The referee's challenge: a threshold process model for decision making in sport games

Judgment and decision making in sporting officials is a challenging task that involves the use of context. Although process models of decision making describe decision contexts, none of the existing models explains when sports officials use rule-driven decision making, or game management. The basic idea of our work is that referees use a subjective threshold to apply game management, which may explain this decision behavior. We propose a new dynamic threshold model that is based on concepts derived from Decision Field Theory (Busemeyer & Townsend, 1993). The model includes two thresholds of game management (high/low) and two contact situations (foul/no foul) as approaching one of these thresholds. Using the example of soccer refereeing, we argue that if the game hits a subjective threshold of aggressive play, then the referee shifts from applying the rules to managing the game. This new approach changes the scientific discussion from one focused on what referees should decide in one situation or the other, to a dynamic model that explains the basic psychological mechanism underlying the referee’s change in behavior during the game, both at the intra-individual as well as inter-individual leve

The past, present and future of research on judgment and decision making in sport

Objectives: The study of judgment and decision-making in sports is at least as old as the anniversary of FEPSAC we celebrate with this special issue. It seems therefore appropriate to look into the past, present and future of this topic. Design: For the past, a focus of the review is relating the European perspective of the co-authors into a larger frame of areas in judgment and decision making within the last 50 years and beyond. Method/Results/Conclusions: For the present, scientific current developments will be structured as judgments from the most influential perspectives such as the economical, social cognition, ecological dynamics or cognitive approaches illustrating some milestones in research on judgment and decision-making in sports of today. For the future, potentials of the field will be structured based on theory, methodology and practical applications showcasing challenges for the next decades of research ahead of us

How should "hot" players in basketball be defended? The use of fast-and-frugal heuristics by basketball coaches and players in response to streakiness.

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Sports Sciences on 8 January 2015, available online: http://www.tandfonline.com/10.1080/02640414.2014.999251 Previous research has shown that changes in shot difficulty may have rendered the hot-hand effect in basketball unobservable and are potentially a result of defensive adjustments. However, it has not been directly analysed whether strategic changes indeed take place in response to streakiness and whether they are effective with respect to winning games. The current work consists of an experimental study with 18 professional coaches and 20 players based on video sequences from National Basketball Association games, where the shown player displayed a streaky performance in half of the sequences. While coaches were asked to devise a defensive strategy after each viewed sequence, players had to assume the role of the shown player and decide whether to shoot or pass the ball. We find that coaches tended to increase the defensive pressure significantly more often on presumably hot players and thus make use of the hot-hand heuristic. Meanwhile, players chose to shoot more frequently in low-pressure and streaky situations but selected "pass" regardless of the previous performance when they faced increased defensive pressure. Assuming that a streaky player's performance is indeed elevated during hot phases, hot-hand behaviour can be considered adaptive in certain situations as it led hot players to pass instead of shoot

The effect of perceived streakiness on the shot-taking behaviour of basketball players.

We examine behavioural changes of basketball players arising from the hot-hand belief and use data of 1216 National Basketball Association games to measure the effect of cold and hot streaks on three proxies of shot difficulty. We find that the more consecutive shots players make (miss), the more difficult (easier) shots become along the three dimensions. Furthermore, most players' performance seems to improve during hot streaks because they attempt more difficult shots while no significant decrease in shooting accuracy takes place. This might explain why most previous studies could not find empirical evidence for the hot-hand belief in basketball when considering in-game field goal shooting

Visual Search Strategies of Soccer Players Executing a Power vs. Placement Penalty Kick

Introduction: When taking a soccer penalty kick, there are two distinct kicking techniques that can be adopted; a ‘power’ penalty or a ‘placement’ penalty. The current study investigated how the type of penalty kick being taken affected the kicker’s visual search strategy and where the ball hit the goal (end ball location). Method: Wearing a portable eye tracker, 12 university footballers executed 2 power and placement penalty kicks, indoors, both with and without the presence of a goalkeeper. Video cameras were used to determine initial ball velocity and end ball location. Results: When taking the power penalty, the football was kicked significantly harder and more centrally in the goal compared to the placement penalty. During the power penalty, players fixated on the football for longer and more often at the goalkeeper (and by implication the middle of the goal), whereas in the placement penalty, fixated longer at the goal, specifically the edges. Findings remained consistent irrespective of goalkeeper presence. Discussion/conclusion: Findings indicate differences in visual search strategy and end ball location as a function of type of penalty kick. When taking the placement penalty, players fixated and kicked the football to the edges of the goal in an attempt to direct the ball to an area that the goalkeeper would have difficulty reaching and saving. Fixating significantly longer on the football when taking the power compared to placement penalty indicates a greater importance of obtaining visual information from the football. This can be attributed to ensuring accurate foot-to-ball contact and subsequent generation of ball velocity. Aligning gaze and kicking the football centrally in the goal when executing the power compared to placement penalty may have been a strategy to reduce the risk of kicking wide of the goal altogether

Dynamics of nearly inviscid Faraday waves in almost circular containers

Parametrically driven surface gravity-capillary waves in an elliptically distorted circular cylinder are studied. In the nearly inviscid regime, the waves couple to a streaming flow driven in oscillatory viscous boundary layers. In a cylindrical container, the streaming flow couples to the spatial phase of the waves, but in a distorted cylinder, it couples to their amplitudes as well. This coupling may destabilize pure standing oscillations, and lead to complex time-dependent dynamics at onset. Among the new dynamical behavior that results are relaxation oscillations involving abrupt transitions between standing and quasiperiodic oscillations, and exhibiting ‘canards’

Time-delayed feedback control of unstable periodic orbits near a subcritical Hopf bifurcation

We show that Pyragas delayed feedback control can stabilize an unstable periodic orbit (UPO) that arises from a generic subcritical Hopf bifurcation of a stable equilibrium in an n-dimensional dynamical system. This extends results of Fiedler et al. [PRL 98, 114101 (2007)], who demonstrated that such feedback control can stabilize the UPO associated with a two-dimensional subcritical Hopf normal form. Pyragas feedback requires an appropriate choice of a feedback gain matrix for stabilization, as well as knowledge of the period of the targeted UPO. We apply feedback in the directions tangent to the two-dimensional center manifold. We parameterize the feedback gain by a modulus and a phase angle, and give explicit formulae for choosing these two parameters given the period of the UPO in a neighborhood of the bifurcation point. We show, first heuristically, and then rigorously by a center manifold reduction for delay differential equations, that the stabilization mechanism involves a highly degenerate Hopf bifurcation problem that is induced by the time-delayed feedback. When the feedback gain modulus reaches a threshold for stabilization, both of the genericity assumptions associated with a two-dimensional Hopf bifurcation are violated: the eigenvalues of the linearized problem do not cross the imaginary axis as the bifurcation parameter is varied, and the real part of the cubic coefficient of the normal form vanishes. Our analysis of this degenerate bifurcation problem reveals two qualitatively distinct cases when unfolded in a two-parameter plane. In each case, Pyragas-type feedback successfully stabilizes the branch of small-amplitude UPOs in a neighborhood of the original bifurcation point, provided that the phase angle satisfies a certain restriction.Comment: 35 pages, 19 figure

Emergent global oscillations in heterogeneous excitable media: The example of pancreatic beta cells

Using the standard van der Pol-FitzHugh-Nagumo excitable medium model I demonstrate a novel generic mechanism, diversity, that provokes the emergence of global oscillations from individually quiescent elements in heterogeneous excitable media. This mechanism may be operating in the mammalian pancreas, where excitable beta cells, quiescent when isolated, are found to oscillate when coupled despite the absence of a pacemaker region.Comment: See home page http://lec.ugr.es/~julya

On distributions of functionals of anomalous diffusion paths

Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in imaginary time. In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random walk. We also derive a backward equation and a generalization to Levy flights. Solutions are presented for a wide number of applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement, and the hitting probability. We briefly discuss other fractional Schrodinger equations that recently appeared in the literature.Comment: 25 pages, 4 figure

Experimental observation of the amplitude death effect in two coupled nonlinear oscillators

The amplitude death phenomenon has been experimentally observed with a pair of thermo-optical oscillators linearly coupled by heat transfer. A parametric analysis has been done and compared with numerical simulations of a time delayed model. The role of the coupling strength is also discussed from experimental and numerical results