Using spatial analytics to study spatio-temporal patterns in tennis

Late last year I introduced ArcGIS users to sports analytics, an emerging and exciting field within the GIS industry. Using ArcGIS for sports analytics can be read here. Recently I expanded the work by using a number of spatial analysis tools in ArcGIS to study the spatial variation of serve patterns from the London Olympics Gold Medal match played between Roger Federer and Andy Murray. In this blog I present results that suggest there is potential to better understand players serve tendencies using spatio-temporal analysis.

The full research paper, and an in depth discussion about the importance of understanding space-time relationships in sport can be read here.

Figure 1: Igniting further exploration using visual analytics. Created in ArcScene, this 3D visualization depicts the effectiveness of Murray’s return in each rally and what effect it had on Federer’s second shot after his serve. (click to enlarge)

The Most Important Shot in Tennis?

The serve is arguably the most important shot in tennis. The location and predictability of a players serve has a big influence on their overall winning serve percentage. A player is who is unpredictable with their serve, and can consistently place their serve wide into the service box, at the body or down the T is more likely to either win a point outright, or at least weaken their opponent’s return [1].

The results of tennis matches are often determined by a small number of important points during the game. It is common to see a player win a match who has won the same number of points as his opponent. The scoring system in tennis also makes it possible for a player to win fewer points than his opponent yet win the match [2]. Winning these big points is critical to a player’s success. For the player serving, their aim is to produce an ace or, force their opponent into an outright error, as this could make the difference between winning and losing. It is of particular interest to coaches and players to know the success of players serve at these big points.

Geospatial Analysis

In order to demonstrate the effectiveness of geo-visualizing spatio-temporal data using GIS we conducted a case study to determine the following: Which player served with more spatio-temporal variation at important points during the match?

To find out where each player served during the match we plotted the x,y coordinate of the serve bounce. A total of 86 points were mapped for Murray, and 78 for Federer. Only serves that landed in were included in the analysis.  Visually we could see clusters formed by wide serves, serves into the body and serves hit down the T. The K Means algorithm [3] in the Grouping Analysis tool in ArcGIS (Figure 2) enabled us to statically replicate the characteristics of the visual clusters. It enabled us to tag each point as either a wide serve, serve into the body or serve down the T. The organisation of the serves into each group was based on the direction of serve. Using the serve direction allowed us to know which service box the points belong to. Direction gave us an advantage over proximity as this would have grouped points in neighbouring service boxes.

Figure 2. The K Means algorithm in the Grouping Analysis tool in ArcGIS groups features based on attributes and optional spatial temporal constraints. 

To determine who changed the location of their serve the most we arranged the serve bounces into a temporal sequence by ranking the data according to the side of the net (left or right), by court location (deuce or ad court), game number and point number. The sequence of bounces then allowed us to create Euclidean lines (Figure 3) between p1 (x1,y1) and p2 (x2,y2), p2 (x2,y2) and p3 (x3,y3), p3 (x3,y3) and p(x4,y4) etc in each court location. It is possible to determine, with greater spatial variation, who was the more predictable server using the mean Euclidean distance between each serve location. For example, a player who served to the same part of the court each time would exhibit a smaller mean Euclidean distance than a player who frequently changed the position of their serve. The mean Euclidean distance was calculated by summing all of the distances linking the sequence of serves in each service box divided by the total number of distances.

Figure 3. Calculating the Euclidean distance (shortest path) between two sequential serve locations to identify spatial variation within a player’s serve pattern.

To identify where a player served at key points in the match we assigned an importance value to each point based on the work by Morris [4]. The table in Figure 4 shows the importance of points to winning a game, when a server has 0.62 probability of winning a point on serve. This shows the two most important points in tennis are 30-40 and 40-Ad, highlighted in dark red. To simplify the rankings we grouped the data into three classes, as shown in Figure 4.

Figure 4. The importance of points in a tennis match as defined by Morris. The data for the match was classified into 3 categories as indicated by the sequential colour scheme in the table (dark red, medium red and light red).

In order see a relationship between outright success on a serve at the important points we mapped the distribution of successful serves and overlaid the results onto a layer containing the important points. If the player returning the serve made an error directly on their return, then this was deemed to be an outright success for the player. An ace was also deemed to be an outright success for the server.


Federer’s spatial serve cluster in the ad court on the left side of the net was the most spread of all his clusters. However, he served out wide with great accuracy into the deuce court on the left side of the net by hugging the line 9 times out 10 (Figure 5). Murray’s clusters appeared to be grouped overall more tightly in each of the service boxes. He showed a clear bias by serving down the T in the deuce court on the right side of the net. Visually there appeared to be no other significant differences between each player’s patterns of serve.

Figure 5. Mapping the spatial serve clusters using the K Means Algorithm. Serves are grouped according to the direction they were hit. The direction of each serve is indicated by the thin green trajectory lines.  The direction of serve was used to statistically group similar serve locations.  (click to enlarge)

By mapping the location of the players serve bounces and grouping them into spatial serve clusters we were able to quickly identify where in the service box each player was hitting their serves. The spatial serve clusters, wide, body or T were symbolized using a unique color, making it easier for the user to identify each group on the map. To give the location of each serve some context we added the trajectory (direction) lines for each serve. These lines helped link where the serve was hit from to where the serve landed. They help enhance the visual structure of each cluster and improve the visual summary of the serve patterns.

The Euclidean distance calculations showed Federer’s mean distance between sequential serve bounces was 1.72 m (5.64 ft), whereas Murray’s mean Euclidean distance was 1.45 m (4.76 ft). These results suggest that Federer’s serve had greater spatial variation than Murray’s. Visually, we could detect that the network of Federer’s Euclidean lines showed a greater spread than Murray’s in each service box. Murray served with more variation than Federer in only one service box, the ad service box on the right side of the net.

Figure 6. A comparison of spatial serve variation between each player. Federer’s mean Euclidean distance was 1.72m (5.64 ft) -  Murrray’s was 1.45m (4.76 ft). The results suggest that Federer’s serve had greater spatial variation than Murray’sThe lines of connectivity represent the Euclidean distance (shortest path) between each sequential service bounce in each service box.  (click to enlarge)

The directional arrows in Figure 6 allow us to visually follow the temporal sequence of serves from each player in any given service box. We have maintained the colors for each spatial serve cluster (wide, body, T) so you can see when a player served from one group into another.

At the most important points in each game (30-40 and 40-Ad), Murray served out wide targeting Federer’s backhand 7 times out of 8 (88%). He had success doing this 38% of the time, drawing 3 outright errors from Federer. Federer mixed up the location of his 4 serves at the big points across all of the spatial serve clusters, 2 wide, 1 body and 1 T. He had success 25% of the time drawing 1 outright error from Murray.  At other less important points Murray tended to favour going down the T, while Federer continued his trend spreading his serve evenly across all spatial serve clusters (Figure 7).

The proportional symbols in Figure 7 indicate a level of importance for each serve. The larger circles represent the most important points in each game – the smallest circles the least important. The ticks represent the success of each serve. By overlaying the ticks on-top of the graduated circles we can clearly see a relationship between the success at big points on serve. The map also indicates where each player served.

Figure 7. A proportional symbol map showing the relationship of where each player served at big points during the match, and their outright success at those points.  (click to enlarge)

The results suggest that Murray served with more spatial variation across the two most important point categories, recording a mean Euclidean distance of 1.73 m (5.68 ft) to Federer’s 1.64 m (5.38 ft).


Successfully identifying patterns of behavior in sport in an on-going area of work [5] (see figure 8), be that in tennis, football or basketball. The examples in this blog show that GIS can provide an effective means to geovisualize spatio-temporal sports data, in order to reveal potential new patterns within a tennis match. By incorporating space-time into our analysis we were able to focus on relationships between events in the match, not the individual events themselves. The results of our analysis were presented using maps. These visualizations function as a convenient and comprehensive way to display the results, as well as acting as an inventory for the spatio-temporal component of the match [6].

Figure 8. The heatmap above shows Federer’s frequency of shots passing through a given point on the court. The map displays stroke paths from both ends of the court, including serves. The heat map can be used to study potential anomalies in the data that may result in further analysis.  (click to enlarge)

Expanding the scope of geospatial research in tennis, and other sports relies on open access to reliable spatial data.  At present, such data is not publically available from the governing bodies of tennis. An integrated approach with these organizations, players, coaches, and sports scientists would allow for further validation and development of geospatial analytics for tennis. The aim of this research is to evoke a new wave of geospatial analytics in the game of tennis and across other sports. Furthermore, to encourage statistics published on tennis to become more time and space aware to better improve the understanding of the game, for everyone.


[1] United States Tennis Association, “Tennis tactics, winning patterns of play”, Human Kinetics, 1st Edition, 1996.

[2] G. E. Parker, “Percentage Play in Tennis”, In Mathematics and Sports Theme Articles,

[3] J. A. Hartigan and M. A. Wong, “Algorithm AS 136: A K-Means Clustering Algorithm”, Journal of the Royal Statistical Society. Series C (Applied Statistics), vol. 28, No. 1, pp. 100-108, 1979.

[4] C. Morris, “The most important points in tennis”, In Optimal Strategies in Sports, vol 5 in Studies and Management Science and Systems, , North-Holland Publishing, Amsterdam, pp. 131-140, 1977.

[5] M. Lames, “Modeling the interaction in games sports – relative phase and moving correlations”, Journal of Sports Science and Medicine, vol 5, pp. 556-560, 2006.

 [6] J. Bertin, “Semiology of Graphics: Diagrams, Networks, Maps”, Esri Press, 2nd Edition, 2010.


Using ArcGIS for sports analytics

The statistical component of sport has always provided a fascinating way to analyze performance and success. This might simply be the final score, but for some sports, such as football, baseball, cricket, golf and tennis, meaningful analysis of every facet of the game and a player or team’s actions is part of the essence of the game itself. It is as common to see statistics and graphical summaries of the action reported as it is to see the action itself and this provides a fascinating insight into strategy as well as an explanation of outcome. In this blog entry we explore the results of the London Olympics Gold Medal tennis match between Roger Federer and Andy Murray to show how you can use GIS to identify particular patterns within the match that may not have been exposed by using traditional non-geographical analysis and display techniques.

Created using ArcGIS, figure 1 shows the location of where each player played a winning shot and their movement during every point of the gold medal match.

Figure 1: An infographic showing the player movement and winning shot positions from the Olympic Gold Medal Match between Roger Federer and Andy Murray.

Whilst figure 1 certainly carries a lot of visual impact it doesn’t actually tell us a whole lot. The player movement lines overlap one another and make it hard to distinguish which line relates to which point. We cannot tell the direction of movement in many cases because there are no directional arrows. The infographic also doesn’t show where the winning stroke landed, or the direction of the shot. It also fails to show the temporal component of the match.

Figure 2: The complete data set from the Olympic Gold Medal Match. 1708 point locations were collected from the 3 set match

Capturing the data

For the study we captured the  tennis match data using ArcScene 10.1 and video footage of the match (see figure 3). We built a court at a scale of 1:1 in its correct geographic location (center court at Wimbledon) and were able to quickly capture the location of each player’s stroke and corresponding ball bounce for the match entirely from the video footage. At each location we collected a set of key attributes like who played the stroke, what type of stroke it was, the stroke number, point number, game number, set number, who was serving etc. The data captured provides a statistical summary of every shot in the match.

Figure 3: Video footage of the match in ArcScene. The red dots represent the player’s stroke position and ball bounce. The green lines represent the direction of ball travel for each shot.

By using ArcScene we were able to plot the player’s position and ball bounces to within +/-20cm using the 3D editing tools. We approximated the camera angle of the video footage and set our data view to match. This made the data capture process rapid and increased accuracy, compared to a 2D environment, because we were able to continuously match the changing camera view in the video by using the Navigate Scene control in ArcScene. This also helped us counter the scale distortion in the camera view when capturing points at the end furthest from the camera.

Once all of the point data was captured, we used the XY To Line tool to create connectivity between the points using the shot, point, game and set number attributes. The lines are instrumental in allowing us to visualize stroke patterns (as you will see later in the blog entry). We ran the same XY To Line process to create player movement lines.

Visualising the data

Statistics from the match tell us that Andy Murray made a total of 18 winners to Roger Federer’s 13. What these statistics don’t tell us is where those winners occurred, the stroke of each winner, when the winner occurred and what led to the winning shot occurring. They also fail to show us any potential stroke patterns during the match. By capturing and storing all of the match data in a file geodatabase (figure 4) we are able to take advantage of the geo-location of these winners and create some interesting visualizations to tell a far more interesting story than single snapshots allow.

Figure 4: Using a file geodatabase to store sports data in ArcGIS

One of the challenges in dealing with sports data is that there are many instances of similar events occurring at the same or similar locations over relative small periods of time. This often results in very tight clusters of points over very small areas of your court, pitch or field. If your data has an element of connectivity, you will additionally have overlapping lines along similar bearings and distances or lines that run in completely random directions, depending on the type of sport you are analyzing. This provides us with an interesting challenge of how to represent and compare this information meaningfully.

One way to make sense of so many overlapping points and lines is to use a visualization technique (often promoted by Edward Tufte) called Small Multiples (see figure 5). Small multiples use a series of common basemaps (in our case a tennis court) with different slices of data on top of each map. The maps are arranged in a logical sequence, much like animated movie frames. Small multiples are useful to disaggregate your data, reducing the visual complexity and quantity of information so that it can more easily be seen and interpreted.

Figure 5: Andy Murray’s winning three shot sequence visualized using small multiples. The green lines represent the forehand winning strokes and the blue lines, the backhand winning strokes.

Figure 5 allows us to very quickly see some important patterns from the match that were not visible using traditional tabular statistics. The most immediate pattern observed is the direction of each winning shot (half of Murray’s backhands were down-the-line winners). You can also quickly identify the position of where the player made the winning shot (half of Murray’s shots were made deep inside the court, near or around the service line) and the type of shot that was played (Murray’s number of forehands to backhands ratio was 10 to 8). Temporally, we can see that 7 of Murray’s winners were made on game point, either for or against him. Figure 6 illustrates the amount of information each small multiple illustrates and, therefore, the potential for recognition of patterns across a game or match.

Figure 6: An explanation of the variables being mapped in the small multiples matrix

Each individual image presents a second level of visual information that is likely to suit coaches, players or die-hard fans who want to know a little more about the game’s pattern of play than maybe your average tennis fan or someone scanning the morning news. We have added some important temporal labels to the images to help users identify when the winning shot occurred, we have varied the colour and lineweight of lines in each image to reflect a level of importance and distinguish between line classes.  Each stroke location is dynamically labeled from the stroke field in our file geodatabase, as is the sequence number. The player movement lines show us where the player has run from to make the winning shot. In 6 of Andy Murray’s winners, he moved a considerable distance across the court to make the winning shot. The player movement lines also allow us to see the previous one or two strokes without actually showing the stroke lines on the map.

You will notice we are only showing the two shots prior to the winning shot being made. We are mapping the ‘set-up‘ stroke (point 1), the opponents returning stroke (point 2) and the winning stroke (point 3). Showing more than two lead up strokes prior to the winning shot can cause confusion and potential distraction to the user (figure 7).

Figure 7: The image on the left displays all of the strokes (14 in total) leading up to the 4th winning shot. The image on the right displays only two shots leading up to the winning shot.

Some generalization is needed to ensure you don’t overwhelm the user with information. Finding the correct balance of generalization is one aspect of the research that we are continuing to explore. Trying to determine how many events, and what type of events led to a particular event happening is incredibly dynamic and problematic so it is vital erroneous assumptions aren’t introduced during generalization.

In order for the small multiples to work better in sequence we rotated the data frame of each image using the Data Frame tools in ArcGIS. This allowed us to map all Murray’s shots from one end and Federer’s from another which enabled clearer patterns in the match to be seen. Whilst it was suitable in this instance to shift all of a players strokes to one end for visualization, in some cases this might not be suitable if, for instance, there were particular weather conditions that made play at one end more challenging.  In this situation, being able to assess how different players react to different conditions might be an important component of the pattern of the match itself.

Having already explored Murray’s winning shot sequence, let’s take a quick look at Federer’s three stroke winning pattern in figure 8, below.

Figure 8: Roger Federer’s winning three shot sequence. The green lines represent the forehand winning stroke and the blue lines, the backhand winning stroke.

Federer made only two winners on his backhand side (indicated by the blue lines) and 10 out of his 13 winners came directly from the result of moving his opponent off the court from a wide serve, leaving an open court for Federer to hit an easy winner into. His two backhand winners were both struck with little or no room for error. These two shots could have easily missed the mark, leaving Federer only 11 winners from 3 sets of tennis, all from the forehand side. Five of Federer’s 13 winners came at either game point against or for him.

The small multiple format was perfect for this type of analysis. We were able to present a series of events over time in a logical, clear and concise manner. The two examples of gameplay explored in this blog entry show how powerful representing the results of sports data in a graphic form can be using GIS. By glancing at the images you take more away from the data than you would by simply seeing the totals of each winner in tabular form. By exploring them in detail we are able to reveal dimensions in the points, games and match that are simply impossible to gauge from other approaches. We are currently working on ways to animate particular scenes and looking into applications that serve the data up in an online environment giving users the ability to query the map for themselves and run their own analysis on the data.

Sport Analytics is a growing field, but currently a less frequented field in the world of GIS. Some of the worlds largest sporting organizations like Manchester City, Adidas, Nike and leagues like the EPL, NBA and AFL and are capturing every movement their players make and recording their actions. The challenge is to understand the best way to present this data to the players, coaches, media and fans.