יום שישי, 19 באוקטובר 2012

FIFA World Cup 2014 European Qualifying Simulations

I finally got the time to work on importing the data to simulate the Fifa World Cup 2014 European Qualifying group stage.
The simulations are based on ELO ratings, and  the number of home and away goals are assumed to be independent Random Poisson Variables with an expectancy of:
Goals for the Home team:
        if Proba < 0.5:
            Home Goals = 0.2 + 1.1*sqrt(Proba/0.5)
        else:
            Home Goals = 1.69 / (1.12*sqrt(2 -Proba/0.5)+0.18)

Goals for the Away team:
        if Proba < 0.8:
            Away goals = -0.96 + 1/(0.1+0.44*sqrt((Proba+0.1)/0.9))
        else:
            Away goals = 0.72*sqrt((1 - Proba)/0.3)+0.3

 where Proba is the probability of the home team by ELO ratings.
This formula made by Lars, the owner of http://clubelo.com/, and it makes the prediction very accurate according to his research.

The worst RU is most likely to come out of group 2, with 27.88%.

After 100K simulations (ordered by chances of winning the group):


Group Team ELO Points 1st 2nd 3rd 4th 5th 6th Worst RU
4 Netherlands 1972 26.75 96.28% 3.45% 0.26% 0.01% 0.00% 0.00% 0.00%
6 Russia 1867 25.64 88.86% 10.92% 0.22% 0.00% 0.00% 0.00% 0.01%
2 Italy 1899 22.75 85.62% 11.11% 2.63% 0.62% 0.02% 0.00% 1.53%
5 Switzerland 1793 22.81 82.18% 16.68% 1.02% 0.11% 0.01% 0.00% 0.56%
9 Spain 2123 19.87 82.08% 17.88% 0.04% 0.00% 0.00% 0.00% 0.03%
3 Germany 2025 25.05 81.94% 17.21% 0.84% 0.01% 0.00% 0.00% 0.02%
8 England 1938 22.19 77.68% 16.27% 5.10% 0.95% 0.01% 0.00% 2.23%
7 Greece 1788 23.46 65.14% 32.88% 1.88% 0.10% 0.00% 0.00% 0.52%
1 Croatia 1853 21.70 55.73% 41.43% 2.43% 0.38% 0.04% 0.00% 2.90%
1 Belgium 1768 20.78 43.65% 53.03% 2.86% 0.40% 0.06% 0.01% 3.26%
7 Bosnia and Herzegovina 1711 21.14 33.68% 56.93% 8.41% 0.95% 0.04% 0.00% 3.39%
9 France 1848 16.96 17.90% 80.66% 1.35% 0.08% 0.01% 0.00% 1.67%
5 Norway 1712 18.86 17.08% 69.84% 9.83% 2.51% 0.67% 0.09% 8.66%
3 Sweden 1866 21.53 16.80% 65.87% 15.67% 1.65% 0.01% 0.00% 2.78%
8 Montenegro 1638 17.91 12.24% 34.84% 35.05% 16.31% 1.55% 0.00% 6.86%
6 Portugal 1884 20.67 10.87% 79.96% 8.70% 0.46% 0.02% 0.00% 5.34%
2 Czech Republic 1741 16.45 8.08% 35.16% 28.97% 21.89% 5.88% 0.02% 8.89%
8 Poland 1681 17.60 8.07% 35.06% 33.51% 21.82% 1.54% 0.00% 6.30%
2 Denmark 1745 15.76 4.23% 31.46% 31.93% 25.04% 7.27% 0.06% 9.47%
4 Romania 1717 19.30 2.36% 53.20% 35.18% 9.08% 0.18% 0.00% 6.02%
2 Bulgaria 1641 15.03 2.02% 20.48% 31.19% 38.12% 8.13% 0.06% 7.06%
8 Ukraine 1673 15.00 2.01% 13.62% 25.07% 52.95% 6.36% 0.00% 1.50%
4 Hungary 1680 18.21 1.34% 39.47% 46.82% 12.11% 0.26% 0.00% 7.73%
3 Republic of Ireland 1711 17.24 1.23% 15.29% 67.40% 16.00% 0.08% 0.00% 2.84%
7 Slovakia 1581 15.12 1.12% 8.73% 60.02% 23.46% 6.65% 0.04% 0.80%
1 Serbia 1635 11.42 0.43% 2.99% 40.16% 27.87% 18.23% 10.32% 0.44%
5 Iceland 1452 12.35 0.27% 4.72% 33.44% 29.53% 22.95% 9.09% 0.62%
6 Israel 1608 14.87 0.27% 8.46% 73.69% 15.03% 2.53% 0.02% 1.85%
5 Slovenia 1582 11.81 0.26% 4.53% 31.33% 28.24% 23.94% 11.69% 1.56%
5 Albania 1470 11.33 0.20% 3.97% 20.51% 29.44% 30.59% 15.30% 0.96%
1 Macedonia 1503 10.03 0.08% 1.12% 21.13% 26.56% 26.28% 24.84% 0.22%
1 Scotland 1626 9.19 0.07% 0.74% 15.83% 22.32% 28.58% 32.45% 0.04%
1 Wales 1551 9.74 0.05% 0.70% 17.59% 22.47% 26.82% 32.37% 0.28%
2 Armenia 1496 10.11 0.05% 1.80% 5.27% 14.24% 76.70% 1.94% 0.93%
7 Lithuania 1450 11.57 0.04% 0.90% 16.36% 40.93% 41.11% 0.66% 0.27%
7 Latvia 1487 10.82 0.03% 0.58% 13.33% 34.44% 50.39% 1.24% 0.25%
3 Austria 1588 12.49 0.03% 1.63% 16.07% 79.85% 2.32% 0.10% 0.15%
4 Turkey 1676 13.72 0.02% 3.86% 17.36% 71.73% 7.03% 0.01% 1.44%
5 Cyprus 1409 8.02 0.02% 0.26% 3.87% 10.18% 21.84% 63.83% 0.05%
9 Finland 1590 6.15 0.01% 0.38% 32.16% 35.58% 31.87% 0.00% 0.08%
9 Belarus 1551 7.75 0.01% 0.89% 51.61% 30.41% 17.09% 0.00% 0.24%
6 Northern Ireland 1420 9.69 0.01% 0.47% 11.24% 44.33% 38.84% 5.12% 0.04%
8 Moldova 1382 9.68 0.00% 0.21% 1.28% 7.97% 90.48% 0.06% 0.10%
6 Azerbaijan 1378 9.06 0.00% 0.19% 6.13% 38.61% 47.68% 7.38% 0.08%
8 San Marino 860 0.65 0.00% 0.00% 0.00% 0.00% 0.06% 99.94% 0.00%
9 Georgia 1477 4.99 0.00% 0.19% 14.85% 33.93% 51.03% 0.00% 0.04%
7 Liechtenstein 1167 2.31 0.00% 0.00% 0.01% 0.12% 1.81% 98.07% 0.00%
4 Estonia 1465 8.48 0.00% 0.02% 0.39% 7.07% 92.22% 0.30% 0.01%
6 Luxembourg 1121 3.64 0.00% 0.00% 0.01% 1.57% 10.94% 87.48% 0.00%
3 Faroe Islands 1191 3.33 0.00% 0.00% 0.01% 1.22% 28.00% 70.77% 0.00%
4 Andorra 973 0.79 0.00% 0.00% 0.00% 0.00% 0.31% 99.69% 0.00%
2 Malta 1202 2.21 0.00% 0.00% 0.01% 0.08% 2.00% 97.92% 0.00%
3 Kazakhstan 1312 5.22 0.00% 0.00% 0.01% 1.27% 69.59% 29.13% 0.00%


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