Wednesday, August 12, 2015

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.


I want to recognize again the work of Francis X. DieboldGlenn 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.

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