Visualizing and understanding player movement in sport has enormous advantages in relation to an athlete’s match day performance, training and recovery. Automated player tracking in recent years has become a must-have tool for sport scientists, coaches, and analysts. The spread of player tracking now spans a multitude of sports from the Australian Football League (AFL) to the NBA. From the EPL to the ATP. Sport scientists and coaches are monitoring a player’s every move, both on and off the field. However, preparing easy-to-understand visualizations of space-time data, like player tracking, that support analysis and decision-making provides an ongoing challenge to data scientists and cartographers alike .
In this article I present a Diorama of Player Movement using a Space Time Cube. The Space Time Cube is a 3D visualization method introduced by Swedish geographer Torsten Hägerstrand in the 1970’s. Space Time Cube visualizations present users with the full spatio-temporal data set in a single, comprehensive view . By contrast, traditional 2D representations of spatio-temporal information require multiple maps, animations, or time sliders to display how the data changes over time.
A Space Time Cube pulls the temporal component of the data apart, stretching it along the vertical axis of the cube, which enables the users to clearly see changes in the data over time. This unique 3D visualization helps better understand the interaction of the spatial and temporal components of player tracking data. In this article I will demonstrate some of the advantages of Space Time Cubes for visualizing and understanding the DNA of player movement in sport.
Hawk-Eye Player Tracking Data
Hawk-Eye began tracking player movement in tennis in 2011. The player tracking system utilizes its core ball tracking technology (Figure 1). Recently I was granted access to official Hawk-Eye player tracking data from the Roger Federer v Paul-Henri Mathieu match at the Swiss Indoors in Basel, 2012, which Federer won 7-5, 6-4, in 1hr 26min.
The Hawk-Eye Data format
Hawk-Eye collects its player tracking data at 0.05 sec intervals. The data is collected at the point level of a match. In the Federer v Mathieu match there were 198 points played resulting in 53,440 data points for the match. Each point in the match is stored in the database as a single xml file. The variables collected by the system are x,y,z co-ordinates plus time (Figure 2). The time variable resets itself at the start of each point. The file name of each xml file represents the set, game and point number, and whether the point is a first or second serve.
Visualizing Player Movement in Tennis
Player movement in tennis is typically summarized by distance covered, direction, and speed of movement of players. For the purpose of this example, I created a player velocity map using a static 2D representation. In order to create the player velocity map I classified the data into four categories.
Figure 4 is a simple way of presenting relative speed using a green to red color scheme for each point in the dataset. However the representation makes it difficult to see how the path of the player and their velocity is changing over time. We also only see a portion of the data at any one time. In this case the most recent player movement ‘paths’ are drawn on top of the earlier ‘paths’, making it difficult to identify the distribution and frequency of player velocity.
In order to improve the representation we might consider animating the data, or, create a series of small static maps which each present a time period from the match. We may also consider introducing an interactive element to the map like a time slider. Each of these methods have the potential to enable us to see how the data is changing over time, and therefore eliminate the issue of overlapping data. Whatever approach is taken the fundamental issue of viewing the data in a two-dimensional plane remains. Animation, small multiples or time sliders all allow us ways to slice through the data and see different moments but none give us clarity when trying to look at the match as a whole.
Introducing a Diorama of Player Movement for Tennis
Perhaps a more suitable, but rarely seen method for visualizing spatio-temporal data in sport is to use a Space Time Cube. By building a Space Time Cube we are able to disaggregate the overlapping player movement lines by using the y axis of the cube to represent time. The min y value represents the start of the match and the max y value the end of the match. Along the base of the cube represents the x, y movement of the players - the planar court (Figure 5).
The Diorama of Player Movement enables us to see the spread and frequency of the four player velocity categories more clearly. By using the third-dimension we can be more confident about making judgments about movement patterns in the match because we have a full view of the dataset.
A drawback of the Space-Time cube has been the presentation of a single view as a static image (as in Figure 5). The inherent problems of trying to understand the data on a perspective view mean that in some respects it creates a mass of data points that are difficult to visually disentangle, much like a 2D static map. Therefore orientation, navigation and human interaction of the cube are central to its appeal and usability. The rapid advancement of web technology, in particular WebGL means these complex visualizations can be rendered directly in the browser to create an interactive version. This gives analysts and sport scientists an opportunity to explore the scene by panning, zooming and titling from any viewpoint and overcomes the drawbacks of a static view. Using the web as a platform means the visualizations can then be shared amongst players, and other stakeholders (Figure 6).
The 360° view of the scene means we can also quickly compare patterns between both players at any angle. For example, from behind each player we can visualize over time the extent of his or her lateral movement throughout the match (Figure 7). There are extended periods of time in the 3rd and 7th game of the 2nd set where Federer’s movement is clearly trending to the left side of center, most likely as a result of Mathieu targeting his backhand during these games. Through games 4 to 9 in the 1st set Mathieu’s movement was often short in both time and length, which perhaps implies the points in each game were short to due to successful serving, or unsuccessful return of serves.
We are also able to analyze who is attacking and playing on the baseline. We can very quickly see the player position change over time during the match (Figure 8). The Diorama of Player Movement diagram shows us that Mathieu spent more time playing inside the baseline than Federer did. Up until the 7th game, Federer was playing mostly from behind the baseline, rarely pressing forward for any extended periods of time. Neither player appear to be playing on average deeper than usual (> 3m) behind the baseline.
From the side perspective we can also see the frequency of forward movement over time by each player, whether it is in attack or defense. In the 1st set Federer moved deep inside the court only 4 times in the first 11 games, where Mathieu was much more active in this area of movement, moving forward 11 times. This trend was reversed in the second set. Federer was far more active in his forward movement (9 times) compared to Mathieu (3 times).
The Diorama of Player Movement presents a unique way of visualizing player movement in a three-dimensional space. The single, comprehensive view offered by a Space Time Cube enables us to see the spread and frequency of player movement more clearly. Using the third-dimension of the cube to disaggregate the data means we can be more confident about making judgments about movement patterns because of the full view of the dataset.
The web is providing teams, coaches, and analyst with a powerful platform to view, share and collaborate their projects. Browsers are fast becoming very capable of rendering large quantities of big data, meaning that representations of data being collected from Optical sensors and GPS, like player tracking can be viewed and interacted with on mass.
There is little value in focusing on singular variables in sport. The interaction with other variables is where the real value lies. For example, in tennis it is not about how fast you move, it is how fast you move relative to the ball . The Space Time Cube has the potential to manage and display this second tier of contextual information. Thus opening up opportunities of linking player movement to other variables like ball speed, direction and success of shot making.
Maps have been used to stimulate visual thinking about geospatial patterns, relationships and trends for centuries .Optical sensors, GPS, and other wearable technologies are collecting never seen before geo data. Different datasets force a different view, different questions force a different representation, and different audiences force a different approach. It is not uncommon to see multiple representations of the same theme in order to fully understand the pattern, relationship or trend. However the Space Time Cube is a powerful stand-alone visualization, that reigns supreme for its ability to convey complex spatio-temporal patterns.
Damien Saunder (formerly Demaj) is a Geospatial Designer at Esri where he designs and builds online interactive maps. He is continually rethinking spatial analytics for tennis via GameSetMap.com.
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Kraak, M. “The Space Time Cube Revisited from a Geovisualization Perspective,” Proc. 21st Int’l Cartographic Conf., pp. 1988-1996, 2003.