Rally Tree: Point Distribution and Win Percentage

Tennis is an "intermittent" sport.  The level of intensity can vary greatly with the rally length of points and the time taken between points (among other factors including surface, ball type, sex and level of play).  When rallies are visualized they are typically depicted temporally from the first point to the last, which gives a jagged chart where it is difficult to discern any pattern at all.  "Rally Tree" is an attempt to bring a different perspective to the analysis of rallies.

 "Rally Tree" depicts the distribution of points across various rally lengths, beginning at the top with rally lengths of Zero, which indicate either Aces, Serve Winners, or Double Faults. Color coding differentiates errors where balls were "netted" vs. hit long.

 

There are several available views. The default view displays all points for a single match or selection of matches. You can filter by player to display only points served by either player (or composite of opponents).  Notice the number of winners among the points won for servers vs. those receiving.

Additionally there is an overlay depicting the percentage chance that a point was won for any given rally length. The offset vertical lines represent 50% either side of center (0%).

For the "served points" views, this gives a graphic representation of the Persistence of Server Advantage, which varies greatly among players. Please note that this is not the same as percentage of points won for a given rally length.

The "Rally Tree" graphics in this post are of Novak Djokovic's matches at Wimbledon in 2014 and 2015. The last two images depict the persistence of Djokovic's server advantage on the left and a composite of his opponents' server advantage on the left. Djokovic's dominance is obvious.  Apart from rallies of seven, he had a greater than 50% chance of winning all points with rallies up to sixteen.  His opponents' composite server advantage only extended to rallies of five.

You can play around with a live version of Rally Tree and explore your favorite players at TennisVisuals.com

In the near future "Rally Tree" will be integrated with "Game Tree" and other TAVA components so that selections in one component can drive views in another.  For instance, a "Point Progression" from 0-0 to 0-15 can be selected in "Game Tree" to view the distribution of points in the "Rally Tree" or "Points-to-Set".  From this point it will be possible to explore whether there are certain points in a match when rally lengths increase...

To read more about "Persistence of Server Advantage" please follow the link to Jeff Sackmann's blog post on the topic.

Points-to-Set: Horizon Corona

I've been searching for a representation of a tennis match that captures the dynamics of play yet remains simple enough and compact enough to use as either an icon or a control structure suitable for selecting a range of points within a match.  I also wanted a graphic that could be used to quickly compare a series of matches, with enough detail to easily differentiate a 6-0, 6-0 win that was a "cakewalk" from a 6-0, 6-0 win where every game went to deuce and beyond.

The Corona/Horizon Graphs above are the result of my early attempts to use Points-to-Set data in a new way, charting the difference between the two players' Points-to-Set numbers rather than the absolute values.

Corona Graphs

Corona graphs are actually formally known as radial area graphs; there are also examples of radial histograms which I would describe as "Corona Graphs". These graphs share a lot in common with Polar Coordinate Graphs (such as TAVA's Radar Chart), but they look like the Corona that surrounds our Sun.  I haven't seen the name used in the Visualization community as yet, but it is fitting, especially considering the formal definition of a Coronagraph: "A coronagraph is a telescope that can see things very close to the Sun. It uses a disk to block the Sun's bright surface, revealing the faint solar corona, stars, planets and sungrazing comets. In other words, a coronagraph produces an artificial solar eclipse".  So, with Corona Graphs I hope to highlight important aspects of a match which normally are obscured by the quantity of data available within the match.

[Update: The term "Corona Charts" (here and here) is used in the financial community.  But it is not a radial structure and doesn't resemble the graphs above.]

Horizon Graphs / Charts

Horizon graphs are a type of Time-Series graph which were developed relatively recently by Panopticon Software (now known as DataWatch).  Here is a paper describing the development of the graph, and here is an in-depth analysis of the Horizon Graph by Stephen Few of Perceptual Edge, a "Visual Business Intelligence" company.

Horizon Graphs excel at displaying a large number of time series at one time.  They are described as a tool for rapidly scanning huge amounts of data to quickly identify "points of concern"; they "preserve data density while preserving resolution."  A Tennis Match can certainly be thought of as a time series, a progression of points through time.  Horizon Graphs seem ideally suited for comparing matches, but it turns out they are also useful for comparing Sets within matches, and for identifying critical moments during play.

When I began this project I was overwhelmed by the variety of chart examples available.  I wanted to try them all, but it wasn't immediately obvious how each type of chart could be meaningfully applied. It wasn't until I generated my first Corona graphs with Point-to-Set data that I realized how I could use Horizon Graphs, and how useful they could be.

Here is the progression from my first Match Corona visualization to my first Match Horizon:

In the first Corona graph, on the left, the difference in Points-to-Set values varies from positive to negative.  For the second Corona graph I simply flipped the negative values and changed the color to represent the second player.  Below you can see the same data values in a standard horizon graph.

The horizon graph is then cut into bands and layered.  The peaks are still visible and no space "under the curves" is wasted.  Color gradations indicate distance from the baseline so that the greater values become darker.

With this realization it became possible to compare sets and matches with a very compact visual.

When you see a Horizon Graph for the first time you might find it to be somewhat confusing.  But with a bit of study and experience I think you'll find them very valuable.  Read the links above or this in-depth overview by a team at Berkeley: "Sizing the Horizon: The Effects of Chart Size and Layering on the Graphical Perception of Time Series Visualizations".

Set Comparison

Here are the sets from the 2001 R16 match at Wimbledon between Pete Sampras and Roger Federer. Federer won the match 7-6, 5-7, 6-4, 6-7, 7-5.  Federer is in blue; Sampras is in Green.  

You can see the winner of each set by the final color of each graph.  The depth of color at any given moment indicates the distance between the two Points-to-Set numbers: darker colors indicate a greater point difference. Turning the graphic into a control structure will enable point and game selection as well as "brushing" to select a range of points in a game. For the next version of TAVA I will add ticks and marks to optionally indicate breakpoints, aces, winners, errors & etc.  I'll save the use of Horizon and Corona graphs as control structures for a future post.  

To illustrate the ability of the Horizon Graph to enable rapid differentiation of sets which have the same score in games but which vary widely in the intensity of play and the distribution of points, here are Horizon Graph for three sets which each finished at 6-0:

In the first example one player dominated completely, winning all points.  In the second example, which is taken from the 2012 Olympics final between Serena Williams and Maria Sharapova, Serena gave up 12 points to Sharapova and needed 28 points to close out the set.  In the third example every game of the set went to deuce and most games were at deuce more than once. Seventy-one points were played in the final example versus only twenty-four in the first example and forty in the second.

Match Comparisons

The screen real-estate provided by Blogger makes these a bit too compact, but I hope this gives some idea of the expressiveness of Horizon Graphs.  You can click on each graph to see the full size image:

 

And finally, here is a link to a video about Interactive Horizon Graphs.  This is a bit orthogonal to my intent to use Horizon Graphs as control structures, but it is interesting nevertheless and may provide some inspiration for a way to compare very large numbers of matches in the future.  I'm discovering that there are many attributes of matches other than Points-to-Set which may be usefully visualized with Horizon Graphs.

Acknowledgements

I want to recognize again the work of Francis X. Diebold, Glenn Rudebusch and Professor Diebold's students at the University of Pennsylvania.  As far as I and they can tell, their work on the concept of Points-To-Set is completely original.

Points-To-Set

The "Points-to-Set" graph was inspired by the work of Francis X. Diebold, Glenn Rudebusch and Professor Diebold's students at the University of Pennsylvania.  In December, 2014, Professor Diebold published "A Tennis Match Graphic" on his blog No Hesitations, and in February when I was just discovering D3 I decided to attempt to recreate his work for the data I had just learned to parse from ProTracker Tennis.  Here is the result of that effort, taken from the 2015 Wimbledon semifinal match between Roger Federer and Andy Murray, where you can view these charts "live":

And here is the latest version:

We can think of the "Points-to-Set" number as the minimum distance from the current number of points won until the end of the Set; it always assumes your opponent wins no additional points.  In TAVA this number is expressed graphically for each player to indicate at any given moment in a Set which player is closer to winning.

To win a standard Set in a tennis match a player must, at a minimum, win six games and be ahead by two games.  Giving no more than two points away, there is a minimum of four points which must be won in each game.  That means that at the beginning of a Set each player needs twenty-four points to win the Set.  The Y-axis of the graph below ranges from 24 up to 0, which is where the Set concludes. The X-axis shows the total number of points within the Set.  In the match depicted in these "Points-to-Set" visualizations you can see the varying number of points which had to be played for Roger Federer to close out each Set.

Every point won brings a player closer to the end of the Set, obviously.  Some games, when they are lost, increase the "Points-to-Set" number.  For instance, at the beginning of a Game when the score is 5-4 in the Set, the first player needs only four points to win, while the second requires twelve.  If the first player loses the game and the score becomes tied at 5-5, each player is then eight points from winning the Set. In fact this scenario occurred twice in this match, in both the first and second Sets which were won by Federer 7-5.  You may also notice that in the first game of both the second and third Sets there was a moment when Andy Murray needed 25 points to win the Set.  This actually occurs quite frequently when the first few games are won by one player.  When a player leads 5-0, the opponent actually needs 28 points to win the set.

In the second Set the game which Federer lost there were seven deuces; you can see this in the "Points-to-Set" graphic below where the lines for both players become jagged. You can also see that Federer failed to convert on six breakpoints before winning the set by finally converting a breakpoint.

As I work on the re-write of TAVA I'm developing a gallery of re-usable visualization components and adding configurable features.  In addition to the "orientation highlighting" demonstrated above, I'm adding "game highlighting", which you can see in the chart for the third set below:

When using the "Points-to-Set" component in TAVA, the corresponding moments of the match are highlighted on the Sunburst and you can see the longest game of the match occurred in the second set and was won by Andy Murray (purple) when Federer failed to convert two breakpoints.

In a recent post, Professor Diebold has updated his Tennis Graphic to include elements which indicate where breakpoints occurred and highlight when tiebreaks take place.  Here is the site where his team has collected the visualizations they've created.  I've taken some of these ideas on board and in the re-write of TAVA I'm going to try to push the features and usefulness of the "Points-to-Set" graphic further.  I am intrigued by the idea of producing some variation of a Points-to-Match graphic as a slider/filter for generating dynamic statistics for a range of points within a match...