## 5 Results and Discussion
### Evaluation of the Overall International Rankings  
This subsection contains the aggregated rankings of the teams playing in the top national championships. The aggregated rankings were based on the joint results of national championships and international cup matches. Tables 3 and 4 contain the first 20 and the last 10 teams, as evaluated by the TH, AL, and RN methods, using W = 1 and W = 4 weights for the international matches. In detail, Table 3 shows the outcome when the results of international cup matches were taken into account in the same manner as the national championship matches, while Table 4 shows the outcome when international matches were considered with four-times larger weights than matches played in national championships. We could observe that teams who won lots of matches in international cups advanced in the rankings. A typical example is Chelsea: this team was the fourth team in the national championship in every evaluation (Table 2). In the unified ranking (W = 1), it reached second place among the English teams but the sixth among all teams according to the TH method, second according to the AL method, and tenth according to the RN method (see Table 3). When we considered the international matches with a weight of four, Chelsea reached second place in the international ranking according to the TH and AL methods and third place according to the RN method (see Table 4). As this team was the winner of both the UCL and the UEFA Super Cup that year, it deserved these positions. When we considered at the overall picture based on the three evaluation methods and two weights applied for international matches, we could establish that the best six teams were the following (in this order): Manchester City, Chelsea, Real Madrid, Bayern Munich, Manchester United, and Liverpool. Furthermore, it could be seen that Manchester City was the top team in all rankings, regardless of whether international matches were weighted or not. \begin{table}
\begin{tabular}{r c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**TH**} & \multicolumn{2}{c}{**AL**} & \multicolumn{2}{c}{**RN**} & \multicolumn{2}{c}{**TM**} \\ \hline
**Rank** & **Name** & **Weight** & **Name** & **Weight** & **Name** & **Weight** & **Name** & **Value (G)** \\ \hline
1 & Manchester City & 0.02974 & Manchester City & 0.023616 & Manchester City & 0.10103 & Manchester City & 1040.00 m \\
2 & Bayer Munich & 0.02767 & Chelsea & 0.02113 & Lille & 0.07739 & Liverpool & 969.65 m \\
3 & Real Madrid & 0.02351 & Manchester Utd & 0.01967 & Inter & 0.06707 & Chelsea & 889.20 m \\
4 & Inter & 0.02158 & Liverpool & 0.01902 & Bayer Munich & 0.06283 & Bayer Munich & 885.23 m \\
5 & All. Madrid & 0.02045 & Bayer Munich & 0.01831 & Real Madrid & 0.0545 & Barcelona & 817.50 m \\
6 & Chelsea & 0.01993 & Real Madrid & 0.01826 & Monaco & 0.03338 & Paris SG & 885.00 m \\
7 & Manchester Utd & 0.01894 & West Ham & 0.01776 & Lyon & 0.03338 & Real Madrid & 787.30 m \\
8 & Barcelona & 0.01718 & Leicester & 0.01776 & Atl. Madrid & 0.03275 & Atl. Madrid & 773.10 m \\
9 & RB Lipidzig & 0.01717 & Tottenham & 0.01681 & Javertens & 0.03186 & Manchester Utd & 770.05 m \\
10 & Liverpool & 0.01679 & Atl.