Roland Garros Men’s Final 2014 – Game Tree

Rafael Nadal continued his dominance on court Philippe Chatrier with an emphatic 3-6, 7-5, 6-2, 6-4 win over Novak Djokovic to take out the French Open for an incredible 9th time. Below are Novak and Rafa’s interactive Game Trees. You can explore the interactive game tree here.

Roland Garros Game Tree

Roland Garros Men’s Final 2014 Game Trees  (click to enlarge).

How the Game Tree Works

Each point is color-coded to reflect the momentum in each game. A match that is dominated by the server is highlighted with a thicker, outside flow through the ‘positive’ blue points of the Game Tree. More tightly contested service games result in thicker lines through the ‘neutral’ (white) and ‘negative’ (red) points of the Game Tree. You can click on each line to reveal how many times the score passed through that point in the match.

A Summary of the Roland Garros Game Tree

  • Nadal won 16 service games. He was broken 3 times.
  • Djokovic won 14 service games. He was broken 6 times.
  • Nadal won 6 service games from 40-30 (38%), and 5 from 40-0 (31%).
  • Djokovic won 9 service games from 40-15 (64%), and 2 from 40-30 (14%).
  • Djokovic lost his serve 3 times (50%) from 40-Ad. He lost his serve twice at 30-40 (33%), and once from 15-40 (16%).
  • Nadal lost his serve 2 times from 30-40 (67%). The one other time he lost serve was at 40-Ad.
  • Nadal won 74% of first points while serving.
  • Djokovic won 70% of first points while serving.
  • Neither player served out a shocker of a service game (loosing from 0-40). However both players found themselves at 0-30 once, but each time they were able to push the score back to 15-30.

Most Frequently Played Points

Game Tree Roland Garros

Roland Garros Men’s Final Most Frequently played points (click to enlarge).

Nadal played most of his points down the outside positive section of the game tree (as indicated by the rich yellow markers on the above diagram). Other commonly played points by Nadal were played at 15-15, 30-30 and 40-30 (as indicated by the lighter yellow markers).

Djokovic played most of his points down the positive section of the game tree, but with a little less safety than Nadal. Most of Djokovic’s points were played within one point of the neutral section of the game tree, whereas Nadal’s were played within two points of neutral section of the game tree.

The Big Difference: 30-30

The big difference between the two player’s game trees is at 30-30.

Nadal played 30-30 seven times, and was able to convert 100% of those into a very positive position, 40-30 (see below). Djokovic also played 30-30 seven times, but was only able to get to 40-30, 3 times (43%). He was forced into a very dangerous position (30-40) 4 times (57%).

Roland Garros_30-30

Nadal                                          Djokovic


The Game Tree was originally developed to give us a better understanding of the final score, and how close a match was. It provides one of many ways to analyse the final result of a tennis match. In this match the game trees for each player were remarkably similar hinting that the match was tightly contested. No player likes to see too many (if any) thick lines extending from the bottom four red circles of the game tree like. In this match Djokovic saw his service broken 6 times (once at 15-40, twice at 30-40, and three times at 40-Ad). (Note: lines extending from any of the four bottom red circles means a player lost his serve). Djokovic played 15-15 point better than Nadal, but clearly Nadal played 30-30 far better than Djokovic. Nether player played through deuce a lot (in comparison to other matches). However, Nadal was able to convert more winning games from deuce than Djokovic. Nadal converted 75% of games played through Deuce, while Djokovic converted only 50% of games played through deuce. At 40-30, Nadal also had a better conversion rate than Djokovic (66% to 40%).

Like we see in so many of these matches, games are won and lost at a few very important points. The game tree suggest there wasn’t much in this match between these two players. It does however suggest that Nadal was perhaps the better ‘big point’ player, and as we know in tennis, big points win matches.

Make your own conclusion about the final using the interactive Game Tree here.


How We Made Nadal’s Interactive Game Tree

Late last year we published an interactive game tree celebrating Rafael Nadal’s historic 2013 season. The Game Tree allows users to visually explore how easily, or not, Nadal won each of his 666 service games in the Masters 1000 Tournaments, Grand Slams and World Tour Finals he played in 2013. This rare point-by-point summary shows where Nadal’s history breaking season was won and rarely lost.

Nadal Game Tree

Figure 1. Nadal’s Interactive Game Tree was released after the completion of the World Tour Finals, November, 2013. Click here to view the application.

How the Project Began…

The idea for the project came about after years of frustration by never really knowing how close a match was by just looking at the final score. For example, a 6-4, 6-4 score-line could mean multiple things; one break of serve, or multiple breaks of serve. The winner may have won their service games easily, or they might have been hotly contested. Clearly, the final score gives no indication of the competitiveness of the match. To ease this frustration we set out to find a way to graphically present how hard Nadal was challenged in his matches during the 2013 season.

Our Inspiration

Inspired by Donato Ricci et al’s, (2008) game tree-like infographic (Figure 2), we set out to illustrate the path to victory using game tree theory. Sometimes referred to as a tree of possibilities, a game tree represents paths from a starting point to an end point, often in a game scenario like chess. Tennis plugs perfectly into a game tree as each player starts at 0-0 and makes a move in one direction only through the tree, depending on their success at the 0-0 point.

Ricci et al’s, (2008) map

Figure 2. Mapping relationships between events. Ricci et al’s, (2008) map of the most common research methodologies used by various Italian design firms.

In order to determine the effectiveness of Nadal during his service games we mapped the frequency of paths from one point in a game to the next. To do this, we borrowed concepts from a 19th century cartographic method, called flow mapping. Flow maps were first introduced by Henry Drury Harness in the Atlas to Accompany Second Report of the Railway Commissioners, Ireland (1837) (Figure 3).

Henry Drury Harness Map

Figure 3: Henry Drury Harness introduced the first flow map in 1837. The map uses a variety of line thickness to convey a quantity of traffic flow between Irish cities.

The lines connecting each point in the Game Tree became the quantitative flow lines, and were scaled proportionally representing the number of times Nadal played through each point. The various line thicknesses allowed us to very quickly identify the most common path during each service game.

The Data & Technology Behind the Game Tree

To create the game tree we began by downloading all of the appropriate matches from the William Hill sports website as XML files. Each match was available as a separate XML file and these files contained high-level information about the match (players, tournament info, date, etc.), along with a detailed point-by-point breakdown of the match. After a preliminary assessment of the data we developed a javascript application, which looped through the files and began to process the points.

William Hill Data

Figure 4. An extract of data from the xml game files used in the game tree.

We then prepared a series of functions using javascript, to mimic the behavior of the game tree. The Game Tree at present only maps Nadal’s service games, therefore all point values of the opponents’ service games were simply skipped over and tie break points ignored. As the points are looped through and processed, we used the Rapheal javascript library to draw and animate the entire game tree using SVG (Scalable Vector Format). Some additional jQuery code was then added to hook up the tournament and match filters. The application was framed using HTML5, CSS3, SASS, Compass, and the Mueller Grid System.

Designing the Application

Our design work started off defining what the users expectations were from the application, and working out the simplest way of fulfilling their needs.

We defined a number of core functions the app should support:

  • The ability to compare game tree patterns at both the tournament and game level.
  • Multiple filtering at the season, tournament, and match level.
  • Interaction with the flow lines should reveal the exact quantities per line.
  • Tournaments should appear in the order they occurred, and the score should appear alongside each match.

Once we defined the core functions of the app we started sketching out how the game tree would support the application, and how we would visually organize the content for mobile, tablet and desktop devices.

Some of the earlier game tree concepts were centered on a circular game tree, before slowly transitioning to a more conventional representation of the tree diagrams (Figure 5).

Sketching out the Game Tree

Figure 5. Sketching the game tree designs. From here it was a matter of refining the triangular game tree until the design begun to solidify.

It was important that we designed the game tree to be responsive across small and large devices. We needed to ensure a seamless user experience regardless of device type or size. To do this we introduced some mobile ready functions into the design. For example we collapsed the menu on smaller devices so the game tree remained the focal point of the application. And we re-arranged the text on the opening page for smaller devices (Figure 6).

Responsive Design

Figure 6. Designing the optimal viewing experience across tablet and mobile devices forced a reshuffle of some of the key elements of the application.

Each point in the Game Tree was color coded to reflect the momentum in each game. Dark blue representing + positive momentum, red – negative momentum and the neutral points down the spine of the tree were colored white (Figure 7).


Figure 7. Each point in the Game Tree is color coded to reflect momentum in the match.

Results and Analysis

Nadal’s (6-2, 3-6, 6-4, 6-1) win against Novak Djokovic at last years US Open final illustrates the analytical power of the game tree (Figure 8).

Nadal v Djokovic Game Tree

Figure 8. The US Open final played between Rafael Nadal and Novak Djokovic. The game tree clearly highlights where Nadal played the majority of points on his serve (Deuce to Ad-40 – 12 times)

The score from the match, 6-2, 3-6, 6-4, 6-1 indicates a fairly one-sided match. But the game tree tells us that Nadal won 6 of his service games from Ad-40, (more than any other point). He and Novak wrestled back-and-forth between Deuce and Ad-40 12 times on Nadal’s serve. The frequency/line thickness through this part of the tree suggests that Novak had many opportunities to break Nadal’s serve, and that perhaps this match was much closer than the score suggests.

Nadal’s victory against Stanislas Wawrinka in the final of Madrid (6-2, 6-4) shows us how brutal Nadal can be when serving (Figure 9).

Nadal v Wawrinka Game Tree

Figure 9. An almost perfect service pattern. Nadal’s victory against Wawrinka in the final of Madrid (6-2, 6-4).

In 9 service games, Wawrinka never saw an opportunity to break Nadal in this match, coming close only once at deuce. Nadal’s remaining service games were won from commanding positions in the game (4 times each from 40-15, and 40-0). Nadal was only twice in the red zone (at 0-15). But each time he quickly pulled the momentum in his favor for a quick path to winning each game. Whilst the final score suggests a relatively straight forward win for Nadal, it’s not until we see his service games visualized in this manner that we truly understand his dominance in the match.


We believe this is the first ever-interactive point-by-point Game Tree of a tennis match covering an entire season for one player.

In both the Djokovic and Wawrinka examples presented above the game tree enabled a better understanding of the match than simply seeing the final score. The game tree presents opportunities for further analysis as well. For example we are able to determine where Nadal is most effective on serve. We can see that at Deuce, Nadal beats his opponents more than any other point. He fights back-and-forth between 40-Ad and Ad-40 (like against Djokovic in the US Open Final), but rarely losses when he is serving at Deuce. Across his 666 service games last season, his opponents only had a 1 in 5 chance (0.2) of winning the game from Deuce onwards.

The simplicity of the Game Tree application, and its ability to graphically present traditional statistical data in a unique and informative way allows users to better understand the final score of a match and how games are played out over time.

Craig O’Shannessy, leading tennis analyst for the NY Times, the ATP, and former panelist at the MIT Sloan Sports Analytics Conference labeled the application, “pioneering, and groundbreaking”.  It has featured heavily on well-respected data visualization websites like, and Nadal’s Game Tree captured the imagination of tennis analyst, fans, and data visualization experts worldwide for it’s originality and function.

Stay tuned for further interactive sports visualizations in 2014!

Click here to view the Nadal Game Tree application.

This article was written for the MIT Sloan Sports Conference.

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 @damiensaunder

David Webb is the web team lead at Rady Children’s Hospital-San Diego, where he builds responsive web sites and web applications. He enjoys experimenting and tackling interesting challenges via

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.


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!


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.

The Comeback. An interactive Game Tree of Nadal’s extraordinary 2013 season.

On February 5, 2013, following a 222 day break from the game, Rafael Nadal returned to tennis ranked #8 in the world. Just 9 months later he completed an almost flawless comeback ending the year ranked the #1 player in the world for the third time.

To celebrate Nadal’s historic season we present his 2013 interactive Game Tree. Nadal’s Game Tree allows you to explore how his 600+ service games played out in the Grand Slams, Masters 1000 and World Tour Finals.


Click here to access Nadal’s interactive Game Tree application. 

This rare point-by-point summary shows where Nadal’s history breaking season was won and rarely lost.

The Game Tree presents an alternate way of visualizing game momentum. The challenge was to come up with a visualization that better reflects game momentum, and therefore shows how easily, or not a player wins their service game.

Each point in Nadal’s Game Tree is colour coded to reflect the momentum in each game. Blue representing positive momentum, and red negative momentum. The spine of the game tree is coloured white indicating neutral territory for Nadal.

About Nadal Game Tree

Mapping momentum through the Game Tree. Each point in the Game Tree diagram is tagged with a colour that matches its momentum classification.

When Nadal dominates a match you will see him flow through the outside ‘positive’ points of the Game Tree. When he struggles to hold serve, or looses his serve his flow will tend to move the through the ‘neutral’, or outside ‘negative’ points. The Game Tree clearly shows how Nadal dominated his opponents on serve this season by the frequency of points through the positive side of the Game Tree.

Game Tree’s are perfect for coaches and players to see where in the game a player is making it, or breaking it. Once they identify the breaking points, they can go to the tape and see what’s happening on court.

And the great news is we have coded the app so we can plug in any ATP, WTA or Challenger match/es into their own Game Tree!

We believe this is the first interactive point-by-point Game Tree that maps an entire season of service games for one player. The Game Tree interactive is an experiment to see what we can do with traditional forms of tennis data. Please let us know what you think; we’d love to hear from you.

A massive thanks to David Webb for coding this up, and Ella Ling for allowing me to use her fantastic Nadal pic on the opening page. Next week we’ll go into a little more detail about the concept, design and development of the app.