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 that account for receiver deployment. The resulting route labels can also be paired with film to enable streamlined queries of game film.
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. …
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…
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…
Predicting the results of sport matches and competitions is an arising research field, benefiting from the growing amount of available data and the novel data analytics techniques. Excellent forecasts can be achieved by advanced machine learning methods applied to detailed historical data, especially in very popular sports such as football (soccer). Here we show that, despite the large number of confounding factors, the results of a football team in longer competitions (e.g., a national league) follow a basically linear trend useful for predictive purposes, too. In support of this claim, we pr…
Recording of events in National Hockey League rinks is done through the Real Time Scoring System. This system records events such as hits, shots, faceoffs, etc., as part of the play-by-play files that are made publicly available. Several previous studies have found that there are inconsistencies in the recording of these events from rink to rink. In this paper, we propose a methodology for estimation of the rink effects for each of the rinks in the National Hockey League. Our aim is to build a model which accounts for the relative differences between rinks. We use log-linear regression to mode…
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…
Modelling football outcomes has gained increasing attention, in large part due to the potential for making substantial profits. Despite the strong connection existing between football models and the bookmakers' betting odds, no authors have used the latter for improving the fit and the predictive accuracy of these models. We have developed a hierarchical Bayesian Poisson model in which the scoring rates of the teams are convex combinations of parameters estimated from historical data and the additional source of the betting odds. We apply our analysis to a nine-year dataset of the most popular…
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）
Scouting is a major part of talent acquisition for any professional sports team. In the National Hockey League (NHL), the market for scouting is set by the NHLs Central Scouting Service which develops a ranking of draft eligible players. In addition to the Central Scouting rankings, NHL teams use their own internal scouting to augment their knowledge of eligible players and develop their own rankings. Using a novel statistical approach we show in this paper that the additional information possessed by teams provides better rankings than those of Central Scouting. Using data from the 1998 to 20…
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…
Continuous-time assessments of game outcomes in sports have become increasingly common in the last decade. In American football, only discrete-time estimates of play value were possible, since the most advanced public football datasets were recorded at the play-by-play level. While measures such as expected points and win probability are useful for evaluating football plays and game situations, there has been no research into how these values change throughout the course of a play. In this work, we make two main contributions: First, we introduce a general framework for continuous-time within-…
We analyse football (soccer) player performance data with mixed type variables from the 2014-15 season of eight European major leagues. We cluster these data based on a tailor-made dissimilarity measure. In order to decide between the many available clustering methods and to choose an appropriate number of clusters, we use the approach by Akhanli and Hennig (2020). This is based on several validation criteria that refer to different desirable characteristics of a clustering. These characteristics are chosen based on the aim of clustering, and this allows to define a suitable validation index a…
Unlike other major professional sports, American football lacks comprehensive statistical ratings for player evaluation that are both reproducible and easily interpretable in terms of game outcomes. Existing methods for player evaluation in football depend heavily on proprietary data, are not reproducible, and lag behind those of other major sports. We present four contributions to the study of football statistics in order to address these issues. First, we develop the R package nflscrapR to provide easy access to publicly available play-by-play data from the National Football League (NFL) dat…
The UEFA Champions League is the major European club football competition, however, most national champions have to play qualification matches to receive a slot in the group stage of the tournament. The paper evaluates the impact of the only reform in the Champions Path of the qualifying system since 2009, effective from the 2018/19 season. While it is anticipated that the reduction in the number of berths decreases the probability of advancing to the group stage, the distribution of the effects among the national associations is revealed here via Monte-Carlo simulations. In contrast to previo…
Statistical applications in sports have long centered on how to best separate signal (e.g. team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport comparisons has been impeded by the difficulty of translating luck from one sport to another. In this manuscript, we develop Bayesian state-space models using betting market data that can be uniformly applied across sporting organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the…
More than 1 million students play high school American football annually, but many health professionals have recently questioned its safety or called for its ban. These concerns have been partially driven by reports of chronic traumatic encephalopathy (CTE), increased risks of neurodegenerative disease, and associations between concussion history and later-life cognitive impairment and depression among retired professional football players. A recent observational study of a cohort of men who graduated from a Wisconsin high school in 1957 found no statistically significant harmful effects of pl…
Analysis of player tracking data for American football is in its infancy, since the National Football League (NFL) released its Next Gen Stats tracking data publicly for the first time in December 2018. While tracking datasets in other sports often contain detailed annotations of on-field events, annotations in the NFL's tracking data are limited. Methods for creating these annotations typically require extensive human labeling, which is difficult and expensive. We begin tackling this class of problems by creating annotations for pass coverage types by defensive backs using unsupervised learni…
Encouraging offensive play: A hidden benefit of incomplete round-robin tournaments
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（布达佩斯科维努斯大学）；University of Vienna（维也纳大学）
本文开发仿真框架量化进攻得失，发现2024/25赛季UEFA Champions League的不完整循环赛联赛阶段比小组赛更能激励进攻性打法，首次证明赛制本身能强烈影响球队行为。
Using high-resolution player tracking data made available by the National Football League (NFL) for their 2019 Big Data Bowl competition, we introduce the Expected Hypothetical Completion Probability (EHCP), a objective framework for evaluating plays. At the heart of EHCP is the question "on a given passing play, did the quarterback throw the pass to the receiver who was most likely to catch it?" To answer this question, we first built a Bayesian non-parametric catch probability model that automatically accounts for complex interactions between inputs like the receiver's speed and distances to…
