Performance analysis of professional soccer goalkeepers by Composition of Probabilistic Preferences

Análise de desempenho de goleiros do futebol profissional por Composição Probabilística de Preferências

Análisis del rendimiento de porteros de fútbol profesional por Composición Probabilística de Preferencias

Luiz Octávio Gavião Erick Vieira Gavião Annibal Parracho Sant’Anna Gilson Brito Alves Lima Pauli Adriano de Almada Garcia About the authors

ABSTRACT

This research aims to assist managers and technical commissions to choose professional soccer goalkeepers. A sample of 64 goalkeepers playing in Argentina and Brazil was studied. Their performance in the matches of two seasons were analyzed considering three criteria: goals against per minute played, percentage of goals and percentage of matches without conceded goals. The Composition of Probabilistic Preferences (CPP) was the method chosen for modeling, considering the random variability in the problem data and in football, considered one of the most unpredictable sports. CPP allowed to compare the choice based on the data analysis to the latest goalkeeper call-ups for these countries’ national teams. The selected goalkeepers corresponded to those presenting the best individual performance, which confirms the model.

Keywords:
Soccer; Evaluation; Goalkeepers; Composition of Probabilistic Preferences

RESUMO

Esta pesquisa teve como objetivo auxiliar gestores e comissões técnicas na escolha de goleiros do futebol profissional. Foi estudada uma amostra de 64 goleiros que atuam na Argentina e no Brasil. Foram analisados seus desempenhos em jogos de duas temporadas, considerando três critérios: gols sofridos por minutos jogados, percentual de gols evitados e percentual de partidas sem sofrer gols. A Composição Probabilística de Preferências foi o método escolhido para a modelagem, por considerar a variabilidade aleatória dos dados do problema e do futebol, considerado um dos esportes mais imprevisíveis. A aplicação comparou a escolha baseada na análise dos dados com as últimas convocações de goleiros para as seleções desses países. Os goleiros selecionados corresponderam aos de melhor desempenho individual, confirmando o modelo.

Palavras-chave:
Futebol; Avaliação; Goleiros; Composição Probabilística de Preferências

RESUMEN

Esta investigación tuvo como objetivo ayudar a gerentes y comisiones técnicas para elegir a los porteros de fútbol profesional. Una muestra de 64 porteros de Argentina y Brasil fue estudiada. Las actuaciones en los partidos de dos temporadas fueran analizadas, considerando tres criterios: goles concedidos por minutos jugados, porcentaje de goles evitados y porcentaje de partidos en los que al portero no le encajaron goles. La Composición Probabilística de Preferencias fue el método elegido, considerando la variabilidad aleatoria de los datos del problema y del fútbol, considerado uno de los deportes más impredecibles. La aplicación comparó la muestra con las últimas convocatorias de porteros de las selecciones nacionales de estos países. Los porteros seleccionados correspondieron a los de mejor rendimiento individual, confirmando el modelo.

Palabras-clave:
Fútbol; Evaluación; Porteros; Composición Probabilística de Preferencias

INTRODUCTION

The individual performance of players still prevails in the call-ups for national football teams. During a recent press conference, the Brazilian coach stated that “[...] the individual performance of the athletes transcends the collective moment of a team [...] the collective is of great help, but the analysis is individual” (UOL, 2020UOL. [Internet]. Tite convoca Gabriel Menino e dupla do Flamengo para seleção. Elimin Sul-Americanas. 2020. [cited 2020 Sep 20]. Available from: https://www.uol.com.br/esporte/futebol/ultimas-noticias/2020/09/18/convocacao---selecao---eliminatorias.htm
https://www.uol.com.br/esporte/futebol/u...
). This mindset is especially applied to goalkeepers, a sui generis position that requires the use of specific and individual-focused indicators rather than collective indicators used to evaluate line players. The rationale and personal preferences behind this decision-making process is relevant to clubs and players, and their benefits include improving training systems and internal performance analysis. However, the decision-making process used to select the best players as well as the criteria for individual performance are not normally disclosed in these press conferences or even published by the staff (Carling et al., 2018Carling C, Lawlor J, Wells S. Performance analysis in professional football. In: Gregson W, Littlewood M, editors. Science in soccer: translating theory into practice. London: Bloomsbury Publishing; 2018. p. 213-39.).

The recent literature in sports sciences presenting an approach similar to the one proposed in this paper is scarce in performance analysis of soccer goalkeepers. Some studies have analyzed individual metrics to assess the movement and motor skills of goalkeepers in their defenses (Ziyagil, 2017Ziyagil MA. Technical performance analysis of goalkeepers with respect to the sidedness in Turkish Soccer Super League. New Trends Issues Proc Humanit Soc Sci. 2017;4(5):66-70. http://dx.doi.org/10.18844/prosoc.v4i5.2677.
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; Lamas et al., 2018Lamas L, Drezner R, Otranto G, Barrera J. Analytic method for evaluating players’ decisions in team sports: Applications to the soccer goalkeeper. PLoS One. 2018;13(2):e0191431. http://dx.doi.org/10.1371/journal.pone.0191431. PMid:29408923.
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; Rodríguez-Arce et al., 2019Rodríguez-Arce J, Flores-Núñez LI, Portillo-Rodríguez O, Hernández-López SE. Assessing the performance of soccer goalkeepers based on their cognitive and motor skills. Int J Perform Anal Sport. 2019;19(5):655-71. http://dx.doi.org/10.1080/24748668.2019.1647042.
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; Szwarc et al., 2019Szwarc A, Jaszczur-Nowicki J, Aschenbrenner P, Zasada M, Padulo J, Lipinska P. Motion analysis of elite Polish soccer goalkeepers throughout a season. Biol Sport. 2019;36(4):357-63. http://dx.doi.org/10.5114/biolsport.2019.88758. PMid:31938007.
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), performance and attitudes at penalties (Furley et al., 2017Furley P, Noël B, Memmert D. Attention towards the goalkeeper and distraction during penalty shootouts in association football: a retrospective analysis of penalty shootouts from 1984 to 2012. J Sports Sci. 2017;35(9):873-9. http://dx.doi.org/10.1080/02640414.2016.1195912. PMid:27292083.
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; Kolbinger and Stöckl, 2019Kolbinger O, Stöckl M. Misbehavior during penalty kicks and goalkeepers holding the ball too long as trivial offenses in football. Front Psychol. 2019;10:844. http://dx.doi.org/10.3389/fpsyg.2019.00844. PMid:31057465.
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), and dimensions other than technique, which include physical, psychological and tactical aspects, as well as training (Park et al., 2016Park Y-S, Choi M-S, Bang S-Y, Park J-K. Analysis of shots on target and goals scored in soccer matches: implications for coaching and training goalkeepers. SA J Res Sport Phys Educ Recreat. 2016;38:123-37.; West, 2018West J. A review of the key demands for a football goalkeeper. Int J Sports Sci Coaching. 2018;13(6):1215-22. http://dx.doi.org/10.1177/1747954118787493.
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).

Other studies evaluated goalkeeper performance in football with an observational methodology or notational analysis. An observational instrument was tested to measure the technical and tactical actions performed in the offensive phase by the player and team with the ball possession (Ortega-Toro et al., 2019Ortega-Toro E, García-Angulo A, Giménez-Egido JM, García-Angulo FJ, Palao JM. Design, validation, and reliability of an observation instrument for technical and tactical actions of the offense phase in soccer. Front Psychol. 2019;10:22. http://dx.doi.org/10.3389/fpsyg.2019.00022. PMid:30733691.
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). Other authors created instruments to collect information for the analysis of offensive action and interaction game (Sarmento et al., 2009Sarmento H, Leitão J, Anguera T, Campaniço J. Observational methodology in football: development of an instrument to study the offensive game in football. Motricidade. 2009;5(3):19-24. http://dx.doi.org/10.6063/motricidade.5(3).191.
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) or to detect behavioral patterns of goalkeepers during the defensive process in soccer (Esteves et al., 2009Esteves A, Martins N, Leitão J, Campaniço J, Oliveira C. Observational methodology in soccer: development of goalkeeper behaviour in the defensive process observational instrument-SOFGr1. Motricidade. 2009;5:92.). All of these studies propose procedures and instruments to produce data of interest to coaches and performance analysts.

Another study brought together performance analysts and students of sports sciences to define sets of performance indicators for each position in soccer, including goalkeepers (Hughes et al., 2012Hughes MD, Caudrelier T, James N, Redwood-Brown A, Donnelly I, Kirkbride A, et al. Moneyball and soccer-an analysis of the key performance indicators of elite male soccer players by position. J Hum Sport Exerc. 2012;7(2).). Goalkeepers’ performance was also investigated in different samples of professional male goalkeepers (e.g. different U-categories) and in women's football (Ortega-Toro et al., 2018Ortega-Toro E, García-Angulo A, Giménez-Egido J-M, García-Angulo FJ, Palao J. Effect of modifications in rules in competition on participation of male youth goalkeepers in soccer. Int J Sports Sci Coaching. 2018;13(6):1040-7. http://dx.doi.org/10.1177/1747954118769423.
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; Peráček et al., 2017Peráček P, Varga K, Gregora P, Mikulič M. Selected indicators of an individual game performance of a goalkeeper at the European Championship among the 17-year-old elite soccer players. J Phys Educ Sport. 2017;17:188.; Sainz de Baranda et al., 2019Sainz de Baranda P, Adán L, García-Angulo A, Gómez-López M, Nikolic B, Ortega-Toro E. Differences in the offensive and defensive actions of the goalkeepers at women’s FIFA World Cup 2011. Front Psychol. 2019;10:223. http://dx.doi.org/10.3389/fpsyg.2019.00223. PMid:30804856.
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).

Other studies explored a similar path to evaluate soccer goalkeepers, although they used different methods, variables and sources for data collection. Liu et al. (2015)Liu H, Gómez MA, Lago-Peñas C. Match performance profiles of goalkeepers of elite football teams. Int J Sports Sci Coaching. 2015;10(4):669-82. http://dx.doi.org/10.1260/1747-9541.10.4.669.
http://dx.doi.org/10.1260/1747-9541.10.4...
, using the ANOVA method and data from the OPTA Sportsdata Spain Company, hypothesized that goalkeepers of high-level teams performed better than those of intermediate and low-level teams, and that goalkeepers of different team levels showed differential performance under different situational conditions. In Gil et al. (2014)Gil SM, Zabala-Lili J, Bidaurrazaga-Letona I, Aduna B, Lekue JA, Santos-Concejero J, et al. Talent identification and selection process of outfield players and goalkeepers in a professional soccer club. J Sports Sci. 2014;32(20):1931-9. http://dx.doi.org/10.1080/02640414.2014.964290. PMid:25429718.
http://dx.doi.org/10.1080/02640414.2014....
, the authors focused on a talent identification process of kids in a professional soccer club, analyzing anthropometric, maturity and performance measurements. Using a discriminant analysis, they studied a sample of 9-10-year-old goalkeepers by collecting data in training sessions, which included players’ velocity, agility, endurance and jump tests. Seaton and Campos (2011)Seaton M, Campos J. Distribution competence of a football clubs goalkeepers. Int J Perform Anal Sport. 2011;11(2):314-24. http://dx.doi.org/10.1080/24748668.2011.11868551.
http://dx.doi.org/10.1080/24748668.2011....
tried to understand a goalkeeper’s performance through their performance in nine different zones of the pitch. They observed ten games from DVDs and camcorder video footage to compute the number of kicks, rolls, throws, heads and their outcome, such as attacks or loss of ball possession.

Soccer is considered one of the most unpredictable among all sports (Schokkaert and Swinnen, 2016Schokkaert J, Swinnen J. Uncertainty of Outcome is Higher in the Champions League than in the European Cup. J Sports Econ. 2016;17(2):115-47. http://dx.doi.org/10.1177/1527002514521628.
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; Pawlowski et al., 2018Pawlowski T, Nalbantis G, Coates D. Perceived game uncertainty, suspense and the demand for sport. Econ Inq. 2018;56(1):173-92. http://dx.doi.org/10.1111/ecin.12462.
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). In addition, performance data available from open sources are not systematized in all matches and competitions, while human observation procedures and manual notation are available for recording and posting data on web sites. These procedures can embed uncertainties in the data (Gavião et al., 2020Gavião LO, Sant’Anna AP, Alves Lima GB, de Almada Garcia PA. Evaluation of soccer players under the Moneyball concept. J Sports Sci. 2020;38(11-12):1221-47. http://dx.doi.org/10.1080/02640414.2019.1702280. PMid:31876264.
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).

The Composition of Probabilistic Preferences (CPP) is a multi-criteria decision aid method (MCDA) that considers uncertainty in its modeling based on decision makers’ preferences (Sant’Anna, 2015Sant’Anna AP. Probabilistic composition of preferences, theory and applications. New York: Springer; 2015.). MCDA methods are adequate tools to evaluate satisfactory solutions to the problem, considering the inexistence of an optimal alternative that performs perfectly under all criteria. CPP has also been applied to similar problems of assessing individual and collective performance in football (Gavião et al., 2020Gavião LO, Sant’Anna AP, Alves Lima GB, de Almada Garcia PA. Evaluation of soccer players under the Moneyball concept. J Sports Sci. 2020;38(11-12):1221-47. http://dx.doi.org/10.1080/02640414.2019.1702280. PMid:31876264.
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, 2017Gavião LO, Sant’Anna AP, Lima GBA. Uma nova abordagem aplicada ao conceito Moneyball com apoio da Composição Probabilística de Preferências. In: Simpósio Brasileiro de Pesquisa Operacional - XLI X SBPO; 2017; Blumenau. Anais. Rio de Janeiro: SOBRAPO; 2017. p. 1-12.; Príncipe et al., 2017Príncipe V, Gavião LO, Henriques R, Lobo V, Lima GBA, Sant’anna AP. Multi-criteria analysis of football match performances: composition of probabilistic preferences applied to the English premier league 2015/2016. Pesqui Oper. 2017;37(2):333-63. http://dx.doi.org/10.1590/0101-7438.2017.037.02.0333.
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; Sant’Anna et al., 2010Sant’Anna AP, Barboza EU, Soares de Mello JCCB. Classification of the teams in the Brazilian Soccer Championship by probabilistic criteria composition. Soccer Soc. 2010;11(3):261-76. http://dx.doi.org/10.1080/14660971003619560.
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; Sant’Anna and de Mello, 2012Sant’Anna AP, de Mello JCCBS. Validating rankings in soccer championships. Pesqui Oper. 2012;32(2):407-22. http://dx.doi.org/10.1590/S0101-74382012005000012.
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).

The proposed methodology was applied for the goalkeeper position and compared to the last call-ups of the Brazilian and Argentinean soccer teams. Did the selected goalkeepers correspond to those with the best individual performance in their countries? Is it possible to compare the performance of Brazilian and Argentinean goalkeepers, to assist club managers in eventual transfers of these players? These research questions guided the modeling in the search for solutions aimed at assisting managers and technical commissions to choose professional soccer goalkeepers.

MATERIAL AND METHODS

Sample

The data sample consisted of 64 goalkeepers with an average age of 30.3 years who played in the main football leagues in Brazil (Serie A – Brasileirão) and Argentina (Superliga). The data correspond to the last two seasons before the Covid-19 pandemic in South America, considered in this study from March 2020. These competitions are played in straight points, with 20 teams in Brazil and 24 in Argentina. This research analyzed all players together, based on the premise of homogeneity of the level of competitiveness in these countries.

This number of goalkeepers was due to the need to consider, separately, a same player who played in both seasons. Thus, for modeling purposes, goalkeeper “X” of the 2018 season is considered different from the same goalkeeper “X” who served in the 2019 season. The initial sample of 84 goalkeepers was finally reduced to 64 goalkeepers. The players who served in the second division in any of these seasons or played a small number of matches were excluded.

On average, goalkeepers participated in 22 matches, with a maximum of 37 matches. The cut-off point was the first quartile (14) of the number of matches played. Thus, goalkeepers who participated in up to 13 matches (inclusive) were excluded from the study. This initial treatment was necessary to avoid distortions and biases caused by over- or undervalued performances in the modeling.

Variables

The modeling considered three aggregate indicators widely used in the scientific literature to assess the players’ performance. The first criterion, “GA/min”, counts the goals against (GA) per minute played in the season, which is also explored in other studies (Clemente, 2018Clemente FM. Performance outcomes and their associations with network measures during FIFA World Cup 2018. Int J Perform Anal Sport. 2018;18(6):1010-23. http://dx.doi.org/10.1080/24748668.2018.1545180.
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; Longo et al., 2019Longo UG, Sofi F, Dinu M, Candela V, Salvatore G, Cimmino M, et al. Functional performance, anthropometric parameters and contribution to team success among Italian” Serie A” elite goalkeepers during season 2016-2017. J Sports Med Phys Fitness. 2019;59(6):969-74. PMid:30024126.; Sainz de Baranda et al., 2019Sainz de Baranda P, Adán L, García-Angulo A, Gómez-López M, Nikolic B, Ortega-Toro E. Differences in the offensive and defensive actions of the goalkeepers at women’s FIFA World Cup 2011. Front Psychol. 2019;10:223. http://dx.doi.org/10.3389/fpsyg.2019.00223. PMid:30804856.
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; Yam, 2019Yam D. A data driven goalkeeper evaluation framework. In: 13th MIT Sloan Sports Analytics Conference; 2019; Boston (MA). Proceedings. Boston: MIT Sloan; 2019. p. 1-18.). GA is also called “goals conceded” in other databases of match analysis (i.e., Footystats, Soccerstats, Statista, Transfermarkt). This criterion has a negative impact on the performance evaluation because the lower the measure, the better the result compared to other goalkeepers. For this reason, this criterion had its signal changed to negative.

The second criterion, “Save%”, represents the percentage of goals prevented by the goalkeeper obtained by dividing the difference between shots on goal and goals conceded by the total number of shots on goal (Dicks et al., 2017Dicks M, Pocock C, Thelwell R, van der Kamp J. A novel on-field training intervention improves novice goalkeeper penalty kick performance. Sport Psychol. 2017;31(2):129-33. http://dx.doi.org/10.1123/tsp.2015-0148.
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; Liu et al., 2015Liu H, Gómez MA, Lago-Peñas C. Match performance profiles of goalkeepers of elite football teams. Int J Sports Sci Coaching. 2015;10(4):669-82. http://dx.doi.org/10.1260/1747-9541.10.4.669.
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; Montesano, 2016Montesano P. Goalkeeper in soccer: performance and explosive strength. J Phys Educ Sport. 2016;16:230.; Sainz de Baranda et al., 2019Sainz de Baranda P, Adán L, García-Angulo A, Gómez-López M, Nikolic B, Ortega-Toro E. Differences in the offensive and defensive actions of the goalkeepers at women’s FIFA World Cup 2011. Front Psychol. 2019;10:223. http://dx.doi.org/10.3389/fpsyg.2019.00223. PMid:30804856.
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, 2008Sainz de Baranda P, Ortega E, Palao JM. Analysis of goalkeepers’ defence in the World Cup in Korea and Japan in 2002. Eur J Sport Sci. 2008;8(3):127-34. http://dx.doi.org/10.1080/17461390801919045.
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; White et al., 2018White A, Hills SP, Cooke CB, Batten T, Kilduff LP, Cook CJ, et al. Match-play and performance test responses of soccer goalkeepers: a review of current literature. Sports Med. 2018;48(11):2497-516. http://dx.doi.org/10.1007/s40279-018-0977-2. PMid:30144021.
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). This criterion has a positive impact on the result because the higher the index, the better for the goalkeeper.

The third criterion, “CS%” (clean sheets), calculates the percentage of matches in which the goalkeeper does not concede goals (Apostolou and Tjortjis, 2019Apostolou K, Tjortjis C. Sports analytics algorithms for performance prediction. In: 10th International Conference on Information, Intelligence, Systems and Applications; 2019; USA. Proceedings. USA: IEEE; 2019. p. 1-4. http://dx.doi.org/10.1109/IISA.2019.8900754.
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; Schultze and Wellbrock, 2018Schultze SR, Wellbrock C-M. A weighted plus/minus metric for individual soccer player performance. J Sport Anal. 2018;4(2):121-31. http://dx.doi.org/10.3233/JSA-170225.
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; Singh and Lamba, 2019Singh P, Lamba PS. Influence of crowdsourcing, popularity and previous year statistics in market value estimation of football players. J Discret Math Sci Cryptogr. 2019;22(2):113-26. http://dx.doi.org/10.1080/09720529.2019.1576333.
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). CS is such a relevant criterion that a trophy is traditionally awarded for it in several tournaments, including the English Premier League and the FIFA World Cup. This criterion also has a positive impact.

Collected data

The data were collected from the website FBref.com, which publishes several individual and collective performance indicators from the major sports leagues and tournaments in the world. This website currently covers 47 countries, 134 competitions, 4,625 squads, 165,635 players and 224,308 match reports (FBref.com, 2020FBref.com. [Internet]. 2019 Brazilian Série a Stats. Sports-reference. 2020 [cited 2020 Sep 17]. Available from: https://fbref.com/en/comps/24/3320/2019-Serie-A-Stats
https://fbref.com/en/comps/24/3320/2019-...
). The FBref datasets have recently been explored by sports science researchers (Blumberg and Markovits, 2021Blumberg Z, Markovits AS. American soccer at a crossroad: MLS’s struggle between the exigencies of traditional American sports culture and the expectations of the global soccer community. Soccer Soc. 2021;22(3):231-47. http://dx.doi.org/10.1080/14660970.2020.1802255.; Bradbury, 2020Bradbury JC. Determinants of Attendance in Major League Soccer. J Sport Manage. 2020;34(1):53-63. http://dx.doi.org/10.1123/jsm.2018-0361.
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; Iehl, 2020Iehl AMA. An empirical analysis on major league soccer player earnings [thesis]. Iowa: University of Northern Iowa; 2020. 34 p.; Zaytseva and Shaposhnikov, 2020Zaytseva I, Shaposhnikov D. Moneyball in offensive vs defensive actions in soccer. Moscow: National Research University Higher School of Economics; 2020.). Sports-Reference, which manages FBRef.com, authorized the authors to use all data available on the website for academic purposes.

Table 1 presents an extract of the data collected from the ten goalkeepers who obtained the best results after modeling. The seasons are found next their names, followed by their country and minutes played. The criteria columns show the aggregated indicators.

Table 1
Data sample.

Probabilistic modeling

CPP associates the observed player's performance in each criterion with a probability of the value measured, which may vary. In soccer, disturbances are produced by a series of intangible factors, such as environmental conditions, game strategies and the psychological, physical, and technical state of players, among others. Thus, a performance measure is transformed into a continuous random variable related to the most probable value of a probability distribution (Sant’Anna, 2015Sant’Anna AP. Probabilistic composition of preferences, theory and applications. New York: Springer; 2015.). In this research, the measures were adjusted by Beta PERT distributions based on the data collected in each criterion. This type of asymmetric distribution is usually applied to randomize variables in risk analysis (Vose, 2008Vose D. Risk analysis: a quantitative guide. New York: John Wiley & Sons; 2008.).

After randomizing the variables, CPP makes the relative comparison among the goalkeepers’ performance in each criterion (Sant’Anna, 2015Sant’Anna AP. Probabilistic composition of preferences, theory and applications. New York: Springer; 2015.). It is possible to verify, for example, to what extent each player could exceed all the others given the random character of their performance. This is measured by the probability that the player will perform above the median of the other players in the criterion considered. The calculation, for each criterion, is performed by integrating a function that corresponds to the product of the probability density of the player considered and the cumulative function of the median of the other players. The R software version 4.0.3 with the CPP package was used in these calculations (Gavião et al., 2018Gavião LO, Sant’Anna AP, Lima GBA, Garcia PAA. CPP: Composition of Probabilistic Preferences. R package version 0.1.0. Vienna, Áustria: R Foundation for Statistical Computing; 2018.).

The probabilities of each goalkeeper maximizing the performance in each criterion can be combined in different ways, providing different points of view for decision-making, as detailed by Sant’Anna (2015)Sant’Anna AP. Probabilistic composition of preferences, theory and applications. New York: Springer; 2015.. In this research, a model by axis was applied, adopting progressive approaches. The progressive-pessimistic (PP) axis composes the probabilities of maximizing seeking the best performance under all criteria simultaneously by multiplying these probabilities. The progressive-optimistic (PO) axis composes the probabilities of maximizing seeking the best performance in at least one of the criteria by complementing the multiplication of the complements of the probabilities of maximizing.

The PP and PO axes generated two goalkeepers' rankings. The sum of these rankings by Borda’s method configured the final ranking where the lowest sum corresponds to the best overall performance.

Statistical tests checked the results of Brazilian and Argentinean goalkeepers, grouped in six data sets. The non-parametric Mann-Whitney U test was used to indicate whether one set of observations was superior to the other. It considers the null hypothesis that the two groups are sampled from populations with identical distributions against the alternative hypothesis that the populations have different distributions.

RESULTS

Table 2 presents an extract of the ten best goalkeepers’ evaluations. The “P Max” columns indicate the probabilities of maximizing the goalkeepers’ performances. The “PP Axis” and “PO Axis” columns show the results of taking these points of view, with their specific rankings, based on the highest numerical value. The “Borda” column adds the axes rankings, leading to the results in the “Final rank” column.

Table 2
Extract of results.

Table 3 summarizes the players’ performances aggregating the two seasons and ranks the top ten Brazilian and Argentinian goalkeepers. The columns indicate the results by axis and the best overall performance in the “Final rank” column, which shows the most relevant results to answer the research questions.

Table 3
Extract of the overall performance of Brazilians.

Initially, the results obtained with the complete sample (64 goalkeepers) were displayed in a boxplot to compare the performances of the goalkeepers of both countries. Based on Figure 1, it is notable that the performance of Brazilian goalkeepers was markedly superior to that of Argentinians in two scenarios: global, without distinction of season (two boxes on the left) and in seasons 2019 (BR) and 2019-2020 (ARG) (two boxes on the right). However, the two central boxes do not clearly indicate superiority of one set over the other. They may be then preliminarily evaluated as equivalent.

Figure 1
Results in boxplots. PP: Progressive-Pessimist; ARG: Argentineans (in blue); BR: Brazilians (in orange).

For the global data scenario in Figure 1, the Mann-Whitney U test rejected the null hypothesis, confirming the visual conclusion that Brazilians' performance is statistically superior for a significance level of 5% (W = 335, p-value = 0.05). The same occurred in relation to the 2019 (BR) and 2019-2020 (ARG) seasons scenario (W = 219, p-value = 0.04). On the other hand, the test of the 2018 (BR) and 2018-2019 (ARG) seasons scenario did not allow us to reject the null hypothesis, indicating that the performances may belong to the same probability distribution (W = 94, p-value = 0.57).

DISCUSSION

Two research questions guided the modeling aimed at assisting managers and technical commissions to choose professional soccer goalkeepers: “Did the selected goalkeepers correspond to those with the best individual performance in their countries?” and “Is it possible to compare the performance of Brazilian and Argentinian goalkeepers in order to assist club managers in eventual transfers of these players?” The proposed model returned the best performing goalkeepers in recent seasons and corresponded to those chosen for the national teams. The model allowed comparing the performance of the two groups with useful information for decision making by soccer managers.

Although the set of Brazilian goalkeepers presented a better overall performance, two Argentine goalkeepers occupied the first three positions in the ranking, as shown in Table 2. GK-1 remained at the top in the two seasons analyzed. Together with GK-2, both have been frequently called up for the national team, a fact that was repeated for the resumption of the South American qualifiers. Regarding the Brazilian goalkeepers, Table 3 indicates the best overall performance of GK-3 and GK-6. They were also called up to the World Cup qualifiers.

Although the CPP model applied to the performance analysis of players is similar to those used in other studies, the focus on selected goalkeepers for national teams is original. In Gavião et al. (2020Gavião LO, Sant’Anna AP, Alves Lima GB, de Almada Garcia PA. Evaluation of soccer players under the Moneyball concept. J Sports Sci. 2020;38(11-12):1221-47. http://dx.doi.org/10.1080/02640414.2019.1702280. PMid:31876264.
http://dx.doi.org/10.1080/02640414.2019....
, 2017Gavião LO, Sant’Anna AP, Lima GBA. Uma nova abordagem aplicada ao conceito Moneyball com apoio da Composição Probabilística de Preferências. In: Simpósio Brasileiro de Pesquisa Operacional - XLI X SBPO; 2017; Blumenau. Anais. Rio de Janeiro: SOBRAPO; 2017. p. 1-12.), the Moneyball approach explored the CPP method with different criteria to suggest good bargains for the transfer market of defenders. In Príncipe et al. (2017), the CPP model focused on team performance in the English Premier League using 23 variables, which included the goalkeeper’s criteria explored in this study (i.e. saves, clean sheets and goals conceded). Other applications of CPP aimed at evaluating soccer championships and teams are found in the sports literature (Sant’Anna et al., 2010Sant’Anna AP, Barboza EU, Soares de Mello JCCB. Classification of the teams in the Brazilian Soccer Championship by probabilistic criteria composition. Soccer Soc. 2010;11(3):261-76. http://dx.doi.org/10.1080/14660971003619560.
http://dx.doi.org/10.1080/14660971003619...
; Sant’Anna and de Mello, 2012).

CPP has the limitations of any multi-criteria decision aid method — different criteria, alternatives and data can change results. In addition, the validation of the model requires the approval of any person responsible for the final decision, which in the case of this study, would be the national coaches themselves. It is possible to assume that these limitations were overcome, in a way, as the modeling confirmed that the final ranking of the best goalkeepers corresponded to the list of players called up for the Brazilian and Argentinean teams. The alignment of the model results with the final choice of goalkeepers may be due to the limited number of variables for the analysis of goalkeeper performance. Line players have dozens of indicators, while goalkeepers are assessed in matches using a few variables. Thus, performance analyses should not show significant variance.

For future research, new data can be included for coming seasons, after the 2020 season. These results can be compared to those obtained in the 2018 and 2019 seasons to verify the trend of performance improvement or decrease in relation to historical results. It is also possible to expand the search to other field positions to assist technical commissions with the replacement of players frequently transferred to the European and Asian markets. Finally, it is possible as well to further study the adequacy of the variables used in the assessment. For example, the third variable (CS%) might exclude goalless matches from the calculation. This score can indicate a strategy of the team favoring the defense and the goalkeeper. Perhaps the fact that Argentine football presently goes through a more offensive phase explains the better results of Brazilian goalkeepers in the study.

CONCLUSION

This research aimed to present a probabilistic method to support managers and analysts in selecting soccer players, focusing on individual performance. The results indicated that the questions were satisfactorily answered. The data confirm the effectiveness of the probabilistic model as it coincides with the goalkeepers selected by the national teams.

The use of this model can also benefit other national team coaches and football clubs in general. A similar model that translates the national coach’s preferences can be useful for clubs to choose their best goalkeepers. National coaches remain in this position for a World Cup cycle (four years) or even longer, as is the case of the German and Brazilian teams. In this context, emulating the decision-making process of a coach who makes call-ups for four or more years is relevant to the club's managers and players. Football managers can adapt their resource planning based on similar decision-making processes. Likewise, players can focus their training on reaching the benchmarks made available. Finally, the transparency of this process benefits fans and the specialized press.

  • FUNDING
    None.

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Publication Dates

  • Publication in this collection
    19 July 2021
  • Date of issue
    2021

History

  • Received
    28 Dec 2020
  • Accepted
    29 Dec 2020
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