Introduction

The footballistic competence is the quality that has a sportsman of being perfect and able to perform a well playing football. It is the skill and ability demonstrated by him at the playing field for successful implementation of this game's rulers during a match or a tournament supported by FIFA organization (1). It should be measured comparatively in relation to other players involved. This parameter changes from player to player and it emphasizes in the development of the footballer's potential as a product of his basic formation and personal experience. Competence is what the player is from a footballistic point of view. This parameter gives an excellent idea about the ability that he has for satisfactorily performing this sport and for that, competence is an effective way for assessing his real effectiveness. It must be calculated or determined through a process in which we can watch how his performance on the Playground is.

Until now there aren't standardized criteria or viewpoints to objectively determine the quality with which a player performs in the field. Footballers, representatives, journalists and those who run the world market of this sport, always use subjective parameters for assessing the individual and collective football team performance. Between these specialists there are serious controversies regarding this issue and most of the time, they do not coincide in their respective points of views. In order to evaluate a player, many experts consider, as the most important parameter, to see the relevant or determining plays made by the sportsman during a game, others feel more important to watch his personal appearance, his look, or to the force with which the player attacks the opponent to take the ball, or the way as he moves in the playing field, or how he comes near the opponent in order to prevent that the last one can receive the ball, or the quality or category of his team, or the obtained by his team results in the last tournament, or the city were he was born, or by his footballistic history or by... (2). Not only there are big controversies among experts, but also a lot of superficiality in their estimates to analyze each parameter. The lack of clear criteria hinders the work of coaches, players' agents, journalists, fans and in general, all members of the international family of football, to recognize and really to know who the best players are in the field. Most likely this problem is also generated because those subjective concepts are produced by expert pundits, who almost always, on insufficient knowledge, make judgments based on their personal information or comments taken from specialized journals or as happens most of the time, from watching video clips, some positive data generated at attack by the player in a match or during a tournament (3). The procedure for assessing individual and collective performance of a team should be a process that must consist of several stages. The first of these is to determine which objective and reliable parameters or indexes should be watched in order to assess the team professional quality for taking care and following them at practice, on the playground, in order to use them as markers or labels of productivity on the field, for all players. It is necessary to carefully write and order the information produced by the players’ work, and then organize, analyze, draw conclusions and if it is possible to make inferences and deductions.

Several years ago, at the Surcolombiana University, located in Neiva, we have standardized a high number of procedures with the above purpose. Many of them have been evaluated in practice, with excellent results (4). We have systematized those procedures and built special software -EVALFUT, an instrument for objectively assessing the individual and collective footballistic competences of a team during a game or a tournament accordingly its player performances on the playground. The general purpose of this article is to familiarize to its readers with the characteristics and results obtained in the individual and collective work’s assessment of all players of the U-20 Colombian teams that have represented our country in all tournaments of the under twenty category, endorsed by FIFA general organization between 2001 and 2011 (5). This paper briefly summarizes everything done on the ground by 108 players from our selection in this category, all who have participated from the qualifying round of the thirteenth tournament of the U-20 FIFA World Cup, played in several Ecuadorian cities in 2001 to the final phase of eighteenth tournament, played recently in our country, in this 2011. In this gathering exercise, we also have introduced that data produced by our selection players in their last five games played in Bogota during that unforgettable world event.

Materials and methods

For this work we have used the information produced on the playground, by 108 footballers who have represented us in several tournaments supported by FIFA since 2001, until the completion of the 18th tournament finals, held recently in Bogotá. We have used the data produced by the software EVALFUT, a special instrument, designed and built at the Surcolombiana University to assess the competence of a football team during a game or a tournament, after these matches:

Nine games of the eliminatory phase of the 13th FIFA world cup's tournament played in Ecuador in 2001. All the official 16 games played by our Colombian team during the fourteenth tournament, which at the beginning, the knockout stage, took place in 2003, in several Uruguayan cities (nine games), and then in its final phase, in United Arab Emirates - UAE (seven games). In this tournament, our team finished third, after their final victory against Argentina 2-1, under the general direction of Reynaldo Rueda. All 13 matches of the 15th tournament, played first in its removal phase, mainly in the stadiums of the richest in coffee Colombian zones, in the middle of 2005. Colombia, underthe technical direction of Eduardo Lara, classified first in this eliminatory phase and won from his zone, a place to the final phase played also that year in Holland,. Data of nine tournament games of the eliminatory phase played in Paraguay in 2007. Because we have had problems in registering matches played by U-20 Colombian team in Venezuela 2009, here we only use data from only four games played in that 17th tournament. We also included data produced by Colombia in five games played by our selection in the Nemesio Camacho stadium against teams of France, Mali, South Korea, Costa Rica and Mexico, during the final phase of 18th Tournament U-20 FIFA World Cup, played recently in Bogota.

Each one of 56 matches played by the U-20 Colombian selection team since 2001 until the present time, were at first recorded on specially designed by us sheets, for this purpose. They have spaces for the entry of data. We obtained the stenogram of each game and then passed that factual information to another blank called by us the datagram. Then each compilation was introduced to a computer which, in its local disk has the EVALFUT (4). The processing of the information by this software gave us several graphics; the most important are the individual Qualifigram, the collective Thirdgram, the Rivalgram, the Goa-Ikeepergram and others ones. For this work we use the Pologram, the Uscogram and the Evolu-gram. As we can see on figure 1, the Pologram is a horizontal bar graph, which in its X-axis shows the footballistic competence's comparative index on a scale of increasing values between minus three and plus three. In the vertical axis are the name's initials of each player. This index allows us relatively to qualify his footballistic competence. If it is greater than two his efficacy is excellent, but if it is between one and two the EVAL-

FUT qualifies the player as good. If the index that labels the player is between zero and one, his efficacy is regular. A competence’s index lower than zero, but above minus one shows a poor footballistic rating. Values below minus one show a very very poor footballistic power, and indicate that the player didn’t have the necessary competences for participating in a FIFA tournament for the U-20 international category.

The EVALFUT gives an absolute index which also indicates the player's footballistic baggage, accordingly his abilities and skills displayed on the playground during a measured interval of time. We used also this parameter for comparing the players’ effectiveness.

The Uscogram (see Fig. 2), is a dispersion graph that has a frame of crossed lines which define the limits of 15 rectangular zones. A statistical background is not required to understand it. The graphic display allows us to compare the player qualification at attack with that at defense and also gives us some indication of what is wrong with the player's competences. The pair of plotted qualifications can be used for ranking the player, for determining his position in a world football hierarchy, for establishing his footballistic competence order according to his characteristic scores at attack and defense.

Plotted qualifications of a player within a rectangle indicate us his true footballistic competences and allow us to suggest him in which football clubs league his performance may be the very best. The table 1 shows the countries league’s hierarchical classification proposed for us.

s-

Figure 2. The Uscograma and its Zones.

Table 1. Countries League’s Hierarchical Classification.

1.    Rest of World.

2.    Caribbean Islands.

3.    Rest of Asia.

4.    Rest of Afrika.

5.    Rest of Central America.

6.    Arab countries.

7.    Australia and Canada.

8.    Japan and Koreas.

9.    Rest of South America.

10.    Costa Rica, Honduras and Central Afrika.

11.    U.S.Aand Mexique.

12.    Rest of Europe.

13.    Germany, Belgium, Netherland.

14.    Brazil and Argentina.

15.    England, Spain, France, Italy.

As we see in Fig. 3, the Evolugram is a box plot that relatively shows the evolution of the collective performance of a team after its participation in several FIFA tournaments. In iwts y-axis shows the qualification at defensive play or at offensive one. On the horizontal axis are the tournaments played by the U-20 Colombian team.

Results

From Ecuador - 2001 to Colombia - 2011 Alvaro Araujo, Reynaldo Rueda, Eduardo Lara y José Helmer Silva, our official national coaches, have used 116 players including eight goalkeepers.

Table 2. Classification of U-20 Colombian Players.

CDQui

Carlos Darwin Quintero

GusRo

Gustavo A. Rojas

EPE

Edixon Perea

CMA

Cristian Marrugo

JAR

Jaime Alfonso Ruiz

LCH

Luis Felipe Chará

2

631-810

WRE

Wason Rentería

JRA

Jamel Ramos

EVA

Edwin Valencia

HMO

Harrison Morales

AndGa

Andrés Gallego

DIV

Diego Valdés

PPA

Pablo Pachón

HUR

Hugo Rodallega

MauCh

Mauricio Chalar

OVI

Oscar Villarreal

MiOr

Michael Ortega

JOM

Johnier Montano

AlBer

Alejandro Bernal

ALR

Aldo Leao Ramírez

ADO

Alvaro Domínguez

HaMar

Harold Martínez

GilGar

Gilberto García

JDB

Juan D Buatista

3

361-630

JimBe

Jimmy Bermúdez

LRO

Leonardo Rojano

AnArb

Andrés F Arboleda

JuCa

Juan Cabezas

JPPin

Juan Pablo Pino

LEN

Leonardo Enciso

HeQu

Héctor Quiñones

JOR

Johnier Ramírez

JJK

John Jaira Culma

CEV

Carlos Enrique Valdés

HenRo

Henry Rojas

RUB

Rubén Bustos

WCO

Willman Conde

DiMo

Didier Moreno

LuMu

Luis Muriel

FRG

Freddy Guarín

PeFr

Pedro Franco

JHA

Johny Acosta

JaRo

James Rodríguez

CrNaz

Cristian Nazarith

JohM

John Mosquera

CriMej

Cristian Mejía

4

181-360

DMO

Dayro Moreno

MCT

Macnelly Torres

Jo Va

José Trencito Valencia

ElkBI

Elkin Blanco

CAL

Carlos Álvarez

OBR

Oscar Briceño

FLO

Fabian Lopez

DwLeu

Dawling Leudo

JAMae

Juan Alejandro Mahecha

Ja Rey

Javier Reyna

JFL

Javier Florez

MaPer

Marcos Pérez

ERC

Erwin Carrillo

EisLo

Eisner Loboa

Ja Rey

Javier Reyna

AnMo

Andrés F. Mosquera

JeMu

Jeisson Murillo

AlxDz

Alex Díaz

5

91-180

DMT

Diego M Toro

RFG

Radamel Falcao García

JAJ

Javier Araujo

ShCar

Sherman Cárdenas

SaAr

Santiago Arias

JFPal

Jairo Fabian Palomino

YaCuR

Yamith Cuesta Romaña

HEPer

Hernán Enrique Pertuz

SVIba

Segundo Víctor Ibarbo

EDM

Edwin Muñoz

JOB

Jimmy Obando

JMA

Jorge Amará

MaArr

Mauricio Arroyo

JuDi

Juan Díaz

AnFOr

Andrés F Ortiz

JulGu

Julián Guillermo

ShCar

Sherman Cárdenas

DuZa

Duván Zapata

JaCa

Javier Calle

6

<90

DdLCa

David Leonardo Castro

YeCa

Yerson Cándelo

SePe

Sebastian Pérez

DAM

Daniel Machacón

LGC

Luis Gabriel Castro

SHE

Sebastián Hernández

ElvPer

Elvis Perlaza

MAJRo

Miguel Angel Julio Rósete

LuOs

Luciano Ospina

JAR

Javier Arizala

FaCa

Fabian Castillo

JoMo

Johnny Mosquera

As we can watch in table 2, the software EVAL-FUT, conventionally has classified the remaining 108 players in six groups, according to their permanence’s time on the playground, during those eleven years. To the first set belong 13 players, who were on the ground more than 810 minutes. In the second group are those who played between 631 and 810 minutes. Here we have 14 players. In the third formation are 29 sportsmen who played between 361 and 630 minutes. There are also 29 players in the fourth group; they were playing from 181 to 360 minutes. In the fifth set are 11 footballers who played in an interval of time between 91 and 180 minutes. In the last one group are 12 players who advanced the ball on the ground less than 90 minutes.

Table 3. Best Colombian Players at Defensive Play

Table 3 shows the best players of each group in defensive play. All of them perform the duties of a defender.

Table 4. Best Colombian Players at Attacking Play

The footballistic competence’s index (FCI), in points, of all Colombian players are presented by groups in horizontal bar graphics located in figures from 4 to 9. Note that the players’ names’ initials have been listed in the vertical axis in a decreasing order of index. Each graph is called by us the

Pologram and is obtained by a statistical descriptive traditional method and a comparative analysis between players, which studies the relative performance of them on the playground. The horizontal scale at the abscissa enables us to read the FCI value for each player.

-3,0    -2,5    -2,0    -1,5    -1,0    -0,5    0,0    0,5    1,0    1,5    2,0

Figure 4.- Pologram Group One: >810 min.- Footballistic Competence's Index (FCI).

Each Pologram can be divided into imaginary rectangles having bases on the horizontal axis, which allow us to classify the players in five groups. Those who, by their efficacy, are excellent or very good in relation with others who belong to the same class by time played. They are first class footballers because their FCI is two or greater than two. The FCI lower limit of the second class players is 1.0 and the upper one is less than two. These footballers are considered by the EVALFUT as profitable, advantageous, competent, skillful players, with optimal qualities required for playing well football. The FCI interval for the third class players is between zero and less than one. A footballer of this group is a normal, natural, usual, ordinary, standard, average player, who shows the necessary skills, abilities and competences for playing normal football. He is not an outstanding player, but he is not a bad footballer. In the left side of each Pologram are the FCI values of players who fail to reach an acceptable standard, who make to the football fans an unpleasant or incorrect impression. They are footba-llistically objectionable. There are two kind of these last players, those who have a FCI equal or higher than minus one but lower than zero, and those with FCI lower than -1. The first ones are classified by the EVALFUT as bad players and the second ones as very bad footballers, with worst footballistic results. They don’t have the experience, nor the adequate ability, nor the quality for being in a country representative team that participates in an endorsed by FIFA world tournament.

As we can observe on figure number four and in table two, to the first group of the EVALFUT classification belong 13 footballers who were on the playground more than 810 minutes. It means they have played with our national U-20 football team, an equivalent of more than nine games during the eight FIFA tournaments previously mentioned.

This graph tells us how many right plays on the playground, behind the leading player, Christian Zapata, each of the other footballers are in the studied eleven years. The index value showed by the Pologram mainly depends on the attack and defensive qualifications of each player. The best U-20 Colombian footballer at defensive play was Christian Zapata. His qualification, during that interval of time was 10.5. He was followed by José Julian de la Cuesta and Camilo Zúñiga. These three leading players are considered by the EVAL-FUT as good players. They can play in any football league around the world with a right performance. With the exception of José Julian de la Cuesta, the majority of these first group players have had a lower than one qualification at attack. It means that they have had a lot of mistakes at the offensive play. The lowest player in this group was Juan Carlos Toja, there are more than four points behind the better of this group - Christian Zapata.

In this and in general in all polograms there appear to be a good connection or association between the quantity of right plays at defensive and the number of good plays at attack.

The graph on figure 5 is similar to that obtained for the first group players. These footballers have stayed on the playground more than the time equivalent to seven games but less than nine ones. One fact is made clear by this graph, only Hugo Rodallega has the necessary footballistic competences for playing well in any world football league. His rating is several times better than the others who belong to this group. Although he is not a good defensive player, his qualification at attack - 15 points is the highest value among the all U-20 Colombian players, thanks to his wonderful capacity for playing well at attack. The EVAL-FUT considers him as an excellent footballer with a FCIndex of 2.3. The lowest player in this group is Carlos Darwin Quintero. His low qualification , less than minus 1.5, is due to his isolated and individual form of playing on the playground. His pretty dribbling game doesn’t allow to him to share the ball with his others playmates.

The FCIndexes’ dates for the third group players on four until seven consecutive games earned by the FIFA organization are shown on figure 6. The most noticeable fact in this graph is that among these 29 of the 3rd group players, are James Rodriguez, Johnny Acosta, Pedro Franco, Freddy Gua-rin and Luis Muriel. All of them have an index of footballistic competences higher than one. Although his index is lower than this, it’s necessary to consider the best qualification - 9.5 for Didier Moreno at defensive play. From this 3rd group the best players at attack were Johnny Acosta - 6.9; James Rodriguez - 6.7 and Luis Muriel 6.1. The lowest of this group was Mauricio Chalar.

In figure 7 as in the above mentioned ones there is a graph where we can easily observe that there are big differences between the FCIndexes of the players who have right horizontal bars and those in which their initial names are insight the left horizontal bars. The highest index value, more than 2.0, belongs to Hernán Enrique Pertuz. Players with index higher than one are Yamith Cuesta Romaña, Jairo Fabián Palomino and Santiago Arias. In this fourth group the best footballers at defensive play were Diego M. Toro, Hernán Enrique Pertuz, Jairo Fabián Palomino and Yamith Cuesta Romaña with 9.8; 9.0; 8.2; and 8.0 points, respectively.

Although it is not commendable or advisable to value the footballistic quality of a player after watching his skills, abilities, attitudes on the playground during three or less than 270 minutes, the EVALFUT has given us the figures eight and nine. The subject of these graphs is the same as the others polograms. In figure eight there are eleven horizontal bars, only four of them are positives. The best players of this fifth group were Javier Calle and Duvan Zapata. The best footballers at defensive play were Julian Guillermo and Andres Felipe Ortiz. Their respective qualifications were 11.0 and 7.0. The best qualified by the EVALFUT, at attack, were Duván Zapata, Javier Calle and Sherman Cárdenas.

Figure 8 shows a graph where we can observe nine horizontal positive bars, but only three left ones. There is a big difference in relation with the others analyzed polograms. Here we don’t have players with indexes higher than one. Very few things we can see on a player who runs the ball on the playground in a time equal or lower than ninety minutes. Nevertheless there are players as for instance Fabian Castillo and Fabian Hernández with qualifications at attack higher than 2.9. There are also good players at defensive as for instance Johnny Mosquera and Javier Arizala with defensive qualifications of 8.2 and 7.7 respectively.

•3.0    -2,0    -1.0    0.0    1.0    2,0    3.0 Figure 7. Pologram - Group 4: 181 - 360 min. - Footballistic Competence's Index (FCI).

As we can see in figure 10 each big rectangle is divided into five little ones. Each delimited zone represents any of 15 created by us, great divisions of the football competitive world, where exist superior league clubs which participate in official tournaments recognized by the FIFA organization (see table 1).

The players’ initial names and their respective location in the Uscogram rectangles are presented in table 5. In this systematic arrangement and in figure 11 we observe that 53 Colombian players gave points inside the right big rectangle, 12 inside the left one and only 25 inside the central one.

Eighteen players gave points outside the three rectangles. From the 53, by time played, ten belong to the first EVALFUT group, eight to the second one, sixteen to the third one, 11 to the fourth one, 4 to the fifth one, and also four to the sixth one. By their position on the Uscogram, which is the result of their own footballistic competences showed on the playground during those eleven years of this millennium, these 53 can not optimally play in tournaments of the superior leagues played in Europe, South America, Germany, Belgium, Netherlands, U.S.A. Mexique, Central Africa, Costa Rica, Honduras, Japan, Koreas, Australia, Canada and Arabian countries.

ENTORNOS num. 25. Septiembre de 2012

-5

Figure 10. Uscograma - Suggested Divisions of the Football Competitive World.

iii.

1 | 2 | 3 | 4 | 5

II

6 | 7 |

CENTRAL

1

n

11 | 12 | 13 I 14 | 15 LEFT

i i i IQ I 2Q | 3Q | 4Q

Table 5. Players Names’ Initials and their Location in the Uscogram (Z=Zone)

From the 25 players who gave points inside the central rectangle only one belongs to the first group, three to the second one, seven to the third one, eight to the fourth one, three to the fifth one and 3 to the sixth one group. It means that they optimally can play in professional leagues of the Arabian countries, Australia, Japan, Koreas, Canada, Costa Rica, Honduras, CenterAfrikan countries, and in other southamerican countries different to Brazil and Argentina.

From the 12 who gave points inside the left big rectangle, only one belongs to the first group, also one to the second, five to the third, three to the fourth, one to the fifth, and one to the sixth. These players, can optimally participate in professional tournaments of superior leagues from all world countries, with the exception of Brazil, Argentina, Spain, Italy, England and France. They don’t have the necessary competitive level for being football principal members or performers of a team, for ranking first in the highest tournaments of these countries. From the 18 players who gave points outside the three rectangles 3 gave them in the first quadrant, four in the second, four in the third, and seven in the fourth quadrant. Points with values consistently high or low at defensive or at attack don’t follow a harmonic footballistic pattern. They suggest that the player was assigned to work in a special football position, performing a defensive or an offensive activity during a tournament. Nobody has the competences for playing well in the major football leagues settled in England, Italy, Spain, France, Brazil or Argentine. According to the Uscogram information twenty one players have the ideal footballistic competences for playing well at international level. To the right big rectangle belong Christian Zapata, Pablo Pachón, Jaira Fabián Palomino, Julián Guillermo. In the center big one are six players: Ruben Bustos, Carlos Enrique Valdés, Freddy Guarin, Sherman Cárdenas, Santiago Arias, Yamith Cuesta Romaña. In the left rectangle are: Luis Muriel, James Rodriguez, Javier Araújo y Johnny Acosta. The best outliers are seven: Duván Zapata, Javier Calle, Hernán Enrique Pertuz, Hugo Rodallega, Radamel Fal-cao Garcia, Diego M. Toro y Eisner Loboa.

Figure 12 clearly shows that the greatest qualification of Colombia at defensive play was 78 during the 3rd third of the game against Italy in Holland 2005 and the minimum borderline was 14.7 on the sixth third in their game against Argentina in Colombia 2005. The preponderant value for the

Colombian defensive qualification was greater than 24 points. With the exception of their participation in Holland, in all remaining games this qualification ever was lower than 60. The width of the qualification changing during those eleven years was variable. The participating teams at the Arabic Emirates and at Colombia 05 have had a narrow interval of variation in their defensive qualification, but for the national teams in Paraguay 07 and Venezuela 09 the intervals of distribution have been very wider.

Figure 12. Evolugram at defensive Play

In all cases the distribution of the defensive qualification has been asymmetric with a positive bias. Figure 13 shows a non homogeneous behavior of Colombia at attack. The distributions of the qualifications at offensive play significantly have changed. In this plot the boxes are bigger than those obtained at defensive play. Each box’ height indicates us that in each game the Colombian players, at defensive, have been more organized in their work than at attack. In very few times the team qualification at attack was higher than 20. It shows that Colombia’s behavior on the playground was most defensive than offensive. Only in the extra time on the Kalifa Al Shein stadium in the Arabic Emirates, in their game against Ireland, their attack qualification was 96. That day the Colombian team has played 14 additional minutes in an extra time until Edwin Carrillo have scored the victory’s golden goal. Colombia has won 3-2.

Discussion

The contemporary world demands the analysis of the quality with which a person makes his daily work (6). At the Surcolombiana University we have standardized a method for evaluating the footballis-tic competences of a player depending on how he works, getting the ball, and passing, kicking, tackling at defense and at attack. Data produced by the player on the playground are collected by an official scorer, who writes them in a special sheet called by us the STENOGRAM. This factual information is introduced in a computer, which has the software EVALFUT (4). This electronic package gives useful quantitative values and graphics, which can be used for objectively evaluating the performance of a footballer. Each player can appraise his footballistic yield by comparing his results with those of a standard player. If the results are not acceptable by him, it also gives to him, some indications of what is wrong in his football work. If he knows the classical basic statistical descriptive procedures, he can use them for understanding many graphs and tables constructed by the EVALFUT. If he doesn’t have an optimal statistical background and he can not understand the EVALFUT statistical techniques, he can use the Uscogram, a very simple graphic technique produced also by that colaboraware to help professionals understand the survey results of his football performance. We have applied this graphic system and the statistical one in several FIFA tournaments with excellent results (2). As a practical example, in this paper we have described the results obtained after pursuing the yield of 108 Colombian football players during their participation in FIFA world U-20 tournaments in an interval of time of eleven years, from 2001 to 2011.

Figure 13. Evolugram at Attacking Play

The best Colombian players at defensive were: According to the all groups’ Polograms there are 15 footballers: Christian Zapata, José Julián de la Cuesta, Hugo Rodallega, James Rodríguez, Johnny Acosta, Pedro Franco, Freddy Guarín, Sherman Cárdenas, Santiago Arias, Yamith Cuesta Ro-maña, Luis Muriel, Hernán Enrique Pertuz, Jairo Fabián Palomino, Duván Zapata y Javier Calle.

In addition to those 15, the Uscogram gives 12 players’ names, more. They are:

In the left big rectangle: Javier Araújo.

In the center one: Jaime Alfonso Ruiz, Carlos Enrique Valdés and Rubén Bustos.

In the right rectangle: Pablo Pachón, Julián Guillermo, Camilo Zúñiga, Abel Aguilar, Diego Valdés, Willman Conde.

The two remainders are among the best outliers, who are six: Duván Zapata, Javier Calle, Hernán Enrique Pertuz, Hugo Rodallega, Radamel Falcao García, y Eisner Loboa.

Bibliographic and Web Sites References.

http://es.fifa.com/worldcup/archive/ger-

many2006/statistics/teams/topgoals.html

Polo, R.E. (2002). Competencias Futbolísticas de los Deportistas de la Copa América. Colección de Investigación. Neiva, Colombia: Editorial Universidad Surcolombiana.

Duran, G., Guajardo, M., Weintraub, A. and Wolf, R. (2009). Scheduling the Chilean League using mathematical programming. OR/MS Today. April.

Polo, R.E. (2006). EVALFUT. Herramienta Básica para Valorar el Rendimiento Individual y Colectivo de un Equipo e Fútbol. Colección de Investigación. Neiva, Colombia: Editorial Universidad Surcolombiana.

http://es.fifa.com/worldcup/archive/southafri-

ca2010/statistics/castrolindex/index.html

Hughes, M. and Franks, I. (2005). Analysis of passing sequence, shots and goals in soccer. J. Sports Sciences 23, 509-514.