Competitive balance in a football league is extremely important from the perspective of economic growth of the industry. Many researchers have earlier proposed different measures of competitive balance, which are primarily adapted from the standard economic theory. However, these measures fail to capture the finer nuances of the game. In this work, we discuss a new framework which is more suitable for a football league. First, we present a mathematical proof of an ideal situation where a football league becomes perfectly balanced. Next, a goal based index for competitive balance is developed. We present relevant theoretical results and show how the proposed index can be used to formally test for the presence of imbalance. The methods are implemented on the data from top five European leagues, and it shows that the new approach can better explain the changes in the seasonal competitive balance of the leagues. Further, using appropriate panel data models, we show that the proposed index is more suitable to analyze the variability in total revenues of the football leagues.
Since March 2020, the environment surrounding football has changed dramatically because of the COVID-19 pandemic. After a few months' break, re-scheduled matches were held behind closed doors without spectators. The main objective of this study is a quantitative evaluation of ``crowd effects'' on home advantage, using the results of these closed matches. The proposed analysis uses pairwise comparison method to reduce the effects caused by the unbalanced schedule. The following conclusions were drawn from the statistical hypothesis tests conducted in this study: In four major European leagues, …
In recent years, data-driven approaches have become a popular tool in a variety of sports to gain an advantage by, e.g., analysing potential strategies of opponents. Whereas the availability of play-by-play or player tracking data in sports such as basketball and baseball has led to an increase of sports analytics studies, equivalent datasets for the National Football League (NFL) were not freely available for a long time. In this contribution, we consider a comprehensive play-by-play NFL dataset provided by www.kaggle.com, comprising 289,191 observations in total, to predict play calls in the…
Most historical National Football League (NFL) analysis, both mainstream and academic, has relied on public, play-level data to generate team and player comparisons. Given the number of oft omitted variables that impact on-field results, such as play call, game situation, and opponent strength, findings tend to be more anecdotal than actionable. With the release of player tracking data, however, analysts can better ask and answer questions to isolate skill and strategy. In this article, we highlight the limitations of traditional analyses, and use a decades-old punching bag for analysts, fourt…
Tracking data in the NFL is a sequence of spatial-temporal measurements that vary in length depending on the duration of the play. In this paper, we demonstrate how model-based curve clustering of observed player trajectories can be used to identify the routes run by eligible receivers on offensive passing plays. We use a Bernstein polynomial basis function to represent cluster centers, and the Expectation Maximization algorithm to learn the route labels for each of the 34,698 routes run on the 6,963 passing plays in the data set. We go on to suggest ideas for new potential receiver metrics th…
We use European football performance data to select teams to form the proposed European football Super League, using only unsupervised techniques. We first used random forest regression to select important variables predicting goal difference, which we used to calculate the Euclidian distances between teams. Creating a Laplacian eigenmap, we bisected the Fielder vector to identify the five major European football leagues' natural clusters. Our results showed how an unsupervised approach could successfully identify four clusters based on five basic performance metrics: shots, shots on target, s…
In this paper, we present betting strategy of a football game using probability theory. We know all betting houses offer slightly unfair odds towards the player. Here we discuss a simple way to figure out which betting house is offering relatively better odds compared to others for English Premier League. However, this methodology can be adopted for another league football match.
Playing time tracks recent exposure in fifteen men's and women's football leagues: the denominator gradient and what it does to per-minute injury rates
School of Computer Science and Statistics, Trinity College Dublin（都柏林三一学院计算机科学与统计学院）；Discipline of Anatomy, School of Medicine, Trinity College Dublin（都柏林三一学院医学院解剖学科）
Beijing Sport University（北京体育大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；Universidad Politécnica de Madrid（马德里理工大学）
Characterizing playing style is important for football clubs on scouting, monitoring and match preparation. Previous studies considered a player's style as a combination of technical performances, failing to consider the spatial information. Therefore, this study aimed to characterize the playing styles of each playing position in the Chinese Football Super League (CSL) matches, integrating a recently adopted Player Vectors framework. Data of 960 matches from 2016-2019 CSL were used. Match ratings, and ten types of match events with the corresponding coordinates for all the lineup players whos…
Fairness has several interpretations in sports, one of them being that the rules should guarantee incentive compatibility, namely, a team cannot be worse off due to better results in any feasible scenario. The current seeding regime of the most prestigious annual European club football tournament, the UEFA (Union of European Football Associations) Champions League, is shown to violate this requirement since the 2015/16 season. In particular, if the titleholder qualifies for the first pot by being a champion in a high-ranked league, its slot is given to a team from a lower-ranked association, w…
In this paper, we introduce an R software package for simulating plays and drives using play-by-play data from the National Football League. The simulations are generated by sampling play-by-play data from previous football seasons.The sampling procedure adds statistical rigor to any decisions or inferences arising from examining the simulations. We highlight that the package is particularly useful as a data-driven tool for evaluating potential in-game strategies or rule changes within the league. We demonstrate its utility by evaluating the oft-debated strategy of $\textit{going for it}$ on f…
On the fairness of single round-robin tournaments: Evidence from European football
Institute for Computer Science and Control (SZTAKI), Hungarian Research Network (HUN-REN)（匈牙利研究网络控制与计算机科学研究所）；Corvinus University of Budapest (BCE)（布达佩斯考文纽斯大学）；University of Pécs, Faculty of Business and Economics（佩奇大学商学院）
Competitive balance is an important concept for professional sports and one of the key issues that European football has to address in order to ensure its long-term prosperity. However, the quantification of competitive balance is not an easy task. The difficulties are mainly associated with its multi-dimensionality character as well as the structure of each particular sport. This article uses data from eight domestic leagues over 60 years to identify the best index for a holistic view of competitive balance in European football. The findings support the longstanding Uncertainty of Outcome Hyp…
Competitive balance is the subject of much interest in the sports analytics literature and beyond. In this paper, we develop a statistical network model based on an extension of the stochastic block model to assess the balance between teams in a league. Here we represent the outcome of all matches in a football season as a dense network with nodes identified by teams and categorical edges representing the outcome of each game as a win, draw or a loss. The main focus and motivation for this paper is to provide a statistical framework to assess the issue of competitive balance in the context of …
We consider the task of determining a football player's ability for a given event type, for example, scoring a goal. We propose an interpretable Bayesian model which is fit using variational inference methods. We implement a Poisson model to capture occurrences of event types, from which we infer player abilities. Our approach also allows the visualisation of differences between players, for a specific ability, through the marginal posterior variational densities. We then use these inferred player abilities to extend the Bayesian hierarchical model of Baio and Blangiardo (2010) which captures …
Statistical modelling of sports data has become more and more popular in the recent years and different types of models have been proposed to achieve a variety of objectives: from identifying the key characteristics which lead a team to win or lose to predicting the outcome of a game or the team rankings in national leagues. Although not as popular as football or basketball, volleyball is a team sport with both national and international level competitions in almost every country. However, there is almost no study investigating the prediction of volleyball game outcomes and team rankings in na…
