Due to the low scoring nature of football (soccer), shots are often used as a proxy to evaluate team and player performances. However, not all shots are created equally and their quality differs significantly depending on the situation. The aim of this study is to objectively quantify the quality of any given shot by introducing a so-called expected goals (xG) model. This model is validated statistically and with professional match analysts. The best performing model uses an extreme gradient boosting algorithm and is based on hand-crafted features from synchronized positional and event data of 105, 627 shots in the German Bundesliga. With a ranked probability score (RPS) of 0.197, it is more accurate than any previously published expected goals model. This approach allows us to assess team and player performances far more accurately than is possible with traditional metrics by focusing on process rather than results.

It is common practice amongst coaches and analysts to search for key performance indicators related to attacking play in football. Match analysis in professional football has predominately utilised notational analysis, a statistical summary of events based on video footage, to study the sport and prepare teams for competition. Recent increases in technology have facilitated the dynamic analysis of more complex process variables, giving practitioners the potential to quickly evaluate a match with consideration to contextual parameters. One field of research, known as machine learning, is a form of artificial intelligence that uses algorithms to detect meaningful patterns based on positional data. Machine learning is a relatively new concept in football, and little is known about its usefulness in identifying performance metrics that determine match outcome. Few studies and no reviews have focused on the use of machine learning to improve tactical knowledge and performance, instead focusing on the models used, or as a prediction method. Accordingly, this article provides a critical appraisal of the application of machine learning in football related to attacking play, discussing current challenges and future directions that may provide deeper insight to practitioners.

A possible objective in analyzing trajectories of multiple simultaneously moving objects, such as football players during a game, is to extract and understand the general patterns of coordinated movement in different classes of situations as they develop. For achieving this objective, we propose an approach that includes a combination of query techniques for flexible selection of episodes of situation development, a method for dynamic aggregation of data from selected groups of episodes, and a data structure for representing the aggregates that enables their exploration and use in further analysis. The aggregation, which is meant to abstract general movement patterns, involves construction of new time-homomorphic reference systems owing to iterative application of aggregation operators to a sequence of data selections. As similar patterns may occur at different spatial locations, we also propose constructing new spatial reference systems for aligning and matching movements irrespective of their absolute locations. The approach was tested in application to tracking data from two Bundesliga games of the 2018/2019 season. It enabled detection of interesting and meaningful general patterns of team behaviors in three classes of situations defined by football experts. The experts found the approach and the underlying concepts worth implementing in tools for football analysts.

A new method for the determination of the equilibrium composition of gaseous mixtures is described. This method is particularly suited for both manual or computer calculations and leads to fast convergence. The mathematical formulation is detailed and a numerical example shows the calculation procedure.

Key Performance Indicators (KPIs) are used to evaluate the offensive success of a soccer team (e.g. penalty box entries) or player (e.g. pass completion rate). However, knowledge transfer from research to applied practice is understudied. The current study queried practitioners (n = 145, mean ± SD age: 36 ± 9 years) from 42 countries across different roles and levels of competition (National Team Federation to Youth Academy levels) on various forms of data collection, including an explicit assessment of twelve attacking KPIs. 64.3% of practitioners use data tools and applications weekly (predominately) to gather KPIs during matches. 83% of practitioners use event data compared to only 52% of practitioners using positional data, with a preference for shooting related KPIs. Differences in the use and value of metrics derived from positional tracking data (including Ball Possession Metrics) were evident between job role and level of competition. These findings demonstrate that practitioners implement KPIs and gather tactical information in a variety of ways with a preference for simpler metrics related to shots. The low perceived value of newer KPIs afforded by positional data could be explained by low buy-in, a lack of education across practitioners, or insufficient translation of findings by experts towards practice.