Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
| Beide Seiten der vorigen Revision Vorhergehende Überarbeitung | Letzte ÜberarbeitungBeide Seiten der Revision |
| wm18:rankings [2018/07/05 17:44] – admin | wm18:rankings [2018/07/05 18:03] – admin |
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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**. But due to the more widespread **ELO** rating, we use for the comparison against other rankings **ELO** instead of **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**. |