The Most Incredible Moments in History of Domestic Leagues

1. Nottingham Forest 1977 - 1978

Forest promoted as 3rd place of second tier in English league system in 1976 - 1977 season. Before that, they consecutively played in top tier 15 seasons between 1957 to 1972.  Beyond miracle, Who imagined that they could win the top flight title when Liverpool was spending their peak years with statistics unbeaten at home matches ! This is considered as the most skipped performance in history of club football. The team comprised only 3 international players are are Peter Shilton who was arguably an only world-class player in this team, Archie Gemmell from Scotland and Martin O'Neil from Northern Ireland.  

2. Hellas Verona 1984 - 1985

Hellas Verona finished 8th in 1983 - 1984 season. During 1980s, Series A is the most competitive league in Europe, people just speculated Torino, Juventus, AC Milan, Inter Milan or AS Roma to have a chance but at its 14th Series A season, Hellas Verona defeated a ton of great teams and lost only 2 games and incredibly came the first place ! The team was led by foreign international stars like Elkjaer and Hans Peter Briegel. The rest of the team all are Italian who was never called for Caps.

 

3. Leicester City 2015 - 2016

In the modern era of English football, it become less possible for smaller clubs to overthrow Top European clubs but Leicester made it wonderfully with only 3 games loss. The club made only 14th place in the previous season and was just promoted in the season before that. Riyad Mahrez, N'Kolo Kante and Jamie Vardy are main superstars of the team. However, there was only Kasper Schmeichel who was an international player before the season started. 

4. Ipswich Town 1961 - 1962

Ipswich never played in top flight before the 1961 - 1962 season but the club won immediately won the title despite its first attempt. If track back to its history, they're a regular member of Division III in the first decade of post-war era and played in Division II only 4 seasons before experience promotion ! However, the standard of competition was questionable as Ipswich lost 10 matches and got only 56 points from 42 games !

5. Central Espanol 1984

Central Espanol was a member in Uruguayan Top league 3 seasons only (1962, 1972, 1973) prior to 1984. Particularly, the club finished the last place in 1972 but no relegation rule at that season. Penarol and Nacional were one of the leading clubs in the world at that time but a new promoted Central Espanol acquire the trophy with more 1 point than Penarol. Before that, only Defensor Sporting could win a champion in 1976. There was no player from central Espanol in 1983 Copa America Uruguay squad. 

6. Manchester City 1937 - 1938

Man City just won its first ever English top league title in 1936 - 1937 season. The club still has the same entire set of players starting eleven led by Frank Swift, Peter Doherty and Eric Brook but finished season at 21th place in the following season and relegated to Second Tier after played in Top flight in consecutive 10 seasons. This is considered as the most fluctuated performance in the football league history. 

7. Tottenham 1950 - 1951

The club was in English second tier from 1935 to 1950 across the war times and previously played in top flight 16 seasons. Tottenham amazed English football when they won the title upon its promotion. Despite, the club was just promoted, there were 3 international players in the team, Ted Ditchburn, Alf Ramsey and Ron Burgress. 

8. Boavista 2000 - 2001

Definitely Boavista could make the Primera liga more attractive when it went beyond the rule of top 3 reservation and suddenly defeated Porto just 1 point. In history, there is only another time that winner were not top 3, Belenense made it in 1946. Boavista started as a regular member of the top flight since 1970s, before realizing champions, they used to finish second place twice. Although winning title, no players from Boavista is in top ten top scorer signifying the great teamwork. The team was led by an only international player of the team is Erwin Sanchez.

9. Kaiserslautern 1997 - 1998

Kaiser won Bundesliga in 1991. The club was then a new promoted team in 1997 - 1998 season after relegated the first time in history in previous two seasons, not like in England that there are 3 clubs in history to win the top flight when they're just promoted, Bundesliga has a less fluctuated when the higher gap between big and small clubs had been maintained. It just like a fairly-tale that Kaiser coincidentally won the title with the same W-D-L as they did in previous 2.Bundesliga season !. The team consists of 6 international players are Olaf Marschall, Pavel Kuka, Martin Wagner,Ciriaco Sforza, Mirsolav Kadlec and Andreas Brehme.

10. Wolfburg 2008 - 2009

Wolfburg was first promoted to Bundesliga in 1997 In its first ten seasons, Wolfburg sustained their status betwen 6th to 15th place in the league. Between 2005 and 2007, Wolfburg survived from relegation suddenly in two consecutive seasons but the next two seasons, the club won the Bundesliga title ! The team was led by two international stars Edin Dzeko and Grafrite but both just played only a few games for their nations prior to season begun.

11. Nuremberg 1968 - 1969

Nuremberg just won Bundesliga as its only national league winner in history in 1967 - 1968 season after playing in top level in consecutive 7 seasons. However, When the club changed only 3 starting players, the performance was dramatically dropped and finished at 17th place in the following season and relegated to Regionalliga Sud. This is considered as the highest drop performance in German football league history. 

 12. Montpellier 2011 - 2012

The club was just promoted to Ligue 1 in 2009 -2010 season after spending 5 seasons in ligue II and immediately finished 5th place, then, finished 17th in 2010 - 2011 season and won the title in 2011 - 2012 season as the only time in its history and incredibly won over Paris-SG. Previously, the club best place in Ligue 1 is 3rd in 1987 - 1988 season.

The World Cup Victory at Ideal History

The World Cup begun in 1930 and in it spent long time in developing step until all top nations decided to enter the major tournament in unison. Moreover, the World War II discontinued World Cup during 1940s and regional war impacted on suspension of some nations. Another factor is the rule that suspended players who played outside country prevented some nations to have its best team. This article is to analyze what history of World Cup would have look like in ideal condition of football history.

The 1930 World Cup

The strong potential team to beat Uruguay is Austria that formed “Wunderteam” led by Hugo Meisl. Although Austria won only one match in 5 friendly games in 1930, lost Hungary twice and Draw England, the mainstay of the team likes Blum, Smistik and Sindelar played only one game or did not play. Had Austria formed the complete team and participated in the tournament with every player as one of international legends in their position, the winner of world cup might belong to Austria.

Austria 1930 Ideal Team : Rudi Hiden, Karl Rainer, Josef Blum, Walter Nausch, Josef Smistik, Leopold Hofmann, Friedich Gschwiedl, Karl Zischek, Anton Schall, Johann Horvath, Matthias Sindelar.

The 1934 World Cup

Austria might not be eliminated in semi-final by World champion Italy if players like Hiden, Nausch, Gschweidl and Binder joined. Argentina and Uruguay as a top South American team that did not enter the tournament did not have the top stars who spent their peak career.
Austria 1934 Ideal Team : Rudi Hiden, Karl Sesta, Karl Rainer, Walter Nausch, Josef Smistik, Leopold Hofmann, Freidich Gschwiedl, Karl Zischek, Anton Schall, Matthias Sindelar, Franz Binder
Main Substitution : Josef Bican

The 1938 World Cup

Had Argentina full team entered to the tournament, Italy might not be able to continue winning World Cup title. From October 1937 to October 1938, Argentina played 5 games and all were victory against Uruguay in small international cup. Argentina might not have a world-class goalkeeper and defenders but its midfielders and attackers all were one of the best players in the world in their position.

Argentina 1938 Ideal Team : F.Bello, J.Alberti, A.Cuello, Jose Maria Minella, Ernesto Lazzatti, Antonio Sastre, Carlos Peucelle, Enrique Garcia, Jose Manuel Moreno, Vicente De La Mata, Herminio Masantonio

The 1942 World Cup

Argentina and England would be the best contenders in the tournament. Argentina did not win 1942 South American Championship as the team wasn’t presented by all of its best players and shared the portion with the 1941 South American Championship team.

England at that time was potentially the best team in Europe.

Argentina 1942 Ideal Team : S.Gualco, J.Alberti, Jose Salomon, Ernesto Lazzatti, Carlos Sosa, Antonio Sastre, Enrique Garcia, J.Carlos Munoz, Jose Manuel Moreno, Adolfo Pedernera, Herminio Masantonio
Main Substitution : Angel Perucca

England 1942 Ideal Team : Frank Swift, Eddie Hapgoods, George Male, Joe Mercer, Stan Cullis, Wilf Copping, Cliff Bastin, Stanley Matthews, Wilf Mannion, Raich Carter, Tommy Lawton

The 1946 World Cup

Argentina and England would still be the best contenders in the tournament. Argentina at that time was coincidentally congregated by world-class stars even in substitution, is arguably the greatest Argentine team in history. In reality, 1946 South American Championship, Argentina won all five games and became the champion.

England 1946 is considered the better team than that of 1942 when world-class defenders like Neil Franklin and Billy Wright joined the team.

Italy led by Valentino Mazzola and players from Torino “Le Grande:” was also a strong candidate with the world-class back-up likes Pietro Rava and Carlo Parola but the outside forwards and scorers are considered not competitive enough.

Argentina 1946 Ideal Team : C.Vacca, J.Marante, Jose Salomon, Carlos Sosa, Ernesto Lazzatti, N.Pecchia, Felix Loustau, Vicente De La Mata, Jose Manuel Moreno, Adolfo Pedernera, Rene Pontoni
Main Substitution : Rinaldo Martino, Norberto Mendez, Angel Labruna

England 1946 Ideal Team : Frank Swift, Neil Franklin, Billy Wright, George Hardwick, Joe Mercer, Stan Cullis, Tom Finney, Stanley Matthews, Wilf Mannion, Raich Carter, Tommy Lawton 
Main Substitution : Stan Mortensen

The 1950 World Cup

Hungary is the best team in Europe in 1950 and its offensive line is slightly greater the 1954 team when Nyers and Kubala joined the team. Hungary is potentially superior to Uruguay although if the team would have been even more dangerous when having Walter Gomez reinforce. Brazil side would also be unparalleled if Tesourinha is added.  
Denmark ideal team comprises six world-class superstars ,that are confirmed by Guerin sportivo, playing in Series A are John Hansen, Karl Aage Praest, Karl Aage Hansen, Helgre Bronee, Jorgen Leschy Sorensen and Alex Pilmark, would be the greatest danish team in history and has a greater potential than Danish Dinamite but the team is lack of top-class defenders and still second to Hungary by significant gap.

Hungary 1950 Ideal Team : Grosics, Sandor Szuc, Ferenc Rudas, Gyula Lorant, Jozsef Zakarias, Jozsef Bozsik, Istvan Nyers, Nandor Hidegkuti, Laszlo Kubala, Ferenc Puskas, Sandor Kocsis 
Main Substitution : Ferenc Deak, Ferenc Szusza

The 1954 World Cup

Sweden is root from 1948 Olympic Games Gold Medal team is another potential team to win the title if Gre-No-Li and other Swedish players playing in Europe during their peak were allowed to join the team. It would be a dangerous team to contend for World Cup winner. 
Sweden 1954 Ideal Team : Karl Oscar Svensson, Orvar Bergmark, Bengt Gustavsson, Ake Johansson, Sigge Parling, Sune Andersson, Lennard Skoglund, Kurt Hamrin, Nils Liedholm, Gunnar Gren, Gunnar Nordahl
Main Substitution : Selmonsson, Jeppson 

The 1958 World Cup

Although Argentina was embarrassingly beaten By Czechoslovakia 6-1 in the group stage, the additional players like Di Stefano and Omar Sivori could turn the history although Di Stefano failed to lead Spain qualified for world cup in more difficult circumstances and potentially achieved runner-up of the tournament as Brazil is invincible particularly at ideal condition that Jose Altafini, Dino Sani, Jose Macia Pepe were added to the team.  

Argentina 1958 Ideal Team : Rogelio Dominguez, Pedro Dellacha, Fernando Vairo, Francisco Lombardo, Nestor Rossi, Alfredo Di Stefano, Omar Corbatta, Raul Belen, Antonin Angelillo, Omar Sivori, Jose Sanfilippo
Main Substitution : Humberto Maschio

The 1966 World Cup

Scotland did not qualify for the final tournament mainly due to the team in qualifying match wasn’t participated by many top stars including Ballon Dor Winner Denis Law. The team could compete with England the winner of 1966 world cup equally in 1966 Historical Friendly match. Scotland in the mid-1960s was abundant in superstars from the European cup winner Glasgow Celtic and many others in English football league. This Scotland team would have been formed by 8 players in all-time Scotland squad.

Scotland  1966 Ideal Team : Ronnie Simpson, Tommy Gemmell, John Greig, Billy Mcneil, Dave Mackay, Billy Bremner, Jim Baxter, Jimmy Johnstone, Bobby  Lennox, Alan Gilzean, Denis Law


The 1978 World Cup
Netherlands with Johan Cruyff is worth thinking that the Oranje would have won its only World Cup winner in history. However, Argentina won the world cup title despite ignoring using service of Diego Maradona, Norberto Alonso and Ricardo Bochini including Osvaldo Piazza the leading defender arguably the best defender to ever play in French ligue. 
  

The 1992 Euro and 1994 World Cup

The Yugoslav war prevented Yugoslavia to approach into its golden era. At that time Yugoslavia produced a ton of world-class stars even in the bench. The team has a full potential to become Europe champion in 1992 and was a strong contender for world cup winner as well.

Yugoslavia 1992 Ideal Team :  Tomislav Ivkovic, Robert Jarni, Vujadine Stanojanovic, Miroslav Djukic, Sinisa Mihajlovic, Srecko Katanec, Dragan Stojkovic, Robert Prosinecki, Dejan Savicevic, Alen Boksic, Darko Pancev
Main Substitution : Vladimir Jugovic, Zvonimir Boban, Davor Suker
Yugoslavia 1994 Ideal Team :  Tomislav Ivkovic, Robert Jarni, Vujadine Stanojanovic, Miroslav Djukic, Sinisa Mihajlovic, Slavisa Joganovic, Zvonimir Boban, Dejan Savicevic, Robert Prosinecki, Predrag Mijatovic, Davor Suker

Main Substitution : Vladimir Jugovic, Dragan Stojkovic, Alen Boksic

       

Introduction

The World Cup Winners

The Intercontinental Cup Winners

The World Club Cup Winners

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)/N_q i

DGD : The descending goal difference

N : The number of matches     

N_q : 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

   [1] http://www.rsssf.com/miscellaneous/torre-sac-best.html

   [2] http://www.rsssf.com/miscellaneous/torre-cam-best.html

   [3] http://www.rsssf.com/miscellaneous/wtatr.html

   [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)/N_q i

DGD : The descending goal difference

N : The number of matches     

N_q : 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, 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 

19 : 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

    [1] http://www.rsssf.com/miscellaneous/wtatr.html

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

    [3] http://www.rsssf.com/miscellaneous/ecqf.html

    [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