Exploring Relationships Between Players and Games

Player-Game graph for 1996 Crew season, highlighting Brad FriedelTeam rosters evolve over time. Between seasons there can be significant turnover, but on occasion a team will also undergo dramatic changes during the course of a season. For teams with a large roster, more subtle variations can emerge: squad rotations, and players who appear in one competition but not another.

Force-directed graphs are one way to explore the changing relationship between players and the games their team play. They are also pretty easy to implement¬†using the d3.js visualization library – as I type this, there are more than two dozen examples of this type of chart on d3’s gallery page. Here on this site, you can use them to explore how players have changed during each season in team history.

The image at the top of this post covers the 1996 team.

In the above example, each player that made an appearance is shown as a dark blue circle. Hovering over each circle reveals that player’s name (I’ve experimented with leaving the labels on at all times, but the graph quickly becomes very crowded). Every other circle represents a game that the team played.

1996 is something of a special case in Crew history, because the team changed coaches in the middle of the year. That transition, from Timo Liekoski to Tom Fitzgerald, is generally credited as being the spark that inspired the team to its improbable run to the playoffs. As the chart above shows, however, Fitzgerald’s ascension was not the only change to the team that season.

Games coached by Timo Liekoski are colored light blue. Games coached by Tom Fitzgerald are orange – light orange are the playoff games, dark orange are regular season games.

As you can see, there are a handful of players who are only (or largely) connected to Fitzgerald’s games. Brad Friedel is one such player, having made his debut for Columbus in Fitzgerald’s second game in charge. Rob Smith is another – he missed most of the season while away with the US Olympic Team. Another trio of players – Ricardo Iribarren, Robert Warzycha, and Paul Caligiuri – joined the team mid-season and played heavily during the stretch run.

All these relationships are visible in a force-directed graph.

Player-Game graph for 2008 Crew season, highlighting Duncan Oughton

These types of graph can also reveal when a team is more stable. The above chart shows the Crew’s 2008 season – when the team ran away with the Supporters Shield and won their only MLS Cup. In this chart all games are colored orange, while players are blue (the lone light blue circle is Eddie Gaven).

Where the 1996 chart shows clusters of games emerging by the players who appeared in them, the 2008 chart is nearly circular. A few players – like Duncan Oughton – played sparingly, and the physics engine that lays out the nodes reacts by sending them to the periphery. Most players, however, are dragged to the center of the circle – even those who did not play every game. The collected force of all the relationships produces a stable shape.

Player-Game graph for first three games of 2014 Crew season, highlighting Wil Trapp

An extreme example of this sort of stability can be seen in the above chart, of the first three games of the 2014 season. The Crew’s roster over these first games has been unsurprisingly stable – the team has won each game, so there has been little need to change things. As a result, the games are evenly spaced in the center while a stable ring of players surrounds them. The few players who have not appeared in every game are displayed at greater distances away, connected by thinner lines proportionate to their actual playing time.

It will be interesting to examine how this season under Gregg Berhalter proceeds, and whether this sort of visualization reveals anything about his roster management in contrast to that of Robert Warzycha, or Sigi Schmid. My hunch is that some different patterns may be visible, but they may not be immediately apparent – no matter who your coach is, some players will see sigificant action while others are used sparingly. Only time will tell, however.

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