Making connections

A game of hockey as a network

I’ve been remiss about getting some content up here so I thought I’d restart things by throwing up some visualisations while I try and sort out material for a talk I will be giving on Ernst Baart’s ‘The Hockey Site’ in early May.

Here is a way of summarising some data from a single international match. It’s an area of analysis I haven’t shown on this site before, and indeed am not really going to talk about too much now, but because I like the visualisations I thought I would show an example of what one kind of network analysis looks like.

This first figure is a representation of ball movement around the pitch by Spain in a match they played against Belgium (hence the ‘Circle’ node is the Belgian’s red circle) during the last Eurohockey competition. The pitch is divided into twelve zones with two outcome circles - the team either gets the ball into their opponents circle and the analysis then moves to a different modelling process, or the team turn the ball over to their opponents (the grey ‘Turnover’ circle), when the analysis begins again from the Belgian perspective.

This is a fairly coarse representation (only twelve pitch divisions when there would normally be at least 48 and as many as 120 for a detailed analysis) but there is still a great deal of information to glean here. The connecting lines show ball movement (dribbles and passes) between pitch areas and the arrows indicate the direction.

Each line has a number associated with it (very small in this example to try and keep the visual a little less cluttered) and these indicate the probability of a team moving the ball from one pitch area directly to another. For example, Spain went directly to the Belgian circle from the attacking top right zone (‘Att25Right’) with a probability of 0.23 - Spain managed to create circle entries with about 23% of the possession they had in that pitch zone.

More importantly, the modelling process underlying this network allows us to calculate the probability of moving the ball from any one pitch area to all the others even if they are not directly connected. This is because the model takes into account all the paths the ball is likely to travel through each pitch area based on the underlying data - the actual pattern of passes and dribbles the Spanish made.

Of particular interest is how well the team got the ball into the circle. Spain did not do well in this regard. The most successful pitch areas for circle entry were, unsurprisingly, ‘Att25Mid’ and ‘Att25Right’ with circle entry probabilities of 0.53 and 0.29 respectively. No other pitch areas had a circle entry probability greater than 0.15.

Naturally, there are two teams in any contest so what does Belgium’s network look like?

If you do a quick visual comparison you can see that the top half of the Belgian pitch (i.e. the defending half of the Spanish pitch) is much ‘busier’, much more connected than the equivalent half of the Spanish pitch. And that’s how it should be because Belgium trounced Spain in this game. Spain had a lot of possession in their half but very few successful attacks. And Belgium’s circle entries? The lowest probability is 0.22 (‘Def25Mid’) and the top half of the pitch all have circle entry probabilities of 0.32 or higher - very different to the generally low values for Spain.

Another bit of information that can be extracted from these networks is the number of actions each team made in their possession chains – a measure of the team’s connectedness and the amount of possession they enjoyed - before there was either a circle entry or turnover, the two endpoints of a team’s possession bout. Interestingly, Spain made more actions on the ball particularly in their defending half of the pitch (an average of 5.1 actions per possession for the six defending half zones, to Belgium’s 4.2), but this didn’t stop Spain losing by five goals.

And I am a little enamoured by the images themselves. If I put the two together side by side….

… it is, I think, a rather nice abstraction of a game of hockey. I can imagine a sequence of these paired networks representing different games, Olympic finals through the ages perhaps, as a framed picture.

Anyway, here then was a very brief look at a particular kind of representation of a game of hockey. In future articles I will be building this kind of approach into an expected threat model - a way of looking at team (and player) effectiveness across the whole pitch.

And of course, what’s missing from the above visualisations, what’s missing I mean to make it a complete summary of the game between Spain and Belgium, is what went on in the circle. For that I’ll show you another kind of network in the next article.