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