Unterschiede
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wm18:pgwm18 [2018/07/15 20:43] – [Conclusion] admin | wm18:pgwm18 [2018/07/15 20:56] (aktuell) – [Conclusion] admin | ||
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===== Predictions for World Cup 2018 ===== | ===== Predictions for World Cup 2018 ===== | ||
- | Here we compare predictions for the outcome of the World Cup 2018 tournament. We only include those predictions with a detailed probability distribution in percent for //the round of the last 16, quarter-final, | + | Here we compare predictions for the outcome of the World Cup 2018 tournament. We only include those predictions with a detailed probability distribution in percent for //the round of the last 16, quarter-final, |
==== Sites / Institutes ==== | ==== Sites / Institutes ==== | ||
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* **SUD =** [[https:// | * **SUD =** [[https:// | ||
* **UBS =** [[https:// | * **UBS =** [[https:// | ||
- | |||
- | /* | ||
- | * **OPT =** [[https:// | ||
- | */ | ||
==== Predictions for R16 ==== | ==== Predictions for R16 ==== | ||
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^JAP | 33.6 | 36.3 | 21.0 | 34.0 | 14.1 | 23.0 | 43.0 | 33.7 | 35.2 ^ 50.9 | 35.1 | 34.5 | 24.0 | 46.3 | 20.5 | 37.2| | ^JAP | 33.6 | 36.3 | 21.0 | 34.0 | 14.1 | 23.0 | 43.0 | 33.7 | 35.2 ^ 50.9 | 35.1 | 34.5 | 24.0 | 46.3 | 20.5 | 37.2| | ||
^#CP ^ 11 ^ 14 ^ 13 ^ 13 ^ 14 ^ 14 ^ 14 ^ 13 ^ 12 ^ 13 ^ 14 ^ 13 ^ 13 ^ | ^#CP ^ 11 ^ 14 ^ 13 ^ 13 ^ 14 ^ 14 ^ 14 ^ 13 ^ 12 ^ 13 ^ 14 ^ 13 ^ 13 ^ | ||
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The chart below shows the averaged prediction to make the round of last 16, together with individual predictions of the sites (colored points). The red error bars are the standard deviation of all predictions. The teams are ordered descending by the [[https:// | The chart below shows the averaged prediction to make the round of last 16, together with individual predictions of the sites (colored points). The red error bars are the standard deviation of all predictions. The teams are ordered descending by the [[https:// | ||
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**The question is: //How should we compare the predictions for the whole tournament?// | **The question is: //How should we compare the predictions for the whole tournament?// | ||
- | All predictions are given in terms of probabilities, | + | All predictions are given in terms of probabilities, |
- | First, suppose we had unrealistically // | + | First, suppose we had unrealistically // |
$$ | $$ | ||
P := \left(\prod_{n=1}^N p_n\right)^{1/ | P := \left(\prod_{n=1}^N p_n\right)^{1/ | ||
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{{wm18: | {{wm18: | ||
- | The ranking is highly dominated by those sites with high scores for favorite teams, which in particular favores **FMS** and **ECO**. The //best// prediction is given by **FTE** with a noticeable gap to the //second best// prediction of **ITM**. The only surprise is the last place of **NOB**, which might be related to wrong assessment of Russia, Switzerland and Sweden. Otherwise the group stage is kind of boring due to the domination of the favorite teams and therefore, the variation of //best// and //worst// prediction is rather small (17%). Let us come to the more interesting knockout stage. | + | The top ranking is highly dominated by those sites with high scores for favorite teams, which in particular favores **FMS** and **ECO**. The //best// prediction is given by **FTE** with a noticeable gap to the //second best// prediction of **ITM**. The only surprise is the last place of **NOB**, which might be related to wrong assessment of Russia, Switzerland and Sweden. Otherwise the group stage is kind of boring due to the domination of the favorite teams and therefore, the variation of //best// and //worst// prediction is rather small (17%). Let us come to the more interesting knockout stage. |
\\ | \\ | ||
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^#CP ^ | ^#CP ^ | ||
- | Only **NOB** has predicted the correct World Champion and furthermore, | + | Only **NOB** has predicted the correct World Champion and furthermore, |
{{wm18: | {{wm18: | ||
- | As in the case of the group stage, the //best// prediction by **GOP** has a noticeable gap to the //second best// prediction of **SUD**. The largest discrepancy in group and knockout stage is given by **ECO**, which drops from 4 to 16. Only **FTE** and **ITM** are in the top five in both stages. Furthermore, | + | As in the case of the group stage, the //best// prediction by **GOP** has a noticeable gap to the //second best// prediction of **SUD**. The distance between best and worst is more than 54%. The largest discrepancy in group and knockout stage is given by **ECO**, which drops from 4 to 16. Only **FTE** and **ITM** are in the top five in both stages. Furthermore, |
\\ | \\ | ||
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==== Conclusion ==== | ==== Conclusion ==== | ||
- | It is hard to judge, which is the best prediction model. First of all, the data number is rather small. We have 16 predictions for the group stage and 15 predictions for the knockout stage, altogether $N=31$. Second, there is not a single criterion for //What is best?// If we chose the correct prediction of World Champion, then **NOB** is the best. But this criterion is too coarse. A bit better might be the number of correct predictions of qualification (**CP**). In this case, the best prediction is done by **GOP,NOB** and **SUD** (CP=20). But keep in mind, a single match that goes differently | + | It is hard to judge, which is the best prediction model. First of all, the data number is rather small. We have 16 predictions for the group stage and 15 predictions for the knockout stage, altogether $N=31$. Second, there is not a single criterion for //What is best?// If we chose the correct prediction of World Champion, then **NOB** is the best. But this criterion is too coarse. A bit better might be the number of correct predictions of qualification (**CP**). In this case, the best prediction is done by **GOP, NOB** and **SUD** (CP=20). But keep in mind, a single match that would have been different |
To give a rough overview about the significance of the result let us assume, that for every single prediction the statistical error is 1% (rough estimate). With usual error propagation one can deduce an error estimation for $P$. This error is shown in the above chart by grey error bars. As can be seen, the first three predictions are within this error bars equal and fourth and fifth place are not that far away. | To give a rough overview about the significance of the result let us assume, that for every single prediction the statistical error is 1% (rough estimate). With usual error propagation one can deduce an error estimation for $P$. This error is shown in the above chart by grey error bars. As can be seen, the first three predictions are within this error bars equal and fourth and fifth place are not that far away. |