The influence of field size, goal size and number of players on the average number of goals scored per game in variants of football and hockey: the Pi-theorem applied to team sports

IF 1.1 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS

Journal of Quantitative Analysis in Sports Pub Date : 2020-09-21 DOI:10.1515/JQAS-2020-0009

J. Blondeau

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引用次数: 1

Abstract

Abstract In this paper, we investigate the correlation between the main physical characteristics of eight variants of football and hockey (such as field size, goal size, player velocity, ball velocity, player density, and game duration) and the resulting average numbers of goals scored per game. To do so, the Pi-theorem in physics is extended to sport science and a non-dimensional parameter of interest is defined. It is based on the ratio between the duration of the game and the order of magnitude of the time needed to cross the midfield, which depends on the average velocity of the ball and the players, the player density and the size of the goals. An excellent correlation is found between the proposed parameter and the average number of goals scored per game during recent international competitions. Using the derived correlation, the effect of any modification of the main characteristics of football and hockey (and their variants) on the scoring pace can be assessed. For instance, it can be predicted that decreasing the length of football fields by 20 m would raise the average number of goals scored to 3.6 (±0.6) per game, versus the 2.6 goals scored during the most recent men’s World Cup.

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场地大小、球门大小和球员人数对足球和曲棍球比赛每场平均进球数的影响:pi定理在团队运动中的应用

摘要本文研究了八种足球和曲棍球的主要身体特征(如场地大小、球门大小、球员速度、球速度、球员密度和比赛持续时间)与每场比赛平均进球数之间的相关性。为此，将物理学中的pi定理扩展到体育科学中，并定义了感兴趣的无量纲参数。它是基于比赛持续时间与穿越中场所需时间数量级之间的比率，这取决于球和球员的平均速度，球员密度和进球大小。在最近的国际比赛中，所提出的参数与每场比赛的平均进球数之间存在很好的相关性。使用导出的相关性，可以评估足球和曲棍球(及其变体)的主要特征的任何修改对得分速度的影响。例如，可以预测，将足球场的长度减少20米，将使场均进球数提高到3.6(±0.6)个，而最近一届男子世界杯的场均进球数为2.6个。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Quantitative Analysis in Sports SOCIAL SCIENCES, MATHEMATICAL METHODS-

CiteScore

2.00

自引率

12.50%

发文量

期刊介绍： The Journal of Quantitative Analysis in Sports (JQAS), an official journal of the American Statistical Association, publishes timely, high-quality peer-reviewed research on the quantitative aspects of professional and amateur sports, including collegiate and Olympic competition. The scope of application reflects the increasing demand for novel methods to analyze and understand data in the growing field of sports analytics. Articles come from a wide variety of sports and diverse perspectives, and address topics such as game outcome models, measurement and evaluation of player performance, tournament structure, analysis of rules and adjudication, within-game strategy, analysis of sporting technologies, and player and team ranking methods. JQAS seeks to publish manuscripts that demonstrate original ways of approaching problems, develop cutting edge methods, and apply innovative thinking to solve difficult challenges in sports contexts. JQAS brings together researchers from various disciplines, including statistics, operations research, machine learning, scientific computing, econometrics, and sports management.