similar population, but a large difference in GI. The only peculiarity is the observation, that nearly half of the countries are located in the vicinity of the upper left rectangle.

#### Global domestic product

The graphics below show the GI versus GDP and GDP per capita for direct comparison. The most interesting observation is, that after normalization of GDP per capita not only a stretch of all points is observed, but also some countries interchange their position, e.g. Belgium and Brazil as well as Denmark and England. And Switzerland jumps from left to right and take the position of Japan, which itself condense to more or less a single point wit South Korea.

#### Comparison to other sports

In many country's soccer is the most popular sport and dominates all other sports. Eventually, let us just for fun compare the world ranking of soccer - measured in ELO - to the number of medals in Olympic games of the last summer and winter games. This is shown in the graphic on the right, which we will not comment. As we said before, it's just for fun!

• Zuletzt geändert: 2018/07/05 19:16