Strategic Behaviour and Risk Taking in Football

This article develops a dynamic game-theoretic model of optimizing strategic behaviour by football teams. Teams choose continuously between defensive and attacking formations and between a non-violent and a violent playing style. Starting from the end of the match and working backwards, the teams' optimal strategies conditional on the current state of the match are determined by solving a series of two-person non-cooperative subgames. Numerical simulations are used to explore the sensitivity of strategic behaviour to variations in the structural parameters. The model is tested empirically, using English football league data. Teams that are trailing are willing to bear an increased risk of a player dismissal in order to increase the probability of scoring. Teams that are leading or level in scores play cautiously. The scoring rates of teams that are trailing are higher than those of teams that are ahead or level. Stochastic simulations are used to obtain probabilities for match results, conditional upon the state of the match at any stage. The article's main theoretical and empirical results constitute novel, non-experimental evidence that the strategic behaviour of football teams can be rationalized in accordance with game-theoretic principles of optimizing strategic behaviour by agents when payoffs are uncertain and interdependent.

A qualitative examination of choking and clutch experiences among performance referees

While much is known about the contexts, mechanisms, moderators, and consequences of excellent (i.e., clutch) and failed (i.e., choke) pressurised performance among athletes, the same cannot be said for officials, who to date, have been largely overlooked within sport psychology literature. This is despite the fact that sporting officials are expected to perform to consistently high standards under pressure, with poor and good performances holding the possibility of significantly affecting the game they are refereeing. Indeed, it is even the case that at the elite level, poor refereeing performances under pressure can impact the career and livelihood of the players, coaches, and managers involved with the game, such are the potential consequences of refereeing errors. Thus, the current study aimed to investigate the psychological factors responsible for clutch and choking under pressure among sporting referees. To achieve this, the study used an interpretive description methodology (Thorne, 2016), whereby semi-structured interviews were conducted with ten UK-based referees (Mage = 28.5, SD = 9.52) who were performing regularly under pressure across a range of sports at the elite and competitive level. Data were then analysed using Braun and Clarke’s (2013) flexible approach to thematic analysis, with the findings revealing that various psychological factors were perceived by the referees to be associated with their clutch and choke performances. Those officials who experienced clutch performances, perceived games of greater importance, effective preparation, and supportive coach relationships increased their attentional and emotional control, and allowed for the demands of the game to be effectively managed. This resulted in the positive performance outcomes, positive affect, exhaustion, and a stronger rapport with players and coaches. However, in terms of choking, the referees reported that games of greater importance, overload, and unsupportive working environments encouraged over-refereeing (self-focus) or distraction. This brought about the significant drop in performance, as well as negative affect, worries over receiving negative evaluation, and disengagement from task. Such findings inform recommendations that can be offered to support the pressurised performances of competitive referees

The Game Theory of Penalty Kicks : A framework for approximating Nash equilibria

This paper presents a game-theoretic analysis of penalty kicks in football. There must exist a Nash equilibrium in penalty kicks, but the nature of it depends on the unique abilities of the penalty taker and the goalkeeper. Thus, this study introduces a flexible framework that approximates a Nash equilibrium, based on a user-inputted set of player-dependent assumptions. The study also seeks to improve our general understanding of the characteristics of Nash equilibria in penalty kicks. This is achieved by investigating a diverse set of playerdependent assumptions, as well as gradually adding new elements of complexity to the models, and observing the shifts in the equilibrium. In the most basic model, the players make a simultaneous choice, where the penalty taker decides where to aim, and the goalkeeper decides which area to cover. The penalty taker isn’t able to shoot with perfect accuracy, so the hit-coordinate will likely differ from the aimcoordinate. In later models, the penalty taker is also allowed to choose the velocity of the ball, which in turn impacts the area coverage of the goalkeeper. In the final model, an element of sequential choice is added, such that the penalty taker may pretend to shoot, and observe if the goalkeeper starts to move. The Counterfactual Regret Minimization algorithm is employed to locate the Nash equilibrium, while an enhanced Coordinate Search algorithm is developed for determining the optimal aimcoordinates for the penalty taker. The most complex and realistic model indicates that the penalty taker should abstain from aiming at the middle region of the goal, and rather either pretend to shoot, or shoot at one of the sides. This is because the goalkeeper needs to stay in the middle fairly often, to avoid revealing their intention in the case where the penalty taker pretends to shoot. It’s also viable for the goalkeeper to commit to diving to either side without waiting to observe the trajectory of the ball.nhhma

Does player specialization predict player actions? Evidence from penalty kicks at FIFA World Cup and UEFA Euro Cup

Penalty-kicks are analysed in the literature as `real life experiments' for assessing the use of rational mixed strategies by professional players. However, each penalty kick cannot be considered a repetition of the same event because of the varying background conditions, in particular the heterogeneous ability of different players. Consequently, aggregate statistics over datasets composed of a large number of penalty kicks mediate the behaviour of the players in \emph{different} games, and the properties of optimal mixed strategies cannot be tested directly because of \emph{aggregation bias}. In this paper we model the heterogeneous ability of players. We then test the hypothesis that differently talented players randomise over different actions. To this aim, we study a dataset that collects penalties kicked during shootout series in the last editions of FIFA World-Cup and UEFA Euro-Cup (1994-2012) where kickers are categorized as specialists and non-specialists. The results support our theoretical prediction

TRACKING FORMATION CHANGES AND ITS EFFECTS ON SOCCER USING POSITION DATA

This study investigated the application of advanced machine learning methods, specifically k-means clustering, k-Nearest Neighbors (kNN), and Support Vector Machines (SVM), to analyze player tracking data in soccer. The primary hypothesis posits that such data can yield a standalone, in-depth understanding of soccer matches. The study revealed that while k-means and spatial analysis are promising in analyzing player positions, kNN and SVM show limitations without additional variables. Spatial analysis examined each team’s convex hull and studied the correlation between team length, width, and surface area. Results showed team length and surface area have a strong positive correlation with a value of 0.8954. This suggested that teams with longer team length have a more direct style of play with players more spread out which led to larger surface areas. k-means clustering was performed with different k values derived from different approaches. The silhouette method recommended a k value of 2 and the elbow recommended a k value of 4. The context of the sport suggested additional analysis with a k value of 11. The results from k-means suggested natural data partitions, highlighting distinct player roles and field positions. kNN was performed to find similar players with the model of k = 19 showing the highest accuracy of 8.61%. The SVM model returned a classification of 55 classes which indicated a highly granular level of categorization for player roles. The results from kNN and SVM indicated the necessity of further contextual data for more effective analysis and emphasized the need for balanced datasets and careful model evaluation to avoid biases and ensure practical application in real-world scenarios. In conclusion, each algorithm offers unique perspectives and interpretations on player positioning and team formations. These algorithms, when combined with expert knowledge and additional contextual data, can significantly enrich the scope of analysis in soccer. Future work should consider incorporating event data and additional variables to enhance the depth of analytical insights, enabling a more comprehensive understanding of how formations evolve in response to various in-game situations

Validation of the IOLF5C instrument for the efficacy of shooting on goal in football for the blind

El objetivo del estudio es diseñar y validar un instrumento de observación para conocer los Indicadores de Rendimiento Competitivo en Fútbol a 5 para personas ciegas a través de jueces expertos. La muestra se compuso por 12 entrenadores expertos en Fútbol a 5. Tras la realización de un estudio preliminar, el IOLF5C quedó estructurado en dos partes: acciones básicas durante el lanzamiento a portería en situaciones de juego, y durante el penalti. La validez de contenido se realizó a través de la V de Aiken y sus intervalos de confianza. Para comprobar la consistencia interna del instrumento se empleó α de Cronbach. Los resultados indicaron que el IOLF5C dispone de niveles óptimos de validez obteniendo valores superiores a 0,875 en todos los ítems durante el juego y 0,96 en penalti. La consistencia del instrumento fue de 0,894. Por tanto, el IOLF5C es un instrumento válido y fiableThe aim of this study was to design and validate an observational instrument to identify essential competitive performance indicators in Football 5-a-Side for blind and partially sighted players through the assistance of expert evaluators. The sample was comprised of twelve Football 5-a-Side expert coaches. After a preliminary study, the OLF5C instrument was structured to include two groups of actions: basic actions during shots on goal in game situations and shooting actions penalty situations. Aiken's V statistic and confidence interval values were used to assess the content validity and Cronbach' value was used to assess the internal consistency of the instrument. Results indicated that the IOLF5C has good validity indices with obtained values reaching .875 in all items during game situations and 0.96 on penalty shot actions. The overall level of instrument consistency was .894. The IOLF5C is considered to be a valid and reliable instrumen

Applications of Sports Data to Study Decision Making

The features and determinants of human decision making, especially under competitive environments, have been a central theme of research in economics and psychology alike. This special issue centers on applying sports data to understand behavior and decision making in competitive environments. In particular, we assemble original research with sports data that provides us with insights into hitherto unanswered questions relating to various strategic and psychological aspects of decision making

Decision-making in the penalty kick: the role of constraints in the perceptual guidance of action

Doutoramento em Motricidade Humana, na especialidade de Ciências do DesportoThe aim of this thesis was to examine how players’ strategies influence available information on movement when performing penalty kicks. An ecological dynamics perspective of the penalty kick is initially presented as a supporting framework for recent research, as well as a plausible path to overcome the shortage of ecological validity of experimental designs that aim to capture the information-based core of players’ performance. The effect of different instructional constraints on movement patterns and outcome was analysed and results showed a significant influence on both players’ performance speed and on goalkeepers’ diving angle, although players’ efficacy remained constant. Penalty takers’ kinematics was then studied in order to understand its relation with ball’s horizontal and vertical directions, as well as the influence of ball direction on penalty kicks’ success. Kinematic variables highly correlated to ball horizontal direction were less affected by deceptive actions, demonstrating that genuine movements cannot be biased if an intended goal needs to be accomplished. Ball height influenced outcome, although physical constraints imposed on penalty takers’ movement variability (compared with other kick types) decreased the correlations between ball’s vertical direction and penalty takers’ kinematics. Developed investigation contributed to 1) clarify the influence of different strategies on players’ movements, 2) identify genuine sources of information for the anticipation of ball direction, and 3) determine the influence of ball height on penalty kick success.Esta tese tem como objectivo analisar a influência das estratégias empregues pelos jogadores sobre a informação disponível para a acção na grande penalidade. A dinâmica ecológica é apresentada como base para o enquadramento da pesquisa recente, e como opção plausível para potenciar a validade ecológica dos designs experimentais que pretendam capturar a informação sobre a qual os jogadores agem. Foi analisado o efeito da instrução sobre o comportamento dos jogadores e eficácia na grande penalidade. Os resultados demonstraram uma influência da instrução na velocidade dos jogadores e no ângulo de estiramento lateral do guardaredes, sem alterações da eficácia. De seguida, a cinemática do rematador foi analisada, procurando entender a sua relação com a direcção da bola. As variáveis cinemáticas correlacionadas com a direcção horizontal da bola foram pouco afectadas pela acção simulatória, demonstrando a impossibilidade de encobrir a acção genuína que cumpre determinado objectivo. A altura da bola influenciou a eficácia, apesar dos constrangimentos físicos impostos sobre a variabilidade de movimento dos rematadores na grande penalidade (comparada com outros tipos de remate) terem forçado uma diminuição das correlações entre a direcção vertical da bola e a cinemática dos rematadores. A investigação desenvolvida contribuiu para 1) clarificar a influência de diferentes estratégias no movimento dos rematadores, 2) identificar fontes genuínas de informação para a antecipação da direcção da bola, e 3) determinar a influência da altura da bola na eficácia da grande penalidade.FCT - Fundação para a Ciência e a Tecnologi