## 5 Results and Discussion
### Evaluation of the Overall International Rankings
Madrid & 0.01619 & Chelsea & 0.02920 & Tottenham & 703.50 m \\
11 & Wolsburg & 0.01673 & Everton & 0.01592 & Manchester Utd & 0.02875 & Inter & 63.60 m \\
12 & Serilla & 0.01650 & Arsenel & 0.01566 & Napoli & 0.02399 & Javertens & 633.00 m \\
13 & Eintenchaft Frankfurt & 0.01643 & Leeds & 0.01548 & Barcelona & 0.02239 & Dortmund & 628.40 m \\
14 & Dortmund & 0.01591 & Aston Villa & 0.01466 & Paris SG & 0.02209 & Arsenel & 619.25 m \\
15 & Lille & 0.01578 & Inter & 0.01465 & AC Milan & 0.02411 & RB Lipzig & 574.95 m \\
16 & Javertens & 0.01577 & Barcelona & 0.01444 & Atlanta & 0.02118 & AC Milan & 547.87 m \\
17 & Atlanta & 0.01541 & Sevilla & 0.01406 & Liverpool & 0.01689 & Napoli & 503.20 m \\
18 & Paris SG & 0.01512 & Lille & 0.01387 & Sevilla & 0.01823 & Everton & 511.20 m \\
19 & Napoli & 0.01508 & RB Lipzig & 0.01357 & Eintenchaft Frankfurt & 0.01521 & Leicester & 510.70 m \\
20 & AC Milan & 0.01501 & Paris SG & 0.01316 & Wolksburg & 0.01470 & Wolewemburg & 450.30 m \\  & & & & & & & & \\
89 & Strasbourg & 0.00530 & Udinese & 0.00613 & Benvenuto & 0.00097 & Spezia & 71.68 m \\
90 & Nantes & 0.00527 & Torino & 0.00613 & Vallalol  
\begin{table}
\begin{tabular}{r r r r r r r r r} \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 & 0.03985 & Manchester City & 0.02575 & Manchester City & 0.14878 & Manchester City & 1040.00 m \\
2 & Chelsea & 0.03276 & Chelsea & 0.02145 & Lille & 0.00484 & Liverpool & 969.65 m \\
3 & Real Madrid & 0.02816 & Manchester Utd & 0.01967 & Chelsea & 0.07968 & Chelsea & 889.20 m \\
4 & Bayern Munich & 0.02791 & Liverpool & 0.01902 & Bayern Munich & 0.06167 & Bayern Munich & 858.23 m \\
5 & Liverpool & 0.02036 & Real Madrid & 0.01803 & Real Madrid & 0.05888 & Barcelona & 817.50 m \\
6 & Manchester Utd & 0.01998 & Bayern Munich & 0.01803 & Lyon & 0.03717 & Paris SG & 805.00 m \\
7 & Atl. Madrid & 0.01276 & Leicester & 0.01776 & Monaco & 0.03552 & Real Madrid & 787.30 m \\
8 & Inter & 0.01278 & West Ham & 0.01276 & Inter & 0.02765 & Atl. Madrid & 773.10 m \\
9 & Leicester & 0.01702 & Totefham & 0.01682 & Manchester Utd & 0.02702 & Manchester Utd & 770.05 m \\
10 & Sevilla & 0.01603 & Atl. Madrid & 0.01623 & Javenta & 0.02851 & Totefham & 703.50 m \\
11 & Wolfsburg & 0.01597 & Everton & 0.01592 & Napoli & 0.02260 & Inter & 663.00 m \\
12 & Totefhamham & 0.01592 & Arsenal & 0.01566 & Liverpool & 0.01896 & Javenta & 633.00 m \\
13 & Eintracht Frankfurt & 0.01553 & Leeds & 0.01549 & Eintracht Frankfurt & 0.01752 & Dortmund & 628.40 m \\
14 & Paris SG & 0.01535 & Inter & 0.01646 & West Ham & 0.01722 & Arsenal & 619.25 m \\
15 & Barcelona & 0.01507 & Astron Villa & 0.01466 & Wolfsburg & 0.01659 & RB Lipzig & 574.99 m \\
16 & RR Leipzig & 0.01477 & Barcelona & 0.01446 & Bayer Leverhaven & 0.01525 & AC Milan & 547.8 m \\
17 & Leeds & 0.01473 & Sevilla & 0.01409 & Leicester & 0.01447 & Napoli & 503.20 m \\
18 & Lille & 0.01469 & Lille & 0.01384 & Sevilla & 0.01232 & Everton & 511.20 m \\
19 & Everton & 0.01463 & RR Leipzig & 0.01356 & Barcelona & 0.01217 & Leicester & 510.70 m \\
20 & Javenta & 0.01447 & Paris SG & 0.01313 & Totefham & 0.01114 & Wobservampton & 450.30 m \\  & & & & & & & \\  & & & & & & & &  
The correlations of the rankings applying different weights for international matches are summarized in Table 5. The use of different weights for each method also led to significant variations in the rankings, and this was clearly shown in the rank correlation indices. The only exception was the AL method, where there was only a slight change in the ranking when using different weights for international matches. The reason was the following: the pairwise comparison matrix \(\mathbf{B}\) hardly changed if we used \(\mathrm{W}=4\) instead of \(\mathrm{W}=1\) due to Equation (8).