Visualizing the Columbus formation with Voronoi diagrams

I had a bit of an epiphany earlier this week when looking back over some photographs I took of the game against New York. This had to do with a way of seeing the field as cells, centered around each player. There is a visualization technique called the Voronoi Diagram, which I've come across somewhat regularly in my day job. Voronoi Diagrams are used to develop cellular systems, structural systems, to analyze geologic phenomena - among many other applications.

Crew_ny_2_voronoi_medium

After the jump are more snapshots of game action from Saturday, with Voronoi diagrams overlaid on top of them.

Below is the image that started my investigation. At this moment, Eric Gehrig and Kenny Cooper (at lower right) are challenging for a loose ball. Gehrig appears to have the advantage, but as I looked at the image a problem became apparent. Of the ten field players for Columbus, very few of them were available to receive any sort of a pass. Eight players are in a large circle around the field, while the two players in the middle (Kirk Urso and Mirovan Milosevic) are masked behind Cooper or other New York midfielders.

Positioning_original_medium

The more I looked at the photograph, however, the more I began to see the players as nodes controlling the space around them - which made me remember the Voronoi Diagram. A few minutes of fiddling with Alex Beutel's interactive Generator had produced the image below.

Joint_positioning_1_medium

Here, the problem stands out in more marked contrast. Bernardo Anor, on the left wing, is one of the best passing options available to Gehrig. Getting the ball to him, however, would still be a challenge given the amount of space to cover and the other flank players in the area.

Unfortunately, I don't believe I have a photograph from the seconds after this - so I can't document what transpired. The experience of seeing this moment in explicit spatial terms, however, made me go back and produce a few more. In the image below, goalkeeper Andy Gruenebaum (right) prepares to punt the ball upfield. The line of New York players, and the options available for him to hit, stand out pretty clearly.

Crew_ny_3_voronoi_medium

In the image below, New York has sent a long ball down the Crew's left flank, and Gehrig and Cooper (right) are anticipating where it is going to land. The three other Crew defenders are similarly backtracking, trying to keep an eye on Dane Richards (behind Francis) and Thierry Henry (with Chad Marshall in the center of the field). The need for a long ball begins to become understood when the Crew's line of defense across the midfield - with Anor, Urso, Mirosevic and Gaven all laid out in a line from left to right.

Crew_ny_2_voronoi_medium

Ultimately, I would love to be able to apply this sort of visualization to video footage, or at least to a burst of images analyzing specific key plays. Some sequences I would love to see under this lens would be Cooper's first goal as he gains separation from Gehrig in the area, and the flurry of Crew chances around the 63rd minute that briefly raised Crew fans' hopes of a comeback.

What do you think - would you enjoy seeing more of this type of work?

Postscript: my last piece, a screencast introducing the concept of a line chart, has been amended with a link to download a PDF report of every player, in every season in Crew history. Go review the screencast, and look for the download link at the bottom of the article.

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