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On the one-shot two-person zero-sum game in football from a penalty kicker’s perspective

Ekhosuehi V.

Operations Research and Decisions

2018

Vol. 28, No. 3

17--27

A penalty kicker’s problem in football has been modelled. The study took into consideration different directions in which the ball can be struck and goalkeepers’ success at defending shots. The strategic form of the game that can be used to predict how the kicker should optimally randomise his strategies has been modelled as a non-linear game-theoretic problem from a professional kicker’s viewpoint. The equilibrium of the game (i.e., the pair of mutually optimal mixed strategies) was obtained from the game-theoretic problem by reducing it to a linear programming problem and the two-phase simplex method was adopted to solve this problem. The optimal solution to the game indicates that the kicker never chooses to kick the ball off target, to the goalpost or to the crossbar, but rather chooses to kick the ball in the opposite direction to the one where the goalkeeper is most likely to successfully defend from past history.

Measuring the force of punches and kicks among combat sport athletes using a modified punching bag with an embedded accelerometer

Buśko K., Staniak Z., Szark-Eckardt M., Nikolaidis P. T., Mazur-Różycka J., Łach P., Michalski R., Gajewski J., Górski M.

Acta of Bioengineering and Biomechanics

2016

Vol. 18, no. 1

47--54

The main aim of the study was to design a new system to measure punching and kicking forces as well as reaction times in combat sport athletes. In addition, the study examined whether there were any intergender differences in the force of punches thrown by boxers and kicking forces delivered by taekwondo athletes. Boxers (male, n = 13; female, n = 7) were examined for the force of single straight punches and taekwondo athletes (male, n = 14; female, n = 14) for force of single Apdolio and Dwit Chagi kicks. The punching bag was equipped with acceleration transducers and gyroscopes embedded in a cylinder covered with a layer to absorb shock as well as a set of colour signal diodes. Value of the punching bag’s acceleration was used for calculating: strike force; the punching location on the bag; and time of a strike. The relative error of force calculation was 3%; the relative error in acceleration measurement was less than 1%. The force of a straight rear-hand punch was greater than the force of a lead-hand punch among male and female boxers. The force of Apdolio kick delivered with a rear leg was greater compared to a lead leg among female and male taekwondo athletes. Significant gender differences were noticed in the force in both types of kicks. In boxers, intergender differences were reported only for the force of a punch thrown with the rear hand. Based on these findings, it was concluded that the modified punching bag is a good diagnostic tool for combat sports.