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wm18:rankings [2018/07/05 17:42] – admin | wm18:rankings [2018/07/05 19:16] (aktuell) – admin |
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Here we compare four popular rankings for the teams of #WorldCup 2018. All rankings are collected right before start of the tournament: | Here we compare four popular rankings for the teams of #WorldCup 2018. All rankings are collected right before start of the tournament: |
* [[https://twitter.com/Goalimpact/status/1006772556345630720|Goalimpact]] | * [[https://twitter.com/Goalimpact/status/1006772556345630720|Goalimpact]] (GI) |
* [[https://www.transfermarkt.de/weltmeisterschaft-2018/teilnehmer/pokalwettbewerb/WM18/saison_id/2017|Transfermarkt.de]] | * [[https://www.transfermarkt.de/weltmeisterschaft-2018/teilnehmer/pokalwettbewerb/WM18/saison_id/2017|Transfermarkt.de]] (TMW) |
* [[https://www.fifa.com/fifa-world-ranking/ranking-table/men/index.html|FIFA World-Ranking]] | * [[https://www.fifa.com/fifa-world-ranking/ranking-table/men/index.html|FIFA World-Ranking]] (FIFA) |
* [[https://www.eloratings.net/2018_World_Cup|Football Elo Rating]] | * [[https://www.eloratings.net/2018_World_Cup|Football Elo Rating]] (ELO) |
* [[https://projects.fivethirtyeight.com/2018-world-cup-predictions/|Soccer Power Index (SPI)]] | * [[https://projects.fivethirtyeight.com/2018-world-cup-predictions/|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**. | 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**. |
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Z(Y) := \frac{Y-E(Y)}{\sigma(Y)}. | 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 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. | 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. |
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Altogether, one would expect that **Goalimpact** is the most meaningful //soccer-ranking//, followed by **SPI**. | 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**. |
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