Probabilistic movement models and zones of control

The dual problem of space: Relative player positioning determines attacking success in elite men's football

The concept of space has been successfully modelled in football using spatiotemporal player data and Voronoi diagrams. Current approaches, however, are narrow in scope by focusing on an inter-team allocation of space to measure space control. The present work extends this widespread perspective with an intra-team application of the Voronoi diagram and its dual Delaunay triangulation to measure space management. Both models are leveraged to derive novel performance metrics, which assess how teams use triangular positioning and how players tie up defenders during attacks. The outcome of N = 128,187 attacking sequences from 306 elite men's football matches is analysed using linear mixed-effects models to validate the proposed performance metrics. Results show that attacking success is characterized by player positioning which promotes forming of large triangles especially in ball proximity, whereas the overall number of triangles is of no relevance. Furthermore, players tie up more defenders and thus create free teammates more often during successful attacks. The results demonstrate that a new perspective on space is helpful to better quantify and understand the effect of space management and player positioning on attacking performance in football.

Validation of a motion model for soccer players' sprint by means of tracking data

In soccer game analysis, the widespread availability of play-by-play and tracking data has made it possible to test mathematical models that have been discussed mainly theoretically. One of the essential models in soccer game analysis is a motion model that predicts the arrival point of a player in t s. Although many space evaluation and pass prediction methods rely on motion models, the validity of each has not been fully clarified. This study focuses on the motion model proposed by Fujimura and Sugihara (Fujimura-Sugihara model) under sprint conditions based on the equation of motion. A previous study indicated that the Fujimura-Sugihara model is ineffective for soccer games because it generates a circular arrival region. This study aims to examine the validity of the Fujimura-Sugihara model using soccer tracking data. Specifically, we quantitatively compare the arrival regions of players between the model and real data. We show that the boundary of the player's arrival region is circular rather than elliptical, which is consistent with the model. We also show that the initial speed dependence of the arrival region satisfies the solution of the model. Furthermore, we propose a method for estimating valid kinetic parameters in the model directly from tracking data and discuss the limitations of the model for soccer games based on the estimated parameters.

Reliability of spatial-temporal metrics used to assess collective behaviours in football: An in-silico experiment

The purpose of this study was to investigate the reliability of spatial-temporal measurements applied within collective behaviour research in football. In-silico experiments were conducted introducing positional errors (0.5, 2 and 4 m) representative of commercial tracking systems to match data from the 2020 European Championship qualifiers. Ratios of the natural variance ("signal") of spatial-temporal metrics obtained throughout sections of each game relative to the variance created by positional errors ("noise") were taken to calculate reliability. The effects of error magnitude and time of analysis (1, 5 and 15 mins; length of attack: <10, 10-20, >20 s) were assessed and compared using Cohen's f² effect size. Error magnitude was found to exert greater influence on reliability (f² = 0.15 to 0.81) compared with both standard time of analysis (f² = 0.03 to 0.08) and length of attacks (f² = 0.15 to 0.32). the results demonstrate that technologies generating positional errors of 0.5 m or less should be expected to produce spatial-temporal metrics with high reliability. However, technologies that generate errors of 2 m or greater may produce unreliable values, particularly when analyses are conducted over discrete events such as attacks, which although critical, are often short in duration.

The Effect of Substitutions on Team Tactical Behavior in Professional Soccer

Player substitutions are one of the main options for the coach to change tactical behavior of his team. Purpose: The present study therefore investigates the effect of player substitutions on tactical behavior in high-performance soccer using positional data. Method: The sample consisted of 659 substitutions from 234 matches played in the German Bundesliga during the season 2016-2017. Substitutions were classified either as neutral (n = 485), defensive (n = 45), or offensive (n = 129) according to the player's roles. The teams' tactical behavior before and after each substitution was analyzed using team centroid, inter-team centroid distance, team length and width, length per width (LpW) ratio, stretch index, and space control for the whole pitch and for each third as the dependent variables. Results: The linear mixed model analysis showed different effects for neutral, defensive, and offensive substitutions. Teams displayed significantly lower stretch index after defensive substitutions. LpW ratio increased with neutral and offensive substitutions, while inter-team distance decreased. The position of the team centroid, space control in the middle third and in the attacking third were also greater following an offensive substitution. Conclusions: These findings demonstrate that player substitutions effectively change tactical behavior of teams. Soccer coaches should perform more offensive substitutions to elicit a higher defensive pressure and improve goal-scoring opportunities, especially due to greater space control in the attacking third. In contrast, defensive substitutions can be used to increase defensive effectiveness through increases in team compactness.

Who can receive the pass? A computational model for quantifying availability in soccer

The paper presents a computational approach to Availability of soccer players. Availability is defined as the probability that a pass reaches the target player without being intercepted by opponents. Clearly, a computational model for this probability grounds on models for ball dynamics, player movements, and technical skills of the pass giver. Our approach aggregates these quantities for all possible passes to the target player to compute a single Availability value. Empirically, our approach outperforms state-of-the-art competitors using data from 58 professional soccer matches. Moreover, our experiments indicate that the model can even outperform soccer coaches in assessing the availability of soccer players from static images.

Expected passes

Passes are by far football’s (soccer) most frequent event, yet surprisingly little meaningful research has been devoted to quantify them. With the increase in availability of so-called positional data, describing the positioning of players and ball at every moment of the game, our work aims to determine the difficulty of every pass by calculating its success probability based on its surrounding circumstances. As most experts will agree, not all passes are of equal difficulty, however, most traditional metrics count them as such. With our work we can quantify how well players can execute passes, assess their risk profile, and even compute completion probabilities for hypothetical passes by combining physical and machine learning models. Our model uses the first 0.4 seconds of a ball trajectory and the movement vectors of all players to predict the intended target of a pass with an accuracy of $$93.0\%$$ 93.0 % for successful and $$72.0\%$$ 72.0 % for unsuccessful passes much higher than any previously published work. Our extreme gradient boosting model can then quantify the likelihood of a successful pass completion towards the identified target with an area under the curve (AUC) of $$93.4\%$$ 93.4 % . Finally, we discuss several potential applications, like player scouting or evaluating pass decisions.

Football player dominant region determined by a novel model based on instantaneous kinematics variables

Dominant regions are defined as regions of the pitch where a player can reach before any other and are commonly determined without considering the free-spaces in the pitch. We presented an approach to football players’ dominant regions analysis, based on movement models created from players’ positions, displacement, velocity, and acceleration vectors. 109 Brazilian male professional football players were analysed during official matches, computing over 15 million positional data obtained by video-based tracking system. Movement models were created based on players’ instantaneous vectorial kinematics variables, then probabilities models and dominant regions were determined. Accuracy in determining dominant regions by the proposed model was tested for different time-lag windows. We calculated the areas of dominant, free-spaces, and Voronoi regions. Mean correct predictions of dominant region were 96.56%, 88.64%, and 72.31% for one, two, and three seconds, respectively. Dominant regions areas were lower than the ones computed by Voronoi, with median values of 73 and 171 m², respectively. A median value of 5537 m² was presented for free-space regions, representing a large part of the pitch. The proposed movement model proved to be more realistic, representing the match dynamics and can be a useful method to evaluate the players’ tactical behaviours during matches.

Space and Control in Soccer

In many team sports, the ability to control and generate space in dangerous areas on the pitch is crucial for the success of a team. This holds, in particular, for soccer. In this study, we revisit ideas from Fernandez and Bornn (2018) who introduced interesting space-related quantities including pitch control (PC) and pitch value. We identify influence of the player on the pitch with the movements of the player and turn their concepts into data-driven quantities that give rise to a variety of different applications. Furthermore, we devise a novel space generation measure to visualize the strategies of the team and player. We provide empirical evidence for the usefulness of our contribution and showcase our approach in the context of game analyses.

Rating Player Actions in Soccer

We present a data-driven model that rates actions of the player in soccer with respect to their contribution to ball possession phases. This study approach consists of two interconnected parts: (i) a trajectory prediction model that is learned from real tracking data and predicts movements of players and (ii) a prediction model for the outcome of a ball possession phase. Interactions between players and a ball are captured by a graph recurrent neural network (GRNN) and we show empirically that the network reliably predicts both, player trajectories as well as outcomes of ball possession phases. We derive a set of aggregated performance indicators to compare players with respect to. to their contribution to the success of their team.

Data-driven detection of counterpressing in professional football

Detecting counterpressing is an important task for any professional match-analyst in football (soccer), but is being done exclusively manually by observing video footage. The purpose of this paper is not only to automatically identify this strategy, but also to derive metrics that support coaches with the analysis of transition situations. Additionally, we want to infer objective influence factors for its success and assess the validity of peer-created rules of thumb established in by practitioners. Based on a combination of positional and event data we detect counterpressing situations as a supervised machine learning task. Together, with professional match-analysis experts we discussed and consolidated a consistent definition, extracted 134 features and manually labeled more than 20, 000 defensive transition situations from 97 professional football matches. The extreme gradient boosting model—with an area under the curve of $$87.4\%$$ 87.4 % on the labeled test data—enabled us to judge how quickly teams can win the ball back with counterpressing strategies, how many shots they create or allow immediately afterwards and to determine what the most important success drivers are. We applied this automatic detection on all matches from six full seasons of the German Bundesliga and quantified the defensive and offensive consequences when applying counterpressing for each team. Automating the task saves analysts a tremendous amount of time, standardizes the otherwise subjective task, and allows to identify trends within larger data-sets. We present an effective way of how the detection and the lessons learned from this investigation are integrated effectively into common match-analysis processes.

Space evaluation in football games via field weighting based on tracking data

In football game analysis, space evaluation is an important issue because it is directly related to the quality of ball passing or player formations. Previous studies have primarily focused on a field division approach wherein a field is divided into dominant regions in which a certain player can arrive prior to any other players. However, the field division approach is oversimplified because all locations within a region are regarded as uniform herein. The objective of the current study is to propose a fundamental framework for space evaluation based on field weighting. In particular, we employed the motion model and calculated a minimum arrival time [Formula: see text] for each player to all locations on the football field. Our main contribution is that two variables [Formula: see text] and [Formula: see text] corresponding to the minimum arrival time for offense and defense teams are considered; using [Formula: see text] and [Formula: see text], new orthogonal variables [Formula: see text] and [Formula: see text] are defined. In particular, based on real datasets comprising of data from 45 football games of the J1 League in 2018, we provide a detailed characterization of [Formula: see text] and [Formula: see text] in terms of ball passing. By using our method, we found that [Formula: see text] and [Formula: see text] represent the degree of safety for a pass made to [Formula: see text] at t and degree of sparsity of [Formula: see text] at t, respectively; the success probability of passes could be well-fitted using a sigmoid function. Moreover, a new type of field division approach and evaluation of ball passing just before shots using real game data are discussed.

Modeling the Quality of Player Passing Decisions in Australian Rules Football Relative to Risk, Reward, and Commitment

The value of player decisions has typically been measured by changes in possession expectations, rather than relative to the value of a player's alternative options. This study presents a mathematical approach to the measurement of passing decisions of Australian Rules footballers that considers the risk and reward of passing options. A new method for quantifying a player's spatial influence is demonstrated through a process called commitment modeling, in which the bounds and density of a player's motion model are fit on empirical commitment to contests, producing a continuous representation of a team's spatial ownership. This process involves combining the probability density functions of contests that a player committed to, and those they did not. Spatiotemporal player tracking data was collected for AFL matches played at a single stadium in the 2017 and 2018 seasons. It was discovered that the probability of a player committing to a contest decreases as a function of their velocity and of the ball's time-to-point. Furthermore, the peak density of player commitment probabilities is at a greater distance in front of a player the faster they are moving, while their ability to participate in contests requiring re-orientation diminishes at higher velocities. Analysis of passing decisions revealed that, for passes resulting in a mark, opposition pressure is bimodal, with peaks at spatial dominance equivalent to no pressure and to a one-on-one contest. Density of passing distance peaks at 17.3 m, marginally longer than the minimum distance of a legal mark (15 m). Conversely, the model presented in this study identifies long-range options as have higher associated decision-making values, however a lack of passes in these ranges may be indicative of differing tactical behavior or a difficulty in identifying long-range options.