On winning the penalty shoot-out in soccer

The penalty shoot-out is used to break tied games in the knock-out stages of soccer competition. The shoot-out, which consists of an alternating series of penalty kicks, is won by the team with the highest goal tally after n kicks per team (n = 5). In the event of a tie after five penalty kicks each, the shoot-out progresses to 'sudden death' by increasing n in iterative fashion (i.e. n = n + 1) until one team obtains a higher goal tally than the other after an equal number of kicks per team. The team to strike first is determined at the end of extra time by the toss of a coin. As each on-field player can be awarded only a single penalty kick, the line-up order in which the penalty kicks are taken allows for the possibility of tactical influence on the final outcome. Consequently, we report a probability analysis of the penalty shoot-out in soccer from which we identify the following pre- and post-game strategies. The best five ranked penalty takers from the on-field players should be assigned to the first five penalty kicks in their reverse order of ability. That is, the fifth best penalty taker should take the first penalty kick, the fourth best penalty taker should take the second penalty kick, and so on. In the event of sudden death, the next highest ranked on-field player should be assigned to the next penalty kick until the shoot-out ends. For this tactic to be successful, players should be ranked a priori on their penalty-taking ability. Similarly, goalkeepers should be ranked a priori on their penalty-stopping ability. These findings indicate that the tactical substitution of on-field players for higher ranked penalty takers, including higher ranked penalty stoppers (i.e. goalkeepers), with a view to an impending penalty shoot-out should be given due consideration. These results are of practical importance in that they are shown to maximize the likelihood of winning the penalty shoot-out under certain initial conditions.     

Relations among basic psychological needs,PE-motivation and fundamental movement skills in 9–12-year-old boys and girls in Physical Education

Background: Many children aged 9–12 appear to have low levels of fundamental movement skills (FMS). Physical education (PE) is important because PE-teachers can teach children a variety of FMS and can influence PE-motivation. However, declined levels of PE-motivation are reported in the final grades of elementary school. Therefore, more insight in the relations between PE-motivation and FMS is needed.

Purposes: In the first phase, instruments to measure the satisfaction of basic psychological needs (competence, autonomy, classmate relatedness and teacher relatedness) and PE-motivation (autonomous and controlled) in 9–12-year-old children were developed and validated. The purpose of the second phase was to examine the influence of basic psychological needs on PE-motivation, the influence of PE-motivation on locomotor skills, object control skills and balance skills, and the direct influence of basic psychological needs on FMS for boys and girls aged 9–12.

Participants and data collection: In the first phase, 172 children (82 boys, 90 girls, M?=?10.72 years?±?0.77) filled out questionnaires assessing the satisfaction of their basic psychological needs and motivation for PE. Forty-eight children completed the questionnaires again 4 weeks later. In the second phase, a total of 138 children (66 boys, 72 girls, 10.8 years?±?.79) (three schools from phase 1 and one new school) participated. Children from the new school also completed the questionnaires and all children conducted the subtest for speed and agility, upper limb coordination and balance of the Bruininks-Oseretsky Test of Motor Proficiency 2.

Data analysis: In phase 1, linear weighted Kappa's and the Mokken Scale Program for polychotomous items were used to test reliability and validity. In phase 2, Pearson's correlations and multiple linear regression analyses were performed to examine the relations.

Findings: Regarding phase 1, all subscales were reliable and the validity was considered moderate to strong except for the autonomy subscale, which was not reliable and valid. With respect to phase 2, all basic psychological needs, except autonomy among girls, had moderate to strong correlations with autonomous PE-motivation. Teacher relatedness was the most important predictor for boys and girls, while the second predictor was classmate relatedness for boys and competence for girls. No positive significant relations between basic psychological needs and FMS and between PE-motivation and FMS were found. In contrary, moderate but negative relations between teacher relatedness and balance skills and between autonomous PE-motivation and balance skills were found for boys.

Conclusions: The results confirmed the importance of the basic psychological needs in the prediction of autonomous PE-motivation in 9–12-year-old children. Although all needs should be supported by the PE-teacher, it is important to be aware of the different impact of the needs on autonomous PE-motivation for boys and girls. Despite the missing relations with FMS, PE-teachers seem to be able to autonomously motivate children for PE regardless of their FMS proficiency.     

An analytical model for flat-ski friction in steady horizontal gliding

This paper addresses sliding friction of a ski during steady horizontal gliding on snow. A simple mathematical theory accounting for both dry and wet friction is developed. The water film evolution along a ski is calculated with a lumped-element thermal model. An analytical solution is obtained for the ski friction force. Representative calculation results are demonstrated for a range of ski velocity, contact surface area fraction, snow temperature, and ski aspect ratio.     

Validity and feasibility of an obstacle course to assess fundamental movement skills in a pre-school setting

Failure to master age-appropriate fundamental movement skills (FMS) at a young age can limit motor skill competence affecting health. Assessments often have issues with feasibility and implementation in a field setting. As such, the purpose of this study was to investigate the validity and feasibility of the Athletic Skills Track (AST), in a pre-school setting. For the validation study sixty-five 3–6 year old children (25 boys and 40 girls) from five pre-schools across Adelaide, Australia participated. Correlations and linear regression analysis (adjusted for age and gender) were used to investigate the association between the time to complete the AST and the raw score of the Test of Gross Motor Development 2 (TGMD-2). For the feasibility study pre-school staff completed a semi-structured interview regarding the feasibility of the AST. The AST took less than a minute per child and the TGMD-2 around 20 minutes for two children. There was a strong negative correlation (r = ?0.63, p < 0.01) between the AST scores and the TGMD-2 scores. All five staff reported strengths of the AST to be its short administration time, setup and appropriateness. These results suggest that the AST could be a feasible and valid method of FMS assessment in Australian pre-schools.