Introduction







The Latin American Clubs Evaluation

I.  Introduction and Historical Literature Review
         
           The South & Central American club football history started when the amateur football in Americas was first ever established in Argentina 1893 and afterwards most Latin American leagues turned professional in the mid-1930s and latest in 1977 for Bolivian football. The Latin American clubs competed football with the extreme irregularity of competition formats has left the complexity and difficulty for us to reach the status of each European club in its whole history. .
          All-Time South & Central American cups ranking[1][2] [Raul Torre, 2017] were evaluated by methodological trophy standard points for each Latin American international competition. The world club team all-time ranking[3] and The Worldwide historical club ranking[4] based on mathematics [Marcelo, 2016) ranks the team based on titles criteria which is set the standard points of title acquisition between the leagues and the point given to any league are equally given between seasons. By this context, there is no proven source of standard point and not represents the actual fluctuation of the league/international cup standard from era to era. The evaluations were also not differentiated the performances to achieve the round or title.
   Accordingly, this work’s objective is to study, integrally regulate and standardize the system of the entire Latin American club history for the evaluation, including all performance characteristics (win-draw-lose, goal difference, place, round and trophy) against the determined standard of competitions within the designed system of methodology conformed to the existed format or condition at any point of evaluation.  

II. Methodology

    1) International Club 
         1.1) Determine the winner of each annual Latin American competition by qualitative analysis. For the non-int-club era, the official friendly results are support to stipulate the value, if no enough record, performance of its national team are applied for consideration.
      1.1) Determine the competitive level by counting goal difference to calculate its average for each round and input by the following formula ; 
         (∑ Goal Difference Average/(Number of Round x 4.5))
         (Number of Round +((6-Number of round)/2))/6
       1.2) The standard of competition (STD) = Top Level X Competitive Level
       1.3) The Status Performance (STS) = SQRT(TLS- (FTC – 1) x GS x STD
             Finished Round Coefficient (FRC) (Winner = 1, Runner-Up = 2, SF = 3, QF = 4, R16 = 5, R32 = 6, R64 = 7, R128 = 8)
             GS = Gap Standard = 0.65+(6- number of round)*0.05
             TLS = Top Level Standard (UCL/EC =5, UC = 4.5, CWC/ERP = 3.7)
      1.4) The Raw Direct Performance (RDRT) is calculated by chain of beaten from top level to the evaluated team. Being beaten 1 goal is equal to – 0.4. For group round format, the difference will be calculated based on following formula ; ∑ ((DGD/N)*0.4)/Nq i
DGD : The descending goal difference
N : The number of matches     
Nq : The number of qualified teams in the group 

Then, the performance will be adjusted +0.75 and x 0.85 to give positive value for negative raw data.   
      1.5) The total performance = SQRT(STS X ADRT)

    2) Domestic League 
     2.1) Determine the raw direct performance (RDRT) by point and goal difference         
         Point Ratio = ((Games win x 2.5) +(Games Draw x 1))/Number of Games  
           Goal Difference Ratio = Goal Difference/Number of Games
           RDRT = (Point Ratio x 0.75) +(Goal Difference Ratio x 0.25)          
       2.2) Determine top level 
         2.21) Top Tier League : Referring to the best performance in international club (TEU) against the competitive level by the formula : PSTD (Primary Standard) = (TEU x (2 – Variance)/2)
          2.22) The Second League : Implementing benchmark method by calculating the average place of the promoted teams between the previous season to the calculated season and to the next seasons. The obtained calculated finished place is applied to the table in the calculated season linked to its raw direct performance that is a top level. The decimal > 0.15 and < 0.85 of the finished place value is required to calculate for average value between places. The obtained value is acted as TRDP in clause 2.23 
             2.23) The Top Level Raw Direct performance (TRDP) is adjusted by + 0.75 x 1.5 to give positive value for negative raw data to be the top level adjusted direct performance (TADP)
           2.24)  The top level performance (TLV) is the direct performance against primary standard 
                TLV = TEU+((Y-(((-X2)/8)+(X/8)+5))/2) ; Y = TADP, X = PSTD
      2.3) Standard of League (STDL)        
           STDL = Top Level Performance x Competitive Level 
           Competitive Level = (2-Sc)/2
            S1= Variance = ∑ (x1-µ)2/number of members ; 
            x1 = point ratio (win = 2.5 point, draw 1 point)
            S2= Variance = ∑ (x2-µ)2/number of members ; 
            x2 = goal difference (Separate positive and negative µ value)
            Sc (Combined Varaince) = S1 (0.75) + S2 (0.25)   
       2.4) Final Calculation
           Final Direct Performance (FDP) = (RDRT+0.75 x 1.5) x (TLV/TADP)
        Status Performance (STS) = SQRT[(5-(FP -1)*0.1) x STDL]for Top Flight
          SQRT[5-(N1-1)*0.1] x STDL1 - [SQRT[(5-(FP -1)*0.1) x STDL2] for 2nd Tier
           N1 = Number of team in top fllight
           League Performance = SQRT[FDP x STS]
    3) Domestic Cup
      Implement the same method as International club and the top level is determined from international club as well as the league competition. 

    4) Final Calculation
        Basic Proportional Weight : Domestic League 52 %, Domestic Cup 16 %, Int. Club 32 %    The performance is calculated in aggregate within a season not separated since the performance between competitions were a mutual dependent factors as football is purpose to mainly win the trophy not optimize the performance in any of competition level. As many of competitions are tournaments formats, it is implemented and calculated in aggregate mini-leagues method. For the season without domestic cup, basically the domestic league proportion is expanded to 60 % and increase more 16 % in non-international club era. Exceptionally the league proportion could be increased between 77 at minimum and 80 % at maximum by compensation from over number of participation (> 38 to 46 games per seasons).  However, if the obtained performance is a negative value, it is not applied to the system and equal to Zero. That mean the lowest value to apply for the system has been standardized.
    To standardize the opportunity of international club participation. The standard value of league performance at 3.25 has been set. The clubs that achieved this value but not get the opportunity because its league is competitive, will be compensated the higher proportion for domestic competition by 50 %. In contrary, the clubs that got the opportunity to play in international club with less than 3.25 of league performance in the previous season will be deducted the entire seasonal int. club points that is less than 2.5 in the over-participated number
    The obtained seasonal performance will be matched to multiply with proportional weight of the best 92 seasons whose number is an average of available league seasons for the 50 qualified teams and calculated the sum to obtain aggregate total.
       The trophy bonus is designed in the following table.


      The league trophy bonus is given for only the club achieved the highest league point among Latin American leagues in each season. The domestic cup is not applied as a single bonus as the South & Central American international cup has represented the teams in elimination format. However, it is applied for double and triple trophies if the club won International competitions and also won domestic cup. The international trophy bonus is applied for only Copa Libertadores Cup for South Americas and CONCACAF Gold Cup for only seasons the central American clubs achieved the standard rating (>4). Other than that is not applied to prevent injustice disadvantage for the teams that get deep round in other competitions but not acquire trophy.
5) The Decisive Factors
      0.2 % is required as a minimum value to unanimously decide the rank. If not, consider if the comparison couple has the other seasons than average, if so, compare its other best season by one. 0.1 is a minimum value to beat, if not, consider another season until match the rule. In case of no other season, the peak season is a decisive value with a minimum 0.1 to significantly differentiate. If not, recomparing in the second peak season or more if necessary.   
                                 
III. Implementation
            
       51 clubs are selected for implementation by considering number of available seasons and the entire finished places. 3 Paraguayan clubs are not implemented as none of available league records. The implementation was done by excel formula database by manual input and correction checking. All related Latin American seasonal league tables are calculated for the club performance and standard of competition. All related cup competition games are count for the goal difference to determine competitive level. Finally, all performance and standards result are input the conclusive table. Each club are input the performance data in each part of competition and calculate for the aggregate seasonal point by competition-level proportional weight conformed to the actual condition at the time.   
      The unavailable record : Paraguayan League (1906 – 1991). The Paraguayan clubs are ranked by international performance comparison against the estimative opportune factor of participation. Mexican Cup (1956 – 1962, 1969, 1971 - 1976). For these related years, Club America and CD Guadalajara has a record of finished place. However the competitive level is set by estimation. In the case of record unavailability, the case is equal to the unavailable competition that allows a higher portion of domestic league.


IV. Result

 The 50 Greatest Latin American Clubs of All-Time




*Remark : Universidad de Chile beat Universitario by third peak season

Statistics by nation (also ranked by performance if equal in number)

12 : Brazil, 10 : Argentina, 5 : Colombia, 4 : Chile, Mexico 
3 : Uruguay, Paraguay, Peru, Ecuador, 2 : Costa Rica, 1 : Bolivia

                   Best League Performer in Americas by Season                   

Statistics by Club

10 : River Plate
8 : Boca Juniors, Penarol
6 : Nacional, 5 : Corinthians, 4 : Independiente
3 : San Lorenzo, Sao Paolo, Palmeiras, Vasco Da Gama, America De Cali, Santos
2 : Olimpia, Racing Club, Cruzeiro, Velez Sarsfield, Colo Colo, Flamengo
   Atletico Mineiro, Universiad De Catolica, Botafogo
1 : Internacional, Millonarios, Universitario, Estudientes, Union Espanola, Sao Caetano


Statistics by Nation 

30 : Brazil, 29 : Argentina, 13 : Uruguay, 5 : Chile
3 : Colombia, 2 : Paraguay, 1: Peru

V.  Discussion

        The methodological implementation allows the rankings to have represented the clubs’ entire performances against the determined standard and greatness throughout the history. However, the qualitative analysis to determine top level performance of the best club in Latin Americas between seasons and eras are provided by author’s cumulative tacit knowledge converted to mathematics that is always debatable but the scale of tolerance is however quite narrowed, possibly effecting on the change of rankings in a minor part. Additionally, the proportional criteria between parts of evaluation and the proportional weight given to highest to lowest performance has a main role to finalize the ranking. 
       The seasonal weight applied to the seasonal rating reduces the disadvantage of the teams that participated in lower seasons than average group in case of achieving a competitive high peak and the teams participated in more seasons than average group is just advantageous as they had more opportunities but the number of calculated seasons is still limited in average value.      
        The result of implementation saw the disqualification of 4 clubs from highest to lowest are LDU Quito, Argentinos Juniors, Atletico Junior and UNAM Pumas. LDU Quito’s total score is lowered than Santa Fe, the last place in the table in the amount that is unanimously differentiable although LDU's aggregate peak is more than that of Santa Fe by 0.8. Argentinos Juniors is the only club that won Copa Libertadores Cup but disqualifies for top 50 ranking list as the majority of club history were spent in the average places of first tier or even second tier.
        Penarol appeared as the all-time best Latin American club ever as approximated, beating the second place River Plate by 0.94 % of point when the aggregate peak is equal between the two clubs. Boca Juniors’ evaluated point is not significantly differentiated to River Plate but the aggregate season enabling River Plate to be eligible for obtaining higher place suddenly.
        The best Brazilian club Sao Paolo appears in top five, considering to beat Olimpia Asuncione, who achieved similar titles and runner-up in Copa Libertadores Cup, by lower value of opportune participation factor. Santos who achieved the highest aggregate peak among Brazilian clubs finished the fourth place among Brazilian clubs. Gremio and Internacional are disadvantageous as the pre-1960s Campeonato Gaucho was competed in elimination format with a few numbers of appearances.    
       Outside the big three nations, Chilean clubs are advantageous in term of domestic cup participation and allows Colo Colo to finish near top 10. Surprisingly, it was Universidad Catolica that achieved the highest aggregate peak season in the continents. In 1962, the club finished runner-up in both domestic league and cup and was defeated by Santos narrowly in semi-final round. The three Paraguayan clubs are ranked by approximation technique with an inevitable large biased as none of league record existence. Colombian and Ecuadorian clubs collected fewer number of seasons than the others and highly impact on its status in history.    
    There are six CONCACAF clubs qualified in top 50 list with the best representative Club America but no one achieve the best league performer in Latin Americas and Only Club America in 1983 achieve the international trophy bonus.  


Reference

   [4] http://www.rsssf.com/miscellaneous/mathclubrank.html



Annex : The Greatest Latin American League Performers Ever




Annex : The Greatest Latin League Performers Ever by Latin American Nation





The European Clubs Evaluation

I.  Introduction and Historical Literature Review
    Throughout the European club football history, there was a chronological evolutionary change of competitions. The first professional football in Europe was formed in England 1892 but most of European leagues turned professional in the 1930s and latest in 1950s. The limitations of football at the early era such as non-existence of international club competition, the irregularity of competition format and qualification, etc has left the complexity and difficulty for us to reach the status of each European club in its whole history. 
   All-Time European club ranking[1] [Van Rijswijck, 2004] were evaluated by methodological standard points for each European international competitions by rounds (QF to Final). The world club team all-time ranking[2] and The Worldwide historical club ranking[3] based on mathematics [Marcelo, 2016) ranks the team based on titles criteria which is set the standard points of title acquisition between the leagues and the point given to any league are equally given between seasons. By this context, there is no proven source of standard point and not represents the actual fluctuation of the league/international cup standard from era to era. The evaluations were also not differentiated the performances to achieve the round or title.
   Accordingly, this work’s objective is to study, integrally regulate and standardize the system of the entire European club history for the evaluation, including all performance characteristics (win-draw-lose, goal difference, place, round and trophy) against the determined standard of competitions within the designed system of methodology conformed to the existed format or condition at any point of evaluation.  
II. Methodology

    1) European International Club 

     1.1) Determine the winner of each annual European competition by qualitative analysis. For the non-int-club era, the official friendly results are support to stipulate the value, if no enough record, performance of its national team are applied for consideration.

     1.2) Determine the competitive level by counting goal difference to calculate its average for each round and input by the following formula ; 
         (∑ Goal Difference Average/(Number of Round x 4.5))
         (Number of Round +((6-Number of round)/2))/6

          The standard of competition (STD) = Top Level X Competitive Level
       1.3) The Status Performance (STS) = SQRT(TLS- (FTC – 1) x GS x STD
             Finished Round Coefficient (FRC) (Winner = 1, Runner-Up = 2, SF = 3, QF = 4, R16 = 5, R32 = 6, R64 = 7, R128 = 8)
             GS = Gap Standard = 0.65+(6- number of round)*0.05
             TLS = Top Level Standard (UCL/EC =5, UC = 4.5, CWC/ERP = 3.7)
      1.4) The Raw Direct Performance (RDRT) is calculated by chain of beaten from top level to the evaluated team. Being beaten 1 goal is equal to – 0.4. For group round format, the difference will be calculated based on following formula ; ∑ ((DGD/N)*0.4)/Nq i
DGD : The descending goal difference
N : The number of matches     
Nq : The number of qualified teams in the group


Then, the performance will be adjusted +0.75 and x 0.85 to give positive value for negative raw data.  

 Then, the performance will be adjusted +0.75 and x 0.85 to give positive value for negative raw data.   
     1.6) The total performance = SQRT(STS X ADRT)


    2) Domestic League 

     2.1) Determine the raw direct performance (RDRT) by point and goal difference         
         Point Ratio = ((Games win x 2.5) +(Games Draw x 1))/Number of Games  
           Goal Difference Ratio = Goal Difference/Number of Games

           RDRT = (Point Ratio x 0.75) +(Goal Difference Ratio x 0.25)          

       2.2) Determine top level 

       2.21) Top Tier League : Referring to the best performance in international club (TEU) against the competitive level by the formula : PSTD (Primary Standard) = (TEU x (2 – Variance)/2)

       2.22) The Second League : Implementing benchmark method by calculating the average place of the promoted teams between the previous season to the calculated season and to the next seasons. The obtained calculated finished place is applied to the table in the calculated season linked to its raw direct performance that is a top level. The decimal > 0.15 and < 0.85 of the finished place value is required to calculate for average value between places. The obtained value is acted as TRDP in clause 2.23 

          2.23) The Top Level Raw Direct performance (TRDP) is adjusted by + 0.75 x 1.5 to give positive value for negative raw data to be the top level adjusted direct performance (TADP)

        2.24)  The top level performance (TLV) is the direct performance against primary standard 
                TLV = TEU+((Y-(((-X2)/8)+(X/8)+5))/2) ; Y = TADP, X = PSTD

      2.3) Standard of League (STDL)        
           STDL = Top Level Performance x Competitive Level 

           Competitive Level = (2-Sc)/2

            S1= Variance = ∑ (x1-µ)2/number of members ; 
            x1 = point ratio (win = 2.5 point, draw 1 point)
            S2= Variance = ∑ (x2-µ)2/number of members ; 
            x2 = goal difference (Separate positive and negative µ value)
            Sc (Combined Varaince) = S1 (0.75) + S2 (0.25)   

       2.4) Final Calculation

           Final Direct Performance (FDP) = (RDRT+0.75 x 1.5) x (TLV/TADP)

        Status Performance (STS) = SQRT[(5-(FP -1)*0.1) x STDL]for Top Flight
          SQRT[5-(N1-1)*0.1] x STDL1 - [SQRT[(5-(FP -1)*0.1) x STDL2] for 2nd Tier
           N1 = Number of team in top fllight
           League Performance = SQRT[FDP x STS]

    3) Domestic Cup

      Implement the same method as International club and the top level is determined from international club as well as the league competition. For tournament championship such as German Championship in pre-bundesliga era, it is implemented in the same concept as performance in knock-out tournament is used for identifying value of top level team.       

    4) Final Calculation

      Basic Proportional Weight : Domestic League 52 %, Domestic Cup 16 %, Int. Club 32 % (Except Mitropa Cup 20 % (1927 – 1933) and 24 % (1934 – 1939)
      The performance is calculated in aggregate within a season not separated since the performance between competitions were a mutual dependent factors as football is purpose to mainly win the trophy not optimize the performance in any of competition level. For the season without domestic cup, the domestic league proportion is expanded to 60 % and increase for 16 % in non-international club era. However, if the obtained performance is a negative value, it is not applied to the system and equal to Zero. That mean the lowest value to apply for the system has been standardized.

       To standardize the opportunity of international club participation. The standard value of league performance at 3.25 has been set. The clubs that achieved this value but not get the opportunity because its league is competitive, will be compensated the higher proportion for domestic competition by 50 %. In contrary, the clubs that got the opportunity to play in international club with less than 3.25 of league performance in the previous season will be deducted the entire seasonal int. club points that is less than 2.5 in the over-participated number .     

    The obtained seasonal performance will be matched to multiply with proportional weight of the best 92 seasons whose number is an average of available league seasons for the 100 qualified teams and calculated the sum to obtain aggregate total.

        The trophy bonus is designed in the following table.
       The league trophy bonus is given for only the club achieved the highest league point among European league in each season. The domestic cup is not applied as a single bonus as the European international cup has represented the European team in elimination format. However, it is applied for double and triple trophies if the club won European competitions and also won domestic cup. The European bonus is applied only the competitions whose winner is a potential best club in Europe. The Mitropa Cup is applied between 1927 - 1939. Cup Winners Cup is applied only for 1961 when Inter Cities Fair Cup was mostly competed between cities all stars and UEFA cup is applied between 1962 - 1997. Other than that is not applied to prevent injustice disadvantage for the teams that get deep round in other competitions but not acquire trophy.

5) The Decisive Factors

    0.2 % is required as a minimum value to unanimously decide the rank. If not, consider if the comparison couple has the other seasons than average, if so, compare its other best season by one. 0.1 is a minimum value to beat, if not, consider another season until match the rule. In case of no other season, the peak season is a decisive value with a minimum 0.1 to significantly differentiate. If not, recomparing in the second peak season or more if necessary.   
                                 

III. Implementation
            
    103 clubs are selected for implementation by considering number of available seasons and the entire finished places. The implementation was done by excel formula database by manual input and correction checking. All related European seasonal league tables are calculated for the club performance and standard of competition. All related cup competition games are count for the goal difference to determine competitive level. Finally, all performance and standards result are input the conclusive table. Each club are input the performance data in each part of competition and calculate for the aggregate seasonal point by competition-level proportional weight conformed to the actual condition at the time.   
    The unavailable record : Czechoslovakian Cup 1960 – 1970, Czech and Slovak Cup 1971 – 1980 ; Hungarian Cup 1934, 1935, 1941 – 1944, 1952, 1955, 1958, 1965 – 1968. For these related years, the competitive level is set by estimation. Ferencvaroc rating is effected little as there are the club result record as well as Slavia Prague. In the case of record unavailability, the case is equal to the unavailable competition that allows a higher portion of domestic league.


IV. Result

 The 100 Greatest European Clubs of All-Time



Statistics by nation (also ranked by performance if equal in number)

11 : England, Germany
10 : Spain, Italy  
7 : Soviet Union, France 
4 : Hungary, Yugoslavia, Czechoslovakia, Scotland 
3 : Holland, Portugal, Belgium, Turkey, Greece, Switzerland 
2 : Austria, Romania, Bulgaria, Sweden, Poland


Remark : FC Porto beat Celtic by the second peak season
           Austria Vienna beat Tottenham in 93th peak season
           Dortmund beat Hamburge by the third peak season
           FC Cologne beat Hajduk Split by the third peak season
           Stuttgart beat Dinamo Bucharest by the second peak season
           Gladbach beat Leeds by the second peak season
                     
                    Best League Performer in Europe by Season                   
Statistics by club

8 : Barcelona, 7 Real Madrid, 6 Bayern Munich, 5 Ajax Amsterdam, Inter Milan
3 : AC Milan, Ferencvarosi, MTK Hungary
2 : Rapid Vienna, Arsenal, Sparta Prague, Torino, Budapest Honved
    Atletico Madrid, Borussia Munchengladbach 
1 : Hamburge, Manchester City, Wolverhampton, Sporting Portugal, Fiorentina,      Glasgow Celtic, Benfica, Bologna, Red Star Belgrade, Nottingham Forest,          Athletic Bilbao, Ujpest

Statistics by nation 

18 : Spain 
15 : Italy
10 : England, Germany
9 : Hungary
6 : Netherlands
3 : Czech Republic
2 : Portugal, Austria
1 : Scotland, Serbia, France


V.  Discussion

        The methodological implementation allows the rankings to have represented the clubs’ entire performances against the determined standard and greatness throughout the history. However, the qualitative analysis to determine top level performance of the best club in Europe between seasons and eras are provided by author’s cumulative tacit knowledge converted to mathematics that is always debatable but the scale of tolerance is however quite narrowed, possibly effecting on the change of rankings in a minor part. Additionally, the proportional criteria between parts of evaluation and the proportional weight given to highest to lowest performance has a main role to finalize the ranking. 
       The seasonal weight applied to the seasonal rating reduces the disadvantage of the teams that participated in lower seasons than average group in case of achieving a competitive high peak and the teams participated in more seasons than average group is just advantageous as they had more opportunities but the number of calculated seasons is still limited in average value.      
       The result of implementation saw the disqualification of 3 clubs from highest to lowest are Ruch Chorzow, Wisla Krakow and Parma. The two Polish clubs were selected as they have a similar number of seasonal domestic places to Legia Warsaw but the results show that they achieved its highest performance in lower level than that of Legia Warsaw for the most parts. Parma is known to achieve one of the highest peaks in their golden era during the second half 1990s. However, the club spent in Series C too long and the post-golden era have also been struggling to sustain their place in the top flight.    
       Real Madrid is unsurprisingly ranked as a number one of Europe. Although the club won league titles much more than Barcelona, they are rated as the best European seasonal league performer less than Barcelona, who is the most winners for this status, 1 time and Barcelona also achieves the higher peak by aggregate season.           
           Bayern Munich’s place implies the absolute difference parts of the club between the pre-Bundesliga and post-Bundesliga era. Between 1920 – 1963, Bayern's place is roughly determined in the same status as German second league around 20 seasons and is also comparable to participate the third tier in 1955 and 1956 when they finished bottom place in Oberliga Sud and the top place in Oberliga Sud second tier.
         Internazionale win in the All-Time Battle of Milan. The overall score is similar. However, Inter achieved higher level within their peak seasons with some of Double and a Triple. AC Milan mostly achieved its peak performance in domestic and international in different seasons.  
        Man Utd VS Liverpool is an important issue. If not applied weight to the seasons and count every available English seasons, Liverpool win by more than 2.5 % of point. Man Utd also would beat Liverpool if applied weights and count all English seasons. For all that, Man Utd surpasses Liverpool more than 0.2 % in the table so they’re eligible to be ranked higher automatically.   
        The non-European international competition era is designed to give the higher point for the highest league performer as well as the point for Mitropa club competition and the result reflected to save the great central European clubs in the pre-European cup era in a high place. The best eastern European club is highly competitive when the Dinamo Kiev, Sparta Prague and Rapid Vienna are ranked adjacently. However, as aforementioned in implementation part, the Czechoslovak and Hungarian Cup record are unavailable in some seasons.    

Reference

    [4] http://www.historical-lineups.com
    [5] http://www.bolletinen.se/


Annex : The Greatest Latin European Leagues Performers Ever




Annex : The Greatest League Performers Ever by European Nation




Continental NT Evaluation


I.  Introduction and Historical Literature Review
         
           The international country’s continental football history officially began at the 1916 South American Championship football tournament although all participants are only 4. The first international tournament ever in Europe is the 1883 British Home Championship. However, most of continental tournaments established in the late 1950s (AFC Asian Cup in 1956, African Cup of Nation in 1957 and European Nations Cup in 1960).   
           The World Football Elo rating[1] is a ranking system to calculate national team performance based on every official matches played, invented by Alpad Elo and implemented in 1872, with a formula that includes various football competition parameters are marginal victory coefficient, level between competitors, importance of matches and finally concludes the ranking of nations by month. The FIFA World ranking system[2] was followed in 1992 with a similar factors of formula to Elo Rating. However, these two systems allows the performance in friendly matches to take advantage although the game is just an uncompetitive trial playing and the game result is meaningless in historical status. Also, the determination between competitors level from previous result could be highly erroneous when the fluctuation of team performance is commonly existed within a single tournament.  Importantly, there has been none of all-time national teams ranking works established to date.  
        Accordingly, this work’s objective is to study, integrally regulate and standardize the system of the entire international country history for the evaluation, including all performance characteristics (win-draw-lose, goal difference, place, round and trophy) against the determined standard of competitions within the designed system of methodology conformed to the existed format or condition at any point of evaluation.  

II. Methodology

1)    International Major Tournament
    Aside from the actual participants in historical tournament, there are some additional participants in the expansive remodel of competition to standardize the opportune factor between eras based on qualifying performance but the additional teams will be given the performance rating just 50 % in comparison to actual participant. The number of additional teams is considered from minimum standard value of qualifying performance and level of participants in qualification round in specific years. The finished round is extended to the existed round and is also based on the ranking of their raw direct performance. 

     1.1) Determine the winner of each major international tournament by qualitative analysis.     
      1.2) Determine the competitive level by counting goal difference to calculate its average for each round and input by the following formula ; 
         (∑ Goal Difference Average/(Number of Round x 4.5))
         (Number of Round +((5-Number of round)/2))/5
       The standard of competition (STD) = Top Level X Competitive Level X CC
       CC = Competition Coefficient (World Cup = 1.2, Continental Cup = 1.1)
        1.3) The Status Performance (STS) = SQRT(FRC x STD)
             Finished Round Coefficient (FRC) = TLSC – (1-GS)  ; (Winner = 1, Runner-Up = 2, SF = 3, QF = 4, R16 = 5, R32 = 6)
             TLSC (Top Level Standard Coefficient) : World Cup =5, Euro/Copa Americas = 4.5, African Cup of Nation = 3.5, AFC Asian Cup = 3.2 
               GS (Gap Standard) = 0.85 (AFC Asian Cup), 0.8 (World Cup, African Cup of Nation), 0.78 (Europe, Americas). These value is from comparative experiment of average performance between World Cup and Continental Cup.
        1.4) The Raw Direct Performance (RDRT) is calculated by chain of beaten from top level to the evaluated team.
               For elimination format, being beaten 1 goal is equal to – 0.35.
              For league format, the difference will be calculated based on following formula ; ∑ ((DGD/N)*0.35)/Nq if number of team > 3
                     ∑ ((DGD*0.75/N)*0.3)/Nq if number of team = 3
DGD : The descending goal difference
N : The number of matches     
Nq : The number of qualified teams in the group
        1.5) The total performance (TP) = SQRT(STS X RDRT)
*Remark : FIFA Confederation Cup is not considered.
    2) Qualification
      2.1) Determine top level in each group : the furthered best performer in major international tournament within a qualification group is set as the top level value in that group.
     2.2) In the pre-1960s, the performance in zonal competition are Central European International Cup, British Home Championship, Balkan Cup, Nordic Cup and Central American Cup could either replace the disappearance of any qualification tournament or combined with existed qualification performance by average if the zonal performance is higher.
     2.3) For the continental tournament without qualifying competition or not participate in qualifying round as a host or a provider, the performance in major tournament overs qualifying performance automatically.  
      2.4) Calculate the raw direct performance in the same procedure as clause 1.5     
    3) Final Calculation
         The obtained tournament performance partition (OPP) =∑ TP x PRT
; PRT = Periodical Ratio between Periodical Coefficients (4 years = 2, 3 years = 1.5, 2 years = 1. 1 year = 0.5) 
OPP will be matched to multiply with proportional weight whose number is an average of available tournaments between continents.
         Each sum of competitions’ performance are aggregated as a basic total score.
           The trophy bonus is given for only the winner in World tournament and designed as following ; World Cup since 1934 : 3 point, 1930/1950 World Cup :2 point, 1920/1924 Olympic Games : 1 point, 1928 Olympic Games : 0.5 Point
Continental : Europe : 2 points, Copa Americas : 2 Points (for 4 years partition)
               African Cup of Nations : 1 point, AFC Asian Cup : 1 point
   4) The Decisive Factors
          0.1 % is required as a minimum value to unanimously decide the rank. If not, consider the aggregate peak value at 0.05 is a minimum value to significantly differentiate, if not, consider second peak partition or even more until match the rule.
                                 
III. Implementation
            
   The implementation is conducted by continent and selected based on the historical record of round performance. In European zone, all qualified 26 nations are implemented. For other continents, 23 African nations, 21 American nations and all 20 Asian & Oceania nations are implemented.  

IV. Result

 The Greatest European Football Nations of All-Time






The Greatest Americas Football Nations of All-Time



*Remark : Haiti beat Panama by aggregate peak.

The Greatest African Football Nations of All-Time


*Remark : South Africa beat Angola by aggregate peak.

The Greatest Asia & Oceania Football Nations of All-Time


*Remark : Japan beat Iran by aggregate peak.

                   
V.  Discussion

        The methodological implementation allows the rankings to have represented the countries’ entire performances against the determined standard and greatness throughout the history. However, the qualitative analysis to determine top level performance of the winner between tournaments and eras are provided by author’s cumulative tacit knowledge converted to mathematics that is always controversial but the scale of tolerance is however quite narrowed, possibly effecting on the change of rankings in a minor scale. Additionally, the proportional criteria between parts of evaluation and the proportional weight given to highest to lowest performance has a main role to finalize the ranking. 
       The partition weight applied to the tournament rating reduces the disadvantage of the teams that participated in lower tournaments than average group in case of achieving a competitive high peak and the teams participated in more seasons than average group is just advantageous as they had more opportunities but the number of calculated tournaments is still limited in average value.      
         In Europe, Germany has become the number one as expected and left the very high gap to the second place Italy. Spain’s greatness in the most recent era ranked them up to the third place ahead of France. Czechoslovakia surprisingly beat Holland thanks to its consistency. In the peak years, Holland performed in a much higher level. However, Holland in the pre-1970s can be classified as a below-average team in Europe and even did not enter to World Cup qualifying rounds 2 times and the same status in the additional period between 2016 to date. Soviet Union first participated in international major tournament very late in 1958 and inevitably impacts in its longevity. Although Scotland was known as one of the best team in Europe during the 1920s, the nation participated in only British home championship and only Olympic Games is applied into the system for that period. For the former union likes Soviet Union, Yugoslavia and Czechoslovakia, the best performance between related independent nations is applied to those unions. Note that Croatia is the best performer among the independence nations that separated from the unions.
          In Americas, Brazil, Argentina and Uruguay is unsurpassable in its place. South American nations dominate the ranking as 8 of them appeared in top 10 and Mexico is the best team outside this zone finished at 6th. USA and Canada’s football disappeared in CONCACAF championship for around two decades that is largely impacted on the ranking. Jamaica is also impacted from the same reason, not enter to four continental qualifying rounds. Costa Rica finished as the best Central American nation as approximated. There are only two nations in the ranking never participated in World Cup are Guatemala and Panama. Cuba is disqualified for the list.
          In Africa, the top places are very competitive and finally Cameroon finished the first place. It is noticeable that 3 North African teams are Egypt. Algeria and Morocco is way equal in total basic score and Egypt became the best of them by trophy bonus from African cup of nations. Although South Africa was one of top African teams in the modern era, the nation just first international football in 1990s and so far to achieve the top group in the ranking. The implementation results saw the disqualification of 3 teams in order are Libya, Ethiopia and Burkina Faso.
          In Asia & Oceania, Korea Republic is the best nation in this zone while Israel and Australia had a potential to get the number one place but the confliction to the Middle East nations essentially conduct Israel to European zone and prevent them to qualify for a prolific major tournaments while there is no zonal competition for Australia until the inaugural OFC nations cup in 1996. Japan increasingly developed themselves since 1990s in contrary to the pre-1990s that the nation was just an average team in Asia. Uzbekistan, who is an independent nation from Soviet Union, a leading Asian team in the modern era, is ascending the ranking chronologically.  

Reference

   [2] http://www.fifa.com/fifa-world-ranking/procedure/men.html