Official WTA finals app likely to open up a can of worms

Today the Women’s Tennis Association (WTA) and SAP announced the launch of the official WTA Finals mobile app just in time for the BNP Paribas WTA Finals in Singapore – press release.

WTA Official AppThe app has been in progress for much of 2015 so I was happy to finally see SAP and WTA deliver on their promise of “taking the fan experience to the next level.”

The app has all the usual features of a tennis app; live scores, news and videos, schedules, draws etc. But what makes this app “groundbreaking” is a feature called Virtual Replay where users can watch an animated point-by-point replay of the match unfolding right before their very eyes. It’s kind of cool to watch the ball trajectory animate over the net between the players (for what it’s worth). Unfortunately it’s not clear which player is playing at which end as the animation runs through. You will need to read the commentary of the point from below the animation to figure that out.

WTA Virtual Replay

The default view of the animation is a normal camera view (from one end of the court) but users have the ability to change the view to 3 other camera angles which is a nice touch.

IMG_0184

Users can then choose which point they want to watch from the point-by-point breakdown, which is a neatly organized commentary of each point from the match showing the point score, and key actions made by each player.

The app also includes additional visualisations like Serve Direction (below).

IMG_0180

Return Strike Points

WTA App

Shot Placement

WTA Shot Placement

Rally Hit Point

WTA App

All of the visualizations allow you to switch between players, and you can change the Set you want to view at any time. It all makes for a very impressive mobile application, and is certainly light years ahead of any other tennis app I have seen. It is also no mean feat to package all of this content up in a very usable, and engaging mobile app that fans are sure to love and embrace.

So how useful is all of this? Well, to be honest we’ve kind of seen it all before. Hawk-Eye through their various relationships with TV Broadcasters like ESPN and the BBC have been publishing these types of visualizations for a number of years. Admittedly we have not had access to this level of information post match and in the palm of our hand before, so this is new ground definitely. But we are not really seeing anything new here.

The visualizations in the app unfortunately lack some valuable context in order to make them really useful for players, coaches and the fans. For example they are simply static representations of the data. You can’t query them (by touch), or filter them, or overlay one player’s points on another in order to perform any additional analysis. There is no significance attached to the data, like winners, unforced errors, big point plays etc. There is no way of knowing whether the patterns we see are expected, or a cause for alarm given the sate of the match, or past performances against this player. Perhaps we’ll see this kind of contextual information added in future releases. SAP and the WTA claim they have worked closely with the players to develop the app to their needs. However my feeling is most astute coaches and players will see these visualizations as nothing more than eye candy (for now).

As a tennis fan, and analyst of the game, the application naturally left me wanting more, and I suspect coaches and players will feel the same. What the WTA has effectively done is open up a big can of worms. The visualizations in the app leave so many questions unanswered, which is not untypical of a all-in-one app like this. But it does provide a wonderful insight into the potential of these kinds of visualizations. In order for players to really benefit from the true potential of this rich dataset from Hawk-Eye they are likely to still undertake independent analysis which dives much deeper in geographic patterns and tendencies than what we see here.

Hats off to the WTA for leading the way with this new-age tennis app. It has raised the bar and expectation going forward, and it definitely takes the mobile fan experience to a new level. I look forward to hearing what the players and coaches really think. My understanding is they will be given a more comprehensive app for on-court coaching, which may pack a few more tricks than what we see here. That may or may not be a good thing given visualisations like these tend to take time to digest, assess, and decide what action to take. This will be a new challenge for coaches, particularly in the heat of the battle. My sense is this kind of information will be primarily used post-match when emotions and the tension from a match have passed. It will also be interesting to see how the ATP respond over the coming months/years. Perhaps they too will partner with SAP to deliver a similar app for the mens tour if this takes off.

The WTA application was tested on an iPhone 6.

ATP World Tour Interactive Map – 2014

With the 2014 ATP World Tour underway in Brisbane, Doha and Chennai this week, I thought I would put together a quick interactive map that locates this year’s 61 tournaments around the world. The ATP World Tour map allows fans to follow the world’s greatest players around the world as they battle it out in 2014.

ATP World Tour Map 2014

The ATP World Tour Map – 2014. Click here to access the map.

The map shows the location of the four Grand Slam tournaments, the nine Masters 1000′s, the eleven 500 and the forty 250 series tournaments, as well as the season ending World Tour Finals played in London.

Use the map to check out the site of the newest tournament on the tour this year, The Rio 500 in Brazil. Remind yourself of where the clay tournament in Umag (Croatia) is played. A tournament that returns to the circuit this year after a one year absence. Check out the latest stop in China in 2014 at the Shenzhen Open, a city that is already familiar with the women on the WTA tour.

Explore each tournament in more detail by clicking on each of the icons to reveal further information about the tournament like the prize money on offer, who is the defending champion, what the tournament surface is and other important information.

ATP World Tour Map WimbledonInteract with each tournament to reveal important statistics about each event.

The map features some of the highest resolution available satellite imagery of the globe, meaning you can see the tournaments up close like never before. Click on the “Zoom To” link in the pop-up to quickly navigate to each tournament. You will find yourself being blown away by some of the global landscapes that sit at the doorstep of some of the lesser known tournaments, like the Credit Agricole Suisse Open.

Gstaad TournamentThe 250 series Credit Agricole Suisse Open, set against the backdrop of the beautiful Swiss Alps.

Valencia Open

Discover the Valencia Open 500 (Spain) played at the stunning Ciutat de les Arts i les Ciències where Mikhail Youzhny triumphed in 2013.

In each of the pop-up’s there is a link to the official tournament website where you can see who’s down to play in 2014, and where you can get tickets. I hope you have fun exploring the map throughout the year, and I hope it inspires you to plot your next tennis adventure!

Read the ATP press release about the 2014 tour here.

To view the full 2014 ATP World Tour calendar in PDF format, click here.

Where are you most likely to win a point on Nadal’s serve?

A couple of weeks back I released an interactive Game Tree of Nadal’s stellar 2013 season. The Game Tree was an experimental infographic that mapped Nadal’s service dominance, and showed us his most common path to victory.

Nadal Game Tree

Nadal’s Game Tree captured the imagination of many for its originality and groundbreaking way of visualizing tennis games. 

The flow lines through the original game tree (above) allow us to see some interesting patterns emerging from his 666 service games.

Using the data from the flow lines, I developed the Proportional Symbol Game Tree (see below). It maps the chances an opponent has of winning a point on Nadal’s serve.

Nadal Proportional Symbol mapA Proportional Symbol Game Tree. Mapping the chances an opponent has of winning a point on Nadal’s serve. <click to enlarge>

Below I’ll talk you through a few interesting observations I’ve made about the Proportional Symbol Game Tree. If you see other patterns, and would like to share them drop a comment at the bottom of the page!

The Bad News (for Nadal’s opponents).

The bad news for Nadal’s opponents is that your best chance at winning a point on his serve is at best, only half a chance! 15-15, 0-30, 30-15 and 30-0 are where your best chances are of taking a point from Nadal on his serve. But even at these points, the data tells us that Nadal’s opponents are on average likely to win only 1 in every 2 (0.5) points. Of these points, 30-15 is your absolute best chance of winning a point, representing a 1 in 1.8 chance (0.56), which is hardly encouraging!

The story only get’s worse…

You might as well head to the chair when you get Nadal to Deuce. You have virtually no chance of winning the game from Deuce onwards (see the smallest circle on the proportional symbol diagram above). Nadal dominates his opponents at Deuce more than any other point. He teases his opponents by going back-and-forth between 40-Ad and Ad-40, but according to his 666 service games, he only gives his opponents 1 in 5 chance (0.2) of winning the game from Deuce onwards. OK, so heading for the chair at Deuce might be slightly over doing it, but you had better step up your game big time at Deuce otherwise Nadal will be notching up another game on serve!

If you’re lucky enough to score the first point on Nadal’s serve then history shows that he pulls out all punches to prevent the score line from going to 0-30. The 0-15 point is a clear turning point in the game tree. However if you can get to 0-30 on Nadal’s serve then you are back in with half a chance to take him to 0-40!

The far right bottom three points (40-30, 40-15 and 40-0) indicate that once Nadal get’s a sniff of the finish line, he makes sure he closes it out.  From this position his opponent only ever has on average 1 in 3.3 (0.3) chance of pegging him back to Deuce.

Interestingly at the most important points in each game (15-30, 30-30, 15-40, 30-40 and Deuce) Nadal gives you a very small window of opportunity compared to other points in the game tree. At Deuce we know he dominates, but he’s not putting the hammer down quite as much as expected at these big points.

Summary

Nadal’s 2013 season was historic – no doubt. He rarely lost any games on serve. In fact he won 88% of his 666 service games that we studied.  Apart from the Deuce point there is little variation between the chances his opponents have of winning a point on his serve (0.35 to 0.55). His brutal consistency is clearly evident in these figures, and in the above graphic. The variable scaling of the circles in the Proportional Symbol Game Tree allows us to easily identify opponents areas of opportunity (even if they are only half chances)!

So it’s now off to the video tape and other supplemental tennis stats to see what Nadal is consistently doing at Deuce that makes him so dominant!

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Source: Nadal’s Game Tree. The Game Tree app is coded so we can plug it into any ATP, WTA or Challenger event. Let us know who you’d like to see mapped next!

Original data source: William Hill

References: 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.

Pinpointing the serve. Who’s better? The Big Boys or the School Boys?

(Part 1 of 3)

We have all been there, standing on the baseline when the coach places three cones in each service box and says “There’s your target, if you hit the cones you’ll get a free can of drink”.  If you were like me, you rarely hit the cone, and if you did, it was more luck than anything else!

Coaches have been using these types of serving drills for many years. Why? Well, in order to develop a successful serve, you need to practice the placement of your serve. In the USTA book titled Tennis Tactics, Winning Patterns of Play, drill 4.2 (p 45) outlines four target zones in each service court to aim for (see Figure 1).  It is in these zones where coaches place their cones to improve the serve placement of their players (and give away free drinks!).

USTA Target Serve Zones

Figure 1. The four recommended serve target zones in each service court as recommended by the USTA. Down the T (T1), a body serve (T2), a wide serve (T3) and short-ish out-wide serve (T4). Source: Tennis Tactics, Winning Patterns of Play, USTA.

Given the continuous emphasis on serve placement I set out to run a simple analysis to see who was the more ‘accurate’ server, the Big Boys (professional players) or the School Boys (college level players)? Included in this analysis are Roger Federer and Andy Murray representing the Big Boys, and the School Boys (whom shall remain nameless) are from the NCAA Division 1 tennis competition.

Some Context:

  • Murray defeated Federer: 6-2, 6-1, 6-4
  • School Boy A defeated School Boy B: 6-1, 6-1

Total number of serves hit by each player:

School Boy A: 58   School Boy B: 54   Federer: 95   Murray: 111

Total number of serves hit IN:

School Boy A: 44 (76%)   School Boy B: 45 (83%)   Federer: 78 (82%)   Murray: 86 (77%)

Total number of serves hit OUT:

School Boy A: 14 (24%)   School Boy B: 9 (17%)   Federer: 17 (18%)   Murray: 25 (23%)

In order to determine which player landed the highest percentage of balls in the four USTA zones (and therefore could claim they were the most accurate server!) I ran a simple select by location algorithm between each serve bounce and the four target zones in each service court. This enabled me to very simply return a count of how many balls landed in each box, for each player. Figure 2 shows the results of the selection.

PinpointingYourServeFig1

Figure 2. The percentage of serves that landed in the USTA defined target zones for each player.

Surprised? Most of us would expect the Big Boys to place a higher percentage of their serves in the target zones than the School Boys right? However the results showed that School Boy A landed 15 out his 58 (26%) serves into the target zones, making him arguably the most ‘accurate’ server of the four players. School Boy B closely followed with 12 out 58 (22%). Murray was next up, landing 23 of 111 (21%) serves into the boxes, while Federer brought up the rear with only 16 out of his 95 (17%) serves landing in the boxes.

Accuracy: If we loosely define accuracy as being how close a measured value is to an actual value, where the actual value are the USTA target zones, then we can with some caution claim the School Boys out served the Big Boys in the accuracy department. Hard to believe I know.

But wait a minute, what if the Big Boys weren’t actually aiming for the USTA target zones, and instead were aiming outside of those zones? Perhaps they were aiming for the lines, which are outside the USTA defined target areas but still legally within the service court? What would the results look like if we extended the target zones further towards the lines? Let’s see…

Playing the Lines

You could argue that the service line is the optimum position for the placement of your serve, and that the corners of each service box are the ultimate targets. However targeting the lines brings a higher degree of risk, and a lower margin or error. Which is why coaches & the USTA don’t recommend us amateurs to go-for these targets every time! However at the top level where the Big Boys play, where there is so much on the line and so little margin for error (in all facets of the game) they are more likely to take the risk. By sending their serves as close to the lines as possible they give themselves a greater chance of setting up the point in their favor. We would also expect that they are more likely to consistently execute a higher level of accuracy, given their higher-level skill set. We shall see…

In order to test this I added two more 12.5cm (4.7 inch) wide target zones around the original USTA target zones. I call these Medium and High risk zones, where the High risk zone abuts and includes the service lines. By running the selection again using these two extra zones we will see who is taking the risk and pushing their serve towards the lines more, the School Boys or the Big Boys?

PinpointingYourServeFig2

Figure 3. The percentage of serves that landed in the two additional High and Medium risk serve zones for each player. The width of each additional zone is 12.5cm (4.7 inches) (roughly twice the width of a tennis ball). In the second part of this blog we will see the spatial spread of serves across all target zones and all services boxes.

Figure 3 starts to tell a different story. By moving the target Federer was now clearly winning the most accurate server competition, landing 13 (14%) serves in the medium risk zone, and 18 (19%) in the high-risk zone. Murray’s success in these zones was a littler lower than Federer, with 10 (9%) for the medium risk zone, and 13 (12%) in the high-risk zone. School Boy A scored, 3 (4%) in the medium risk zone, and 5 (13%) in the high risk zone, while School Boy B scored, 2 (5%) and 7 (8%).

Clearly Federer was able to consistently pop more serves in the high-risk zones than any of the other three players. This would suggest that the Fed is arguably the most accurate server of the bunch? Most commentators of the game are unlikely to argue with that statement, but of course it depends on where the target is and where the players are aiming! School Boy A has every right to claim he is the most accurate server given he landed the highest proportion of his serves in the USTA target zones.

Some Further Ponderings

Given that each of the four USTA target zones in each service box are roughly 0.75m (2.46 ft) square I am surprised that the Big Boys are not landing a higher percentage of serves in these areas. No disrespect to the School Boys, they aren’t playing NCAA Level 1 tennis for no reason, but I expected the professional players to have a higher percentage of serves land in the target zones than the School Boys. I also expected Federer and Murray to land more serves in the higher risk zones. The results showed this was partly the case. Murray’s numbers in these zones are a little surprising given he swept aside Federer in straight sets on that day.

Perhaps at the highest level, simply aiming your serve at the USTA zones is not enough. Maybe the margin is too great. And in doing so you make life a little too easy for the returner?

So why do the School Boys have such a high percentage of serves in the USTA zones (compared to the Big Boys)? Is it because they serve with less speed and spin, therefore allowing them to slow things down and hit the ‘safe’ targets? Perhaps at this level, the players are taught to play the percentages? Perhaps their skill level forces them to do so?

The School Boys will no doubt develop their serving skills, and pop more serve speed and aggressive ‘kick’ on the ball as they mature. Being able to maintain that accuracy as they increase their serve speed and spin will be on ongoing player development challenge.

It is worth noting that each School Boy in the study served just over 50 times in their match, less than half that of Federer and Murray. Would they be able to maintain their high serve percentage into the USTA zones over a longer match where they may be required to serve 100+ serves? Would we see the same consistency, or could we expect it to see it drop off?

So what do these figures mean, if anything? What if I miss the USTA zones by a ball width or two? Am I still an accurate server? What if I’m only a little bit too short, or a little bit too central to the service box on my serve? Will I still win the same number of points if I’m a few centimeters or inches wide of the mark?

In part 2…

In the second part of this three-part blog I will endeavor to determine if there is a positive relationship between serve position, and outright success. I’ll explore if it’s possible to determine if the game of serving is really about a few centimeters or inches here and there? And in part 3 we will answer the most important question of all, who takes home the most free drinks!

Note: This study only looked at a very small sample of data from all players, so we need to be careful about making gross assumption based on the findings.

Around the world in 80 days, talking maps and tennis!

For those of you who follow my twitter feed you will have noticed that I’ve been traveling quite a bit lately. It’s been a busy Summer to say the least. So what’s been going on at GameSetMap? Plenty in fact…

During August I took a trip back to Australia and presented to a group of students from the School of Mathematical and Geospatial Science at my former university, RMIT. It’s always great to re-visit the place where so many seeds were planted for my career that lay ahead. And of course it’s rewarding to share your work with the students to give them a taste of what’s possible with their geo-spatial knowledge. Thanks to Gita and Lucas for having me!

RMIT University

Back where it all started at RMIT University, Melbourne.

After Australia I set off for Dresden, Germany where I presented my tennis work at the 26th International Cartographic Conference (ICC).  The conference is the premier bi-annual global cartographic/geospatial meet-up in the world, attracting over 1300 delegates. I presented my work under the stream of 4D Cartography. As we know, much of sports analytics is preformed across 4 dimensions, space (x,y,z) and time, so this was a perfect slot for my spatio-temporal tennis analysis. It was great to see a packed house in for my talk, it certainly raised a few eyebrows!

Google Glass and Tennis

Talking about wearable technology and Google Glass for tennis at ICC in Dresden.

After Germany I was invited to talk at the IE Sports Analytics Innovation Summit in Boston, MA. There were some big names on the program from Manchester United, New York Knicks, NFL, Nike and Adidas so it was humbling to share the same space with some of the big guns of the sports world. Much of the talk from the conference was about data, in particular geo-sports data, what to do with it, how to make sense of it etc. This area is about to blow up big time!

The slides from the conference can be viewed below:



Over the journey I met so many great people, and collected many new ideas! My mind is buzzing with endless possibilities. In the next few months you’ll start to see the results of these ideas come to fruition on GameSetMap.com. Stay tuned…

Mapping Roger Federer’s backhand

With the 2013 Wimbledon Championships just around the corner, I thought I’d take this opportunity to explore how Andy Murray exposed Roger Federer’s backhand in last year’s Olympic final on centre court at SW19.

Analysts claim that if Federer has one weakness it’s his backhand. But what is the most effective way to draw an error on the Federer backhand? Some say it is to force Federer to hit his one handed backhand above shoulder height. Whilst this may be true, as we have seen against Rafael Nadal many times there may be other ways to beat the Federer backhand.

Data from the Gold Medal Olympic match shows there is potential to draw a high error rate on Federer’s backhand by moving him backward into the shot.

Mapping Federer's BackhandMapping Federer’s backhands. The green swooshes indicate Federer’s movement to a backhand error or success. (Click image to enlarge).

Backward Movement to the Shot

We know that the direction and length a player must cover from their previous shot has a significant influence on the player’s next shot. In order to better understand the Federer backhand I plotted a vector of his movement to each shot (from his previous shot location). The map above shows his movement to a backhand error or outright success from his backhand. We can see from the map that 12 of Federer’s 14 backhand errors (86%) came from a backward movement to the shot. Some of the movement vectors are clearly more ‘backward’ in direction than others, but in any case there is a pattern here that may warrant further investigation. The length of movement to each error on his backhand varies from half a court to only a few steps.

Time: Success at important points wins you matches!

With a little more digging we can see further patterns emerging in the data. The map shows us that 52% of Federer’s backhand errors occurred on game point for or against him, compared to 22% on his forehand. To see this pattern a little clearer I labeled each of his errors with a time stamp, indicating when each of his errors (and winners) was made.

Federer Map Important PointsAdding a time stamp annotation to the map (like Ad-40, 15-40) allows us to understand the temporal component of Federer’s shot making tendencies.

The data from the match suggests that Federer is more likely to make an error at an important point on his backhand than his forehand. Perhaps his opponents at Wimbledon this year might want to take note of this!

Visual Exploration of Spatial Data

GameSetMap is always searching for new ways to visually explore the spatial component of tennis and I hope you agree that this infographic of Federer’s backhand begins to the lay the foundations of a potentially interesting story, a story that perhaps tells us a little more about how to draw an error on Federer’s backhand, and when to attack his backhand.

Examples like this are just the tip of the iceberg. We have much work to do in sports analytics for tennis, but hopefully this example and others like it ignite further work and discussions about what’s possible with spatial tennis data!

Notes: As discussed in my earlier research there are other spatial components that could be integrated into the map that could potentially help improve the analysis and strengthen the argument. Clearly the speed and spin on the ball are other important variables that if available would further enhance the story.

“OK Glass, show me Tennis Analytics”. How Google Glass will revolutionize the way we see tennis.

Early in 2012, the tech world was buzzing with the news that Google was about to release a wearable augmented reality device. Enter Google Glass.  Google Glass puts augmented reality right in front of your eyes, literally!

Sergey-Brin-Wearing-Google-GlassSergey Brin, co-founder of Google models Google Glass earlier this year.

There has been plenty of hype surrounding the product since it’s preview early last year, and we have seen examples how Google Glass can be used to take a picture, record a video, or get directions.

But what else might one do with Google Glass?

To activate Google Glass, you start by saying “OK Glass”. Then you ask Google Glass to show, do, or tell you something. So let’s give it a try:

Lets start with a simple question. “OK Glass, show me the weather forecast at the Australian Open today”

Google Glass Australian Open

Imagine sitting courtside at the Australian Open and wondering what the weather is going to be like for the afternoons play. Up pops the current weather conditions. It’s as simple as that.

Google Glass has the ability to overlay all kinds of information in your field of view. So let’s try this:

“OK Glass, show me Federer’s second shot placement”

Google Glass Federer

Imagine sitting courtside at the Cincinnati Open and wondering where Federer had previously played his second shot after Novak’s return of serve. Bam, up pops the trajectory lines of Federer’s second shot to show you where he’s likely to hit his next shot. Excited yet? Let’s try one more example.

“OK Glass, show me a stroke pattern heat map”

French Open Heat Map

Imagine sitting in the stands at court Philippe Chatrier and wondering where this player is going to hit his forehand? Google Glass immediately overlays the stroke pattern right onto the court so you can see where his shots have been passing on the court. Wow!

These images are a few quick examples that I put together to show you the potential of Google Glass in tennis. Google Glass will enhance our viewing experience of tennis (and all sports) by 10 fold! Sitting court side, we will be able to control when we see the stats, what stats we see and for how long. Whether it is seeing a live heat map, or 3D ball trajectory the potential is endless.

Of course, if tennis analytics isn’t your thing you may find Google Glass useful to find a friend in the crowd, or to video a point and share it on Facebook. You might even ask Google Glass for directions to Arthur Ashe Stadium!

The real time visualization of sports statistics and Google Glass are a match made in heaven. Let’s hope the ATP, WTA, and ITF fast track the delivery of real time tennis analytics to everyone so when Google Glass goes live, the game and our eyes will be ready!

To find out more about Google Glass visit their homepage.

Image Credits:

Sergy Brin wearing Google Glass: Copyright CBS Interactive

Australian Open: http://madamebonbon.com.au/blog/archives/7968

Roland Garros pic: http://lewebpedagogique.com/alaricenglishspeakers/the-tennis-and-roland-garros/

Cincy Tennis: https://shop.cincytennis.com/SeatViewer.aspx

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.

Results

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).

Conclusion

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.

References

[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, http://www.mathaware.org/mam/2010/essays/

[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.