PassVizor: Toward Better Understanding of the Dynamics of Soccer Passes

In recent years, soccer analysts have proposed a series of works to investigate players’ passing. Based on the adopted theories, existing methods can be mainly divided into two categories, namely, the network-based and the sequence-based.

Network-based. The network-based methods aggregate passes to create a directed graph in which nodes represent players and edges represent the frequency of passes between players. With traditional graph analysis methods, experts can extract passing patterns from the derived passing network method [8, 24, 10]. For example, to explain why Spain won the World Cup in 2010, Peña and Touchette [24] constructed passing networks for Spain and Netherlands. The node centralities showed that the players of Spain, relative to those of the Netherlands, were equally involved in the passing network and thus presented a steady and consolidated playing style. As aggregating passes of different times may obscure important variations, the sliding window method has been applied to create temporal passing networks [9, 15, 36, 11, 14]. For example, Cotta et al. [11] computed several network measures for passing networks at different time steps to inspect the evolution. Yamamoto et al. [36] visualized the numbers of triangle structures in each 5-min timespan of a soccer match to show the dynamics. However, as a result of the aggregation process, the network-based method break a series of passes into multiple independent passes between players. This characteristic poses challenges for analysts when investigating multi-step passing patterns (e.g., wall passing). The sequence-based methods were therefore introduced to preserve these details.

Sequence-based. The sequence-based methods regard a series of consecutive passes in a soccer phase as a sequence where each element represents for an action of players (e.g., passing) [20]. With the sequence representation of passing, Gyarmati et al. [16] extracted three-step passing patterns of different teams and found that FC Barcelona tended to pass the ball back and forth, which is a playing style that differs from those used by others. Lucey et al. [22] proposed a technique called occupancy maps to characterize the passing patterns in different regions of the field. By comparing the frequent sequence patterns that lead to goals, Bekkers and Dabadghao [4] provided a list of case studies, such as the effect of trading players and the replacement of coaches. On the basis of the ball-movement data, several works [12] further detected frequent trajectory patterns of passing by using techniques such as dynamic time warping. These methods have been widely used to extract typical passing patterns to characterize players’ passing behaviors. However, this type of analysis largely discards the temporal dynamics of passing (e.g., when a team changes their passing behaviors) as well as other important context information (e.g., defense of the opponent). Therefore, we develop PassVizor to help experts discover and understand such dynamics of passing behaviors.

Researchers have proposed a set of visualization techniques and tools to analyze different sports data, such as the basketball [6, 5, 21], the baseball[23], and racquet sports [34, 33, 37, 32]. Specifically, a number of approaches have been introduced to present and analyze soccer data from different aspects. For situation awareness, Legg et al. [19] created glyphs of different sports events and visualized ongoing matches in real-time. Soccer Scoop [26, 27] developed a visualization tool for comparing performances of players. Sacha et al. [28] provided a visual abstraction method to address the issue of visual clutter in visualizing the massive trajectories of players, which eased the detection of movement patterns. Andrienko et al. [3] concentrated on evaluating the defense of players, contributed an approach to compute the pressure exerted by defenders, and applied heat map-based visualizations to present the values. In order to strengthen the traditional video analysis, Stein et al. [30] designed an automatic method that can embed the visualizations of players’ regions and movements into videos. In addition to advanced techniques, several visual analytics systems have been proposed for in-depth analysis. SoccerStories [25] divided a match into different phases based on players’ actions and designed an interface to support the navigation of phases. Tailored facet views were provided to investigate the details of different actions (e.g., shooting and passing). Janetzko et al.[17, 29] visualized a time series of multiple soccer features that capture the complex soccer context, which facilitated the player-centric performance analysis. Wu et al. [35] contributed a Spatio-temporal design to visualize formation changes in a match and developed a system called ForVizor to support comprehensive analysis.

Despite the diverse focuses of soccer visualizations, players’ passing behaviors were presented in most previous works as a necessary part of soccer analysis. For example, SoccerStories [25] proposed multiple designs, e.g., adjacency matrix, node-link diagram, and hive plot, to visualize the passing behavior in a soccer phase. Multiple soccer phases that involve shooting events were juxtaposed for the investigation of a whole match. However, according to experts, visualizing these phases is not sufficient as most phases are disrupted by the defense and only a few phases end with shootings. These disrupted phases also involve valuable information on players’ passing behaviors and need to be analyzed concurrently. These drawbacks pose challenges to existing visualizations because juxtaposing hundreds of phases could lead to a heavy cognitive load for users. Moreover, how to visually connect these soccer phases to show the dynamics of passing behaviors remains unsolved. Therefore, we propose PassVizor, an interactive system to support an in-depth analysis of evolving passing behaviors.

We collaborated with four soccer experts for one year to develop a visual analytics system for analyzing the dynamics of soccer passing. The four experts included one soccer coach (E1, with a coaching certificate issued by a continental football confederation), one senior sports analyst (E2), and two PhDs majoring in sports science (E3 and E4, both are former professional players of a top soccer league in a country). To understand domain problems, we collected related works and interviewed experts through weekly meetings. During the meetings, experts stated that traditional video analysis approaches are cumbersome to use when investigating passing behaviors. E1 and E2 emphasized that revealing the dynamic changes of passing behaviors can facilitate the understanding of the adjustment of a team. The outcomes can help answer questions such as, When would a team change to a defensive passing? and What kind of defensive passing would they employ? Moreover, E3 and E4 shared their experiences in the decision-making process related to passing.

Inspired by experts’ comments and feedback, we identified a set of important questions and problems. We further distilled the problems into the following requirements.

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  Match-level Summarization.

  1. M1

     How many kinds of passing patterns do a team involve? As a team could have hundreds of phases in a match, a clear overview of passing patterns can be a good starting point for experts to conduct an in-depth analysis of passing. For example, they can quickly learn which kinds of passing patterns have frequently occurred.

  2. M2

     What are the characteristics of each passing pattern? The demonstration of passing patterns’ characteristics is also required. This can help experts quickly focus on their interesting passing patterns. Specifically, revealing characteristics such as involved players, active spatial regions, and frequent passes can facilitate the understanding of the tactical intentions of passing.

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  Phase-level Analysis.

  1. P1

     How do passing behaviors evolve over phases? A team could dynamically change the passing behaviors (e.g., from defensive possession to aggressive attacking) according to the game situation and performance. Therefore, tracing the evolution of passing behaviors empowers experts to realize the decision making process of coaches and players.

  2. P2

     How do passing behaviors change according to defenses? Experts state that players’ passing behaviors are related to defenses. Generally, defenders may apply different defensive strategies (e.g., man-marking) in a match. Experts are eager to know how a team copes with different defenses through changing passing behaviors.

  3. P3

     How do passing behaviors benefit the team? Different passing behaviors could lead to different results for a team (e.g., offside, corner, and shooting). Experts want to learn the efficiency of players’ passing and figure out what kind of passing can create better opportunities.

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  Individual-level Investigation.

  1. I1

     How does a player complete a pass? Passes can have different appearances. Players can dribble the ball before passing or they can complete the pass by a one-touch play. The different processes of passing can cause different effects on the attack. Hence, inspecting such processes is essential for justifying and evaluating the passing behavior.

  2. I2

     What are the characteristics of each player? The different passing skills and personalities of players result in different types of passes. Thus, experts are eager to investigate the characteristics of each player, so as to learn players’ strengths, weakpoints, and compatibility with team strategies. This knowledge can further ease tasks such as the lineup selection and player substitutions.

We prepare our data according to the requirements. There are two types of data that we need for conducting passing analysis, namely, the position data and the event data (e.g., passes, goals, and shoots). We use a semi-automatic method to collect these data from raw videos. For the position data, the methodology of data collection is similar to ForVizor [35] and requires nearly 6 hours for collecting all the position data of a soccer game by two users. Specifically, we have an interface that allows users to inspect the object tracking result and interactively adjust the tracking result when the tracking target is missed or mistakenly labeled. For the event data, it requires nearly 90 minutes for collecting the soccer event data of a soccer game by one user. Users need to watch the video and stop when an event occurs. They further fill the information of each event with the interface. Users do not need specific expertise for collecting the data.

Researchers have proposed different methods to accomplish the detection task. In recent years, a popular method is to transform the detection of passing patterns to a task of mining frequent sequential patterns. The sequential pattern is defined as a subsequence $(a_{i_{1}},\dots,a_{i_{k}})$ where $1\leq i_{1}<i_{2}<\dots<i_{k}\leq n$. Hence, a frequent sequential pattern is a sequential pattern that commonly occurs with a frequency higher than a threshold (Fig. 1). With this definition, Gyarmati et al. [16] defined passing patterns as a sequential pattern of player roles (i.e., $a_{i}\in\{midfielder,forward,backward\}$) and tried to investigate the passing relation between different player roles. Decroos et al. [12] focused on the spatial positions of passing and defined $a_{i}$ as a tuple of events and its spatial regions. Despite the usefulness, these methods encounter problems when applied to a detailed-level analysis of passing since the personal information of players is neglected (Fig. 1). This poses difficulties for experts to communicate the finding from passing analysis with existing studies such as the profiling of players.

Therefore, we aim to provide a new passing pattern detection method that can address this limitation. We have surveyed the works of pattern mining in sequence data and find that the task of passing pattern detection is similar to the topic modeling of text sequences. Specifically, the co-occurrence of players, which is what we can observe in the passing data, is the result of coaches’ strategies (which is latent in the data). This is similar to topic modeling, which uses the observed co-occurrence of words to encode the concept of latent topics.

During the exploration of passing modeling, we presented this co-occurrence based passing pattern to our experts. Experts commented that this passing pattern definition is consistent with their experiences. Following coaches’ strategies, players usually have a tendency to pass. For example, when applying the long passing strategy, players of guards would tend to pass the ball to the center-forward directly to conduct an attack. Such attacks would cause a co-occurrence of the forwards and the guards, while the midfielders would be seldom seen in those attacks. Hence, different strategies would lead to different co-occurrence patterns and finding these patterns can lead to a deeper understanding of the strategies. Therefore, we decide to use topic modeling to detect passing patterns.

We use $p_{T}(v_{i})$ to represent the probability that the player $v_{i}$ is involved in the pattern $T$. Based on the player co-occurrence, a passing pattern is defined as a tuple of each player’s participation probability,

where $0\leq p_{T}(v_{i})\leq 1$. With this definition, the order information is ignored. Nevertheless, this can improve the robustness of passing patterns since we can hardly see a strictly consistent order of players in multiple passing sequences.

Given the pattern definition, we aim to decompose a team’s players into different groups, in which players tend to pass the ball among one another in a soccer phase. We propose a topic-based method for mining passing patterns. We refer to each player as a word, each phase as a document, and each passing pattern as the keyword set of a topic.

As shown in Fig. 3 (A), we first build a dictionary of players. For each soccer phase, we extract the players involved in each pass and transform a list of passes into a player sequence (Fig. 3 (B)). This sequence is analog to a sequence of words, and we refer to it as a document. With the player dictionary, we convert each player sequence into a one-hot vector using the bag-of-words representation (Fig. 3 (B)). Here we do not use tf-idf to adjust the weight of players since the meaning of tf-idf is quite confusing in the soccer context.

From multiple soccer phases, we can obtain a list of documents which form a special corpus of passing. We refer to this corpus as $X\in\mathbb{R}^{m\times n}$, where $n$ is the number of soccer phases and $m$ is the number of players (Fig. 3 (C)). We employ the nonnegative matrix factorization (NMF) [18] to extract the topics because it can easily support parallel accelerations. However, we do not limit the usage of other topic modeling methods. To clarify the detection process, we first provide an illustration of the traditional NMF. The detection can be modeled as:

where $W\in\mathbb{R}^{m\times k}$, $H\in\mathbb{R}^{k\times n}$, $\|\cdot\|$ is the $L^{2}$ distance, and $k$ is the number of topics. Topics are represented as the columns of $W$, which are the distribution of players (Fig. 3 (D)). To transform this distribution to a passing pattern, we can apply the method of extracting keywords (key players) from the topic. As these extracted player groups might share the same players, the overlapping problem is resolved. To determine the passing pattern of each soccer phase, we can utilize matrix $H$. Each column of $H$, $\textbf{c}_{i}$, encodes the topic distribution for the $i$-th soccer phase. We follow previous methods and assign each soccer phase to the topic with the largest proportion. With this approach, we can obtain multiple passing patterns and the pattern labels for the soccer phases.

Preprocess. We first divide the soccer phases into two categories, namely, the phase with a counter-attack and the phase with a build-up strategy. Specifically, a counter-attack represents a straightforward playing style, i.e., the attack is completed within only a few passes, whereas build-up prefers a control of the ball possession by a series of passes. Due to their different characteristics, the experts aim to separate these two kinds of phases when conducting the tactical analysis. We manually label the soccer phases by inspecting the video.

Flexible definition of words. The definition of a word is flexible. Specifically, users can also apply this topic-based method to investigate the spatial information of passing patterns. For example, we can discretize the spatial position into spatial regions and transform the passing in each phase into a sequence of regions. Referring each spatial region as a word, we can thereby detect passing patterns that characterize the relationship between different spatial regions of the passing. We decide to refer to the player identity as a word since it can provide detailed information of personal characteristics and part of the spatial information, i.e., players’ spatial movements are largely affected by their roles in formations, which can be revealed by player identities.

Substitutions. We can enlarge the player dictionary to handle the substitution. For example, a team of the Premier League could totally have 25 players. We can create a dictionary of 25 words and obtain the Bag-of-Word (BOW) representation of each passing sequence accordingly. Topics from these BOWs contain the weight of substitutes and can be used to explain substituted players’ passing patterns.

Pattern diagram. In this diagram (Fig. 4 (B)), we intend to visualize the characteristics of passing patterns (M1 and M2). The characteristics are twofold: one refers to the players involved, and the other refers to the spatial context. As shown in Fig. 4 (B), each node at the left represents a specific player and each soccer pitch encodes a passing pattern. Users can hover on a pattern and the related players are highlighted (Fig. 4 (B2), Player 11 and 7). Specifically, we connect a player with a pattern by links if the player is involved in that pattern (Fig. 4 (B2)). In particular, the pattern at the bottom (Fig. 4 (B3)) encodes the passing of counter-attack while the others encode the build-up. We decided to use a node-link diagram to encode the detected patterns since it is more intuitive compared with the matrix (i.e., a common representation for topics) when the number of topics is not very big.

We use a heatmap (Fig. 4 (B2)) to encode the spatial information of passing. The spatial information of passing can be represented by a trajectory of players’ positions. Sacha et.al. [28] regard the start and the end position as the most important information of a trajectory. We follow this simplification and collect the start and end positions of all passing trajectories for a passing pattern. We then visualize these positions on the soccer pitch with a heatmap (Fig. 4 (B2)).

We also show additional statistics of passing patterns in this diagram. The bar next to the player (Fig. 4 (B)) encodes each player’s number of passes. When hovering on a pattern, a dark bar (Fig. 4 (B)) is presented to show the number of a player’s passes in that passing pattern. This can help users confirm the importance of a player. The bar on each pattern (Fig. 4 (B2)) encodes its frequency in a match.

Pattern flow. We employ a timeline-based visualization to show the temporal distribution of passing patterns (P1-P3). Each circle (Fig. 4 (C3)) represents a phase and we place them from left to right in a chronological order. The vertical position of a circle is aligned with the corresponding passing pattern in that phase (Fig. 4 (C1)). Phases of the first half and the second half are separated (Fig. 4 (C4)). Users can hover on each circle and the corresponding passing pattern will be highlighted. This can help users identify the change of passing patterns.

To provide the context of each phase (P2), we place a bar on the top to show the defense in each phase (Fig. 4 (C2), the higher the height the worse the defense). We use the covered region of the opponents to represent the defense. A small covered region means that a team is using a good defense formation. We also place event glyphs (Fig. 4 (C5)) at the bottom to show the ending (P3). We only show the event of shooting at the beginning of the analysis to reduce the cognitive load. We use the metaphor to design the game event glyphs. For example, we design the kicking behavior to encode the shooting event and use the icon of conversion to encode the substitutions. We also borrow existing designs from common soccer icons (e.g., cards and goals).

According to the change of passing, users could be interested in certain passing patterns. For an in-depth analysis of a passing pattern, we allow users to zoom in by clicking the pattern (Fig. 4 (B2)) and a fine-grained visualization of the corresponding phases will be shown (Fig. 7). The temporal distribution of the selected pattern is preserved on the top (Fig. 7 (A)). In this visualization (Fig. 5), each column, which is composed of multiple glyphs, provides a multivariate summarization of the passing in each phase. There are a set of techniques that can visualize multivariate data, such as parallel coordinates and projections. However, the parallel coordinates can not preserve the spatial information and the result of projection is hard to interpret. Hence, we decide to use glyph techniques which have high efficiency in encoding the multivariate information [7] and good readability for users.

Summarization of a phase. According to experts’ suggestions and previous works [28], the first (the first passer) and the last point (the last receiver) are considered as the most prominent information of a phase. Therefore, we visualize the multivariate information of the two points respectively. For a phase, we provide the formation (Fig. 5 (A)), the identity (Fig. 5 (B)), and the position (Fig. 5 (C)) of the two points respectively. The end event (Fig. 5 (D)) is placed at the bottom. The density of triangles in the middle encodes the number of passes in this phase. By juxtaposing the multivariate information of multiple phases, users can obtain a deeper understanding of passing patterns.

Formation. The formation glyph (Fig. 5(A)) shows the numbers of formation lines. For example, 4-4-2 is encoded by three lines while 4-2-3-1 is encoded by four lines. The highlighted line (Fig. 5 (A)) indicates the position of the first/last in the formation. This design is derived from previous work [35] who used a Sankey to encode the formation. We drop the thickness channel of lines (which is used to encode the proportion of players in each line) for two reasons. First, considering the limited visual space, it is hard for users to perceive the thickness of lines. Second, the target of the formation glyph is to notify users which kinds of players are possessing the ball (e.g., the strikers or the midfielders). Such information is encoded by the position. For these two reasons, we propose the current design.

Spatial position. The shape of the glyph (Fig. 5 (E)) indicates the spatial region in which the pass is conducted. Specifically, we divide the soccer pitch into nine different spatial regions (Fig. 5(G)) and design glyphs to represent the regions respectively. The design of the glyph is inspired by the most prominent visual features in each spatial region. For example, we use the circular shape in the middle of the pitch to represent the midfield (Fig. 5 (E)). A mapping between the glyph and the corresponding spatial region is available in Fig. 5 (E). We have designed two design alternatives to encode the spatial regions. The first one is the most primitive idea, using nine panels to encode the spatial regions respectively (Fig. 5 (F)). For example, to represent the midfield, we highlight the panel at the center. However, given a relatively large number of glyphs, it would be difficult for users to discern them as they would look similar in small, let alone distinguish from each other. To improve the discrimination, we tried to embed the distinctive feature of each spatial region into the design of the glyphs and therefore propose the current design (Fig. 5 (E)). According to the expert comment, it is easy for them to understand the encoding of this glyph design since they are familiar with the embedded glyph shape.

Interactions. This view supports interactions as follows.

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  Ranking. Users can rank the passing patterns by clicking on the ranking button (Fig. 4 (B1)). The layout of the pattern flow will be re-organized, which can help users more easily perceive the temporal patterns. Users can select different ranking attributes, such as the number of occurrences and the number of shootings.

• •

  Hovering. Users can hover on the player node (Fig. 4 (B)) and the soccer phase that contains this player will be highlighted (in both the two levels of pattern flow). This can help users analyze the passing characteristics of a player.

• •

  Switching. We allow users to switch between the passing of the two teams in a match. Users can click on the team name (Fig. 4) to inspect the passing and the dynamic changing of the passing pattern of the two teams respectively.

This part is provided to present the soccer phase selected in the evolution view in detail. We provide three different modes to facilitate the passing analysis, namely, the static mode (Fig. 4 (D1)) to show a static summarization of all passes, the dynamic mode (Fig. 4 (D1)) to visualize the animated movements of the players during passing, and the video mode (Fig. 4 (D1)) to present the raw soccer video. The time interval of the three modes is coordinated. As shown in Fig. 4 (D1), in the static mode, we use a node-link diagram to visualize the whole process of players’ passes in a soccer phase. Players are placed according to their position when they pass or receive the ball. We use the solid line to encode a pass between the two connected players (Fig. 4 (D2)) and a dashed line to encode the movement of a player when dribbling (Fig. 4 (D2)). To reduce the visual clutter, we remove the slight movements of players. For the end event of the phase, we use an arrow to show the shooting event, a cross to show the intercepted pass. Users can also select a specific pass to see the context information at that time. When users click on Player 10, the positions of 11 opposing players (when Player 10 passes the ball) are shown. With the information, users can quickly learn how Player 10 is being defended.

For a deep analysis, users require quantitative context information to know the actual situation that faced by players during a passing. Therefore, we provide a statistical table and a set of coordinated interactions to show the necessary context. In the statistical table (Fig. 4 (D3)), we provide the following indicators to facilitate the analysis.

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  Covered area. This describes the covered area of the opposing players. We calculate this based on the polygon generated by players’ positions on the pitch. Generally, a smaller value of covered area represents a better defense.

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  Pressure value. This is to estimate the pressure imposed on the ball-possessing player. A closer defender would pose a higher pressure on the player. We calculate this value based on Andrienko et al.’s method [3].

Apart from the statistics of passing, we further provide statistics (e.g., maximum speed, dash distances, etc) of individual players (Fig. 4 (D4)). Players are placed according to the lineup of the team. Users can click on the player to show the corresponding statistics.

In this work, we focus on analyzing the dynamics of passing patterns to reveal the adjustment of passing (including self-adjustments by players and proactive adjustments by coaches). We contribute a topic-based passing modeling approach to capture the passing pattern and propose a glyph-based visualization to demonstrate the multi-variate context of passing in multiple soccer phases. With PassVizor, users are enabled to identify the valuable changes of passing that contribute to the lead and examine the detailed passing process to disclose the key pass and core players. The expert interviews demonstrate the usability of our system.

Lessons Learned. One applicable lesson is the representation of soccer phases. Initially, we represent each soccer phase as a network of players and regard the dynamics of passing patterns as a temporal passing network. We try to use a temporal network embedding method to address the problem. However, different from the continuously evolving process of general temporal networks, the change of the network of each soccer phase is discrete as one soccer phase is not built on the previous phase. The other lesson is the visualization of the spatial region in the sports domain. Although our spatial glyph is mainly designed for the soccer data, the strategy of utilizing the intrinsic signs on courts can be applied for other sports. In many kinds of sports, the court is also divided into different regions with different signs according to the disciplines. For example, in basketball, the court is divided into different areas with different shapes, such as the free-throw lane and the area beyond the three-point line. Integrating such visual features can improve the usability and the comprehensibility of visualizations (according to the expert comments), thereby facilitating the analysis.

Scalability. Although the current system is designed to analyze the passing of one match, both the passing pattern detection and the passing visualization are able to be adapted to the analysis of multiple matches. The adaptation mainly depends on two issues, i.e., the detection of multiple matches’ passing patterns and the visualization of soccer phases in multiple matches. For the passing pattern detection, multiple matches of a team share the same player dictionary. Hence, it is possible to conduct topic-based passing pattern detection on multiple matches’ passes and find a shared set of passing patterns. Moreover, topic modeling has been widely applied to process large text datasets. Hence, the model can even be used to analyze a season’s matches. If there are too many patterns, we can control the parameter of topic models to acquire a limited number of the most significant passing patterns. Moreover, since topic modeling has been widely applied to process large text datasets, it is possible to apply the topic-based passing pattern detection to one or more seasons’ matches. For the visualization of soccer phases, there will be multiple lines of pattern flows when analyzing multiple matches. Regarding passing patterns as the vertical axis and the order of soccer phases as the horizontal axis, we can transform a pattern flow to a line chart and investigate the different evolution by comparing the trend of lines. To ease the comparison, we can utilize sequence alignments to automatically find similar passing trends between multiple matches and highlight these similar time slots in the line chart. Hence, it is possible to adapt the system to multiple matches.

Reproducibility. This work is the same as many topic modeling works in terms of reproducibility. The major parameter here is the number of topics. In our cases, since the data is not very large, we tried different numbers of topics and inspected the result to choose the best parameter. Specifically, as we state in the last paragraph of Section 5, whether a soccer phase is a counter-attack or build-up is manually labeled. We then input all the phases of build-up into the topic model. Currently, as the data is not big, we can obtain the result of topic modeling in only a few seconds and it was easy for us to find that an appropriate number of topics. For a large dataset, there are several widely adopted methods for automatically choosing the parameter. For example, when using LDA, HDP (Hierarchical Dirichlet Processes) [31] can be used to determine the number of topics. There are also heuristic approaches[38] to set the parameter. Therefore, our work can be reproduced and we will use a larger dataset to illustrate the reproducibility in the future.

Limitations. The limitations are twofold. The first limitation lies in the limited consideration of the opponent team. The experts suggested that the analysis can be further improved by considering the behaviors of the opponents, which can disclose more detailed features of the passing. For this issue, we regard the passing patterns as the observed result that is influenced by different factors, such as opponents’ defense strategy and players’ personal status (e.g., fatigue). To consider these factors, we can model the relationship between players’ passes and these factors. For example, for each soccer phase, we can build the connection between the opponent’s defense strategy and the observed passing pattern. We can learn the probability of using passing pattern A when the opponent applies certain defense strategy. This can answer questions like how the player will pass the ball when the opponent adopts a deep defense. In the future, we plan to develop appropriate methods for modeling the defense and investigate how to establish the relationship between the defense and the pass. The second limitation lies in the presentation of the spatial regions of passing behaviors. Although we have designed intuitive glyphs to encode the spatial regions in soccer, the problem of demonstrating the transition of spatial regions for passing remains challenging. To create scoring chances, players would progressively move from the backward positions to the forward positions, thereby causing a smooth transition of the spatial regions. Specifically, different attacking strategies would lead to different transition patterns of the spatial regions. Thus, it is worth to reveal such transitions for further analysis of passing.