This post illustrates some simple tracking data visualisations that highlight some interesting characteristics of player motion. To demonstrate I take some tracking data from a match played between Stoke and Liverpool in 2015. Stoke, the home team won this match 6-1.  Here’s how the teams lined up (Stoke are shown on the left.)

## Individual Tracking Data: The Dashboard

Individual tracking data is usually visualised in a heat map which shows the distribution of player locations. This is very useful, but there are other features of individual player motion that can be easily summarised as well. (By the way, an alternative to the location heat map is described here.)

The aim of the dashboard is to visualise features of player activity that are not apparent from the usual heatmap and to facilitate comparisons between players.    The figure below shows the dashboards for the Stoke forward Mame Diouf and Liverpool’s Steven Gerrard.

The dashboard consists of six charts. The chart on the top left shows how a player’s speed changes throughout the period. The smoothed speeds represented by the blue lines suggest that both players are slowing down slightly as time progresses.

The chart drawn on the top left shows high speed runs (speeds > 5 m/s).  Both players make runs from deep, though it looks like many of Gerrard’s runs stop before reaching the halfway line.  There are a number of possible explanations for this, such as Gerrard being tackled as he approaches the half-way line, to passing to a team-mate. A closer look at the data would answer the question, but for the purposes of this post I’m leaving it unanswered, and a matter for speculation.  Diouf makes fewer runs than Gerrard in his own half, and his high-speed runs from there generally continue into opposition territory. Both players show some high-speed activity in the box, Diouf somewhat more than Gerrard.

The chart on the middle left is a plot of speed versus direction. Diouf’s profile shows that he moves quickly in the forward direction, but is much slower moving backwards. Gerrard on the other hand has a more symmetrical profile, which probably indicates he tracks back more enthusiastically than Diouf.

On the middle right is a  relative motion sonar.  This is essentially a histogram showing changes in direction, that is changes in angle of motion relative relative to the current direction.  As shown by the the two largest leaves, both players tend to drift left more than right when going forward.  This turns out to be a common pattern. A few players (for instance Martin Skrtel and Emre Can) show an equal distribution, and a few like Jordan Henderson show an even more pronounced inclination to move right.

The bottom left chart shows player displacement, or distance  from his own goal. Early in the match, Diouf plays on average a few metres further forward than Gerrard, but gradually drops back. Gerrard on the other hand moves further into opposition territory as the match progresses. The final chart on the bottom left shows the frequency distribution of the displacements. We can clearly see a difference in the two players.

## Multiple Players: Comparing Displacements

The charts below compare the displacements of the central defenders in each team.  The left hand chart is for Liverpool and the right hand chart is for Stoke.

We can see a clear difference between the coordination of the central defenders in each team.  Sakho and Skrtel’s movements are highly synchronized.  Both players move away from goal and towards goal together, and by almost exactly the same distance.  Muniesa and Shawcross’s displacements however frequently diverge, with one player often venturing forward, while one stays  more than the other. This is reflected in their displacement statistics. The Liverpool pair’s displacements diverge by 4.0 metres on average, and the standard deviation of the difference is 3.7 metres.  The Stoke pair’s displacements differ by 5.6 metres on average and the standard deviation of the difference is much larger, at 7.5 metres.  This

## Match Overview: Dynamic Organization

Finally, we can summarise player movements by means of hierarchical clustering.  Here, I show a cluster solution for the speeds of all 20 outfield players (when both teams are moving).  The chart below shows how the motions of the players are related to one another; players plotted close together in the hierarchy are moving together (i.e. at the same speed).  Liverpool players are shown in red, and Stoke players are shown in blue.

We can see here how the Liverpool centre backs Sakho and Skrtel are grouped together  as was suggested by the displacement charts.  We can also see that they are grouped with Diouf, so it appears they are responding to his attacks, with Adam, the next player in this hierarchical group, playing a supporting role.  In contrast the Stoke centre-backs operate alongside their left-back Pieters.  There are other interesting pairs and triplets in the chart. For instance ,Can the Liverpool right back is coupled with Stoke’s Arnautovic on one side of the field, and the Liverpool pair Moreno and Allen are contesting Stoke’s Walters on the other.

Speed is not the only thing we can cluster. I also clustered the player movement trajectories.

The high-level structure of the clustering looks quite similar - for example the Sakho/Skrtel/Diouf combination is retained and so is the Arnautovic/Can combination, but there are some differences of detail.

I would suggest that hierarchical structuring of player movements is a fairly rich type of visualisation, which can be used to discover interesting combinations of play. They could potentially be used in opposition analysis, for example to see how teams play against particular formations.