Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- wm18:rankings [2018/07/05 17:39] – admin
+++ wm18:rankings [2018/07/05 17:44] – admin
@@ Zeile 22: / Zeile 22: @@
 <columns 100% 40% 60%>
 === Z-score comparison ===
-Another way to compare completely different scales of ratings is given by [[ https://en.wikipedia.org/wiki/Standard_score|Z-score]]-normalization. This is a normalization in terms of expectation $E(Y)$ value and standard deviation $\sigma(Y)$, defined as:
+Another way to compare completely different scales of ratings is given by [[ https://en.wikipedia.org/wiki/Standard_score|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)}.
@@ Zeile 28: / Zeile 28: @@
 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.
-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**.
 <newcolumn>