The success of the Roman Triplex Acies formation in ancient battles (1) and the power efficiency of migratory birds' V-shaped flight (2) are just two examples that demonstrate the benefits of collective behavior. Formations have also been studied in other domains, including transportation (3), robotics (4), space exploration (5), video games (6), choreography (7), and sports such as American football (8), field hockey (9), handball (10), and association football¹ (11).

In football, formations have been present since the early versions, as evidenced by available drawings from a festive match played in Italy in 1688, which depict team arrangements on the field, including players' defined distances (12). After the codification of football and its split from rugby in 1863, the first observed formations were 2-2-6, 1-2-7, and 2-3-5 (pyramid). Historically, formations have been modified to balance defensive and offensive capabilities while adapting to rule changes such as offside in 1925. Arsenal's 3-2-2-3 (W-M) from the 1930s, Brazil's 4-2-4 in the 1950s, and the 4-2-3-1 formation used in recent decades are a few examples of this continuous evolution (11) because there is no optimal formation as each has its pros and cons (13, 14).

We define “formation”² as an abstraction summarizing each team's spatial arrangement on the pitch over a match using labels (16) that are usually short to communicate useful and relevant information to the target audience in a consistent manner. While this definition means there is no requirement for a standard and unified set of these labels, they are commonly reported using three to five digits denoting the number of outfield players from defense to attack in each horizontal line³ usually in a symmetric manner, like 4-4-2 (four defenders, four midfielders, and two attackers), as shown in Figure 1.

Formations can change in a match for various reasons (18) including the match score (19), coach instructions (20), substitutions (21), tactical position⁴ switches, match phases (22–25), opponent (26), mental pressure, injuries, and yellow/red cards. This definition aligns with football as a dynamic interaction process (27) and contrasts with the traditional belief that formations are fixed throughout a match, as reported in “starting formation”⁵ graphics in media and history books (11, 28).

Formations are important to ensure a team operates cohesively, without confusion or delay, while taking advantage of each player's abilities and conserving energy. Therefore, players' confidence is boosted and they can inflict maximum damage on their opponents while remaining less susceptible to attacks (1). Moreover, it serves as a reference (29) for players to remember their organization and responsibilities when distracted (30), helps coaches reduce communication overhead, and shapes the team's collective behavior by creating desired scenarios (31), such as passing options and numerical superiorities. All these reasons could explain why formations are covered in coaching programs, interviews (22, 32–34), training sessions (20), dressing room discussions (35), and media (36).

Formations are also among the first considerations in opposition analysis (13, 20), as highlighted by the spygate incident (37). This is because coaches have the freedom to choose any⁶ formation consisting of a goalkeeper and six to ten other starting players to counter opponents (11, 39–41). In addition, there are other factors that can influence a formation choice such as the skills of available players (19), tradition (11), recent results (42), coach and club's principles (43), league (30, 44), home or away (45), and pitch elevation (46).

Formation analysis is often carried out qualitatively (47) relying on previous matches using isolated observations (16), most seen arrangements (48), or only out-of-possession moments (49, 50) resulting in a time-consuming and subjective process (51). For instance, comparing the starting formations recorded by two industry data providers for the 2022 Men's World Cup shows only a 65% agreement (52, 53) highlighting the lack of ground truth formation labels (54).

To address these issues, dozens of data-driven studies have been conducted over the past decades to identify formations in a more automated, scalable, and objective manner. These solutions also can have player/coach recruitment in addition to performance and match analysis applications such as studying the relationship between formation choice and various success metrics (e.g., goals, expected goals, scoring zone entries) (30, 55, 56), examining the physical load implications of different formations (57–59), and comparing the identified formations with the instructed ones. Ideally, these approaches, given data availability, can also support real-time applications for media, fans, and specifically the coaching staff to facilitate in-game interventions.

Given the ongoing interest in this problem and the time required to get informed about the relevant developments and their limitations, we recognized the need for a survey on the subject of “formation identification principles in football using event and tracking data” to structure the body of knowledge, prevent redundant efforts, and establish a foundation for future research.

Our survey is not a systematic review but rather an extensive overview of the principles used to identify football formations⁷ using event and tracking data⁸ in the past decades⁹. We put together similar attempts for each principle found in academic papers, presentations, books, theses, and patents starting with the seminal publications in football and their reference lists. Next, we monitored sources that cited the initial publications and subsequently expanded them to relevant principles from other sports and fields.

In summary, these principles are preprocessing the input data, followed by choosing either the team or position level. Regardless of the choice, there is a data representation and identification step followed up by evaluation. The goal at the team level is to directly report the formation for the entire team while the position level first starts by identifying individual player positions and then maps the set of those positions to a formation label using a pre-defined lookup table. Therefore, this survey also covers tactical position identification methods relevant to formation identification.

An overview of these principles and their concepts is depicted in Figure 2. Each step is explained through the remainder sections and subsections of this paper.

In this section, we introduce the event and tracking data sources. Event data is used only in “Match Segments” while tracking data is employed in all steps shown in Figure 2.

In this section, the input data is preprocessed by transforming teams to have a consistent attacking direction (e.g., from bottom to top) to negate the effect of half-time side switches, or ignoring the goalkeeper locations, as they may not be relevant. Moreover, the pitch sizes are standardized since they can differ per stadium¹⁰. The other preprocessing tasks are explained in “match segments” or “normalized locations” subsections.

Several studies focused on reporting team formations bottom-up by starting from smaller units called positions¹³, which are defined based on where on the pitch players spend most of their match time. Positions are commonly communicated with labels such as center back and right midfield, as shown in Figure 7, for an example.

The reason behind considering positions rather than player identifiers is that players can swap positions, be substituted or sent off during a match, or differ across matches while the set of all possible positions on the pitch remains fixed. Similar to the team-level approach, an appropriate data representation is chosen and later either template or clustering is applied to identify positions. The key assumption employed in the position-level approach is that no two teammates can occupy the same position simultaneously (9). Therefore, a one-to-one mapping is applied to assign either a template or cluster position by solving the assignment problem (161).

Similar to Table 1, we compiled the list of position labels from the same three industry data providers see Table 2 by merging labels with identical descriptions or spatial arrangements on the pitch. This comparison shows a 79% agreement, indicating a stronger consensus than for formations.

Regardless of the approach, previous studies have generally fallen short in terms of reporting their accuracy, execution time, and required storage. This is understandable given the variations in validation datasets, evaluation metrics, labeling quality, granularity, and expert interpretations (106).

While quantitative evaluation in this area remains difficult due to the lack of ground truth in sports analytics (180), there are other aspects to an evaluation, as suggested for mathematical models in general and sports analytics ones in particular (181, 182). We divide them into design and qualitative categories.

In design, aspects such as realistic assumptions, output robustness to small input data changes, output stability over time, reproducibility, and interpretability can be covered. In the qualitative category, one can address whether the outputs behave as expected in known and boundary scenarios and if the results are intuitive, insightful, and actionable for practitioners (183).

While the definition of formations remains an ill-defined problem, we aimed to provide more clarity by defining them as the spatial arrangement of players on the field. Our paper offers an overview of more than 20 years of research on team tactical formations starting from the late 1990s in simulated robotic soccer and American football. The importance of formations is highlighted through opposition analysis, training sessions, and media coverage and the formation identification still is carried out qualitatively to a large extent by counting the number of players in each horizontal line overlooking the vertical disposition.

The main principles were structured as first preprocessing and later taking either a team or position-level approach. The two main concepts employed in the preprocessing step were match segments and normalized locations. The objective of dividing the match time into smaller windows, known as phases of play, is to move beyond reporting one fixed formation for the entire match. Normalized locations aimed to report the same formation for the same arrangements, regardless of where they occurred. However, the potential unintended consequences were not fully understood. Moreover, the same objective can be achieved through other steps of the pipeline without the need for normalization.

After preprocessing, two different paths were followed: The team-level approach looks at a whole team at once while the position level starts with positions as smaller units to build on. In both, the first step is data representation and later, the detection using either qualitatively labeled data (templates) or clustering methods.

Among the data representation options, average locations were the simplest and most commonly used. However, they lead to misleading statements due to the natural outcome of compactness resulting from averaging. When utilizing hand-engineered features or graph representations, it is crucial to carefully select the elements to include in those representations. These elements should align with the references coaches use to instruct team arrangements. Additionally, the representation should be unique for the same arrangements, or arrangements that are not distinguishable due to small player location differences.

After data representation in the team or position levels, formation identification has been achieved by employing domain knowledge through templates or relying on data through clustering. While templates are relatable to public understanding and can be widely accepted, preparing a list of labels and qualitatively assessing them could be cumbersome, especially since there is no worldwide consensus and they change over time. This could be why some adopted clustering to bypass the issues associated with templates. Clustering avoids these issues but on the other hand, requires tracking data of a large number of matches and will limit the future observations to be mapped to one of the existing formation clusters seen in the selected set of matches.

Since our comparison has shown more consensus in position labels than formations, we suggest carefully considering match segments and choosing the position-level approach. For data representation, a graph choice seems reasonable because it can achieve the objectives of the normalization step without facing its drawbacks. When deciding between templates or clustering, it is important to consider the drawbacks of each.

The limitations identified in each step were documented in their respective sections and Table 3 highlights the major ones. Future research can address these limitations and then provide the most value by reporting identified formations and player tactical positions over match time, incorporating contextual factors such as phases of play, substitutions, red cards, scoreline, halftime, and stoppage breaks to reveal formation and position dynamics. Finally, large-scale studies could identify patterns across leagues, seasons, coaches, and teams, as well as how formations counter each other, considering relevant success factors. These advancements will also significantly influence sports science studies that focus on physical load monitoring.