Applying decision tree induction for identification of important attributes in one-versus-one player interactions: A hockey exemplar

Abstract

Decision tree induction is a novel approach to exploring attacker-defender interactions in many sports. In this study hockey was chosen as an example to illustrate the potential use of decision tree inductions for the purpose of identifying and communicating characteristics that drive the outcome. Elite female players performed one-versus-one contests (n = 75) over two sessions. Each contest outcome was classified as either a win or loss. Position data were acquired using radio-tracking devices, and movement-based derivatives were calculated for two time epochs (5 to 2.5 seconds, and 2.5 to zero seconds before the outcome occurred). A decision tree model was trained using these attributes from the first session data, which predicted that when the attacker was moving at ≥ 0.5 m · s^?1 faster than the defender during the early epoch, the probability of an attacker's win was 1.00. Conversely, when the speed difference at that time was below this threshold the probability of a loss was 0.78. Secondary attributes included defender speed in the lateral direction during the early epoch, and angle of attack (i.e., angle between the respective velocity vectors of the attacker and defender) during the late epoch. The model was then used to predict outcomes of one-versus-one contests from the second session (accuracy = 0.643; area under the Receiver Operating Characteristic (ROC) curve = 0.712). Moreover, decision trees provide an intuitive framework for relating spatial-temporal concepts to coaches, and the suitability of decision trees for analysing the features of one-versus-one exchanges are discussed.     

Multi-Level Modeling of Dyadic Data in Sport Sciences: Conceptual,Statistical, and Practical Issues

The goal of this article is to present a series of conceptual, statistical, and practical issues in the modeling of multi-level dyadic data. Distinctions are made between distinguishable and undistinguishable dyads and several types of independent variables modeled at the dyadic level of analysis. Multi-level modeling equations are explained in a non-technical manner. A database of 66 athletes regrouped in 33 undistinguishable dyads is used to illustrate the steps from initial preparation of multi-level databases to the interpretations of output files. The data are used to examine null, intercept-as-outcome, and slope-as-outcome models, as well as to present a formula to calculate percentage of variance explained at different levels of analysis. A simple slopes procedure is showed to probe significant cross-level interactions (slope-as-outcome model) in a manner consistent with the approach generally used in ordinary least square regression. Potential extensions and limitations of this multi-level approach are presented in the discussion.     

Multiple solutions in dyads or alone – Fostering the acquisition of modeling competencies in mathematics

Generating multiple solutions is a promising approach in order to foster deep insight and understanding in mathematical contexts. However, in complex domains, students often struggle to generate just one solution, let alone more than one. This study investigates whether collaboration supports learners to generate multiple solutions, and to what extent collaboration and generating multiple solutions foster the acquisition of modeling competencies. In an experiment, students either learned alone or in dyads which were homogeneous or heterogeneous with respect to the level of prior knowledge, and they were prompted to generate one or multiple solutions in the learning phase (N = 193 seventh and eighth graders). Learning in homogeneous dyads fostered the acquisition of modeling competencies. Being prompted to generate a second solution was beneficial only for learners with high prior knowledge; overall, actually generating a second solution had positive impact.     

Understanding equity as an asset to national interest: developing a social contract analysis of policy

Alongside the influence of market-based reforms in education policy has been the growth of policy that has largely been overlooked – those that outline social contracts. This paper draws on policies that connect with equity as a way of illustrating this social contract turn in policy and develops a conceptualisation of social contracts as they apply to education policy. The argument provides three principles that underpin social contracts, including informed consent, negotiation and accountability. This paper applies these principles to three levels of social contract. At the first level are broad social contracts, which are associated with debates about the kinds of things that states should expect from its citizens, and the things that citizens could expect from governments and the state. The second level of social contract is an institutional or field-based social contract, which spells out the obligations and connections between a specific field and other fields. This level names a kind of social contract that is often exemplified in policies or statements by specific institutions. The third level of social contract deals with contract-like mechanisms embedded in fields that make tangible the obligations and expectations of citizens in fulfilling the expectations of fields.     

Informational constraints on the emergence of passing direction in the team sport of futsal

Abstract

This study investigated compound spatial and temporal measures of interpersonal interactions purported to constrain the emergence of affordances for passing direction in the team sport of futsal. For this purpose, attacker–defender interactions in 37 sequences of play from a futsal competition in which 24 male professional players participated (M=30.04 years, SD=4.10) were filmed and analysed using TACTO software. Relative angle data were used as measures to study coordination tendencies that emerged between players during performance. Results showed that the direction for a pass emerged from relative angles between: (1) the vector from a ball carrier to ball receiver and the vector from the ball carrier to the nearest defender (70°) (p<0.01) and (2) the vector from a ball carrier to ball receiver and the vector from the ball carrier to a ball receiver's nearest defender (31°) (p < 0.01). Furthermore, passing direction was also constrained by temporal information from the emergence of both angles, since the pass was performed to attacker–defender dyads with the highest velocities of these angles (p < 0.05). Results suggested that decisions on selecting the direction of a pass in the team sport of futsal emerged at critical values of these key compound motion measures.