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.
      1.2) 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
       1.3) The standard of competition (STD) = Top Level X Competitive Level
       1.4) 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)
      1.5) 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. 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. 

    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.  



Annex : The Greatest Latin American League Performers Ever

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

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