A bit more on Game State


In my last post Goals Change Games, I explored how different Game States affect a team’s attacking play.   Other things being equal, teams that are in front decrease their rate of shooting, and teams that are behind increase their rate of shooting.  The model I developed assumed that the effects of Game State were constant throughout the match.  (The model is presented in full on the OptaPro Forum).

Common sense suggests however that Game State effects would intensify towards the end of a match. For example, a team that is in front by the odd goal might go for a second early in the match, but might be inclined to retreat into a defensive shell if there were only a few minutes left.

In this post I want to explore how Game Sate affects shooting intensity as the  match progresses and the final whistle approaches.   In statistical terms this means including  a Time* Game State interaction effect in the model.  I also added two more season’s data, so the results shown here based on all Premiership matches in the four seasons 2010-11 to 2013-14.

The diagram below shows how Game States were represented in the model.  Each time a team scores, a new game segment starts.  Each segment is associated with a Game State, and each has a length (how long it lasts)  and now also a time, represented by the temporal mid-point of the segment.

Segment descriptors

I first ran  a 3-category Game State model in which the three Game States were Behind, Level, and In front . This model was exactly the same as the 3-category model in my OptaPro presentation, except for the addition of the new Time*Game state interaction term.  The outcome variable was the number of shots.

The significance of the model coefficients are shown in Table 1. (Note there is no coefficient for segment length because it enters the model as an “exposure”)

Coefficient Significance
Game State .001***
Team .000***
Opposition .000***
Venue .000***
Time .000***
Game State * Venue .624
Game State *Team .000***
Team* Venue .005**
Game State* Team *Venue .006**
Game State * Time .000***


The important point to note is that the new term, Game State* Time is statistically significant. This means that the effect of Game State varies throughout the match.

To see what this implies, I plotted the model estimates for three specific times: 25% into the match, 50% into the match and 75% into the match.  The y-axis of the chart represents shooting intensity (expressed as number of shots per 90 minutes), and Game State is recorded on the x-axis.

Game State x Time Interaction

The results are quite clear. Early on in the match (represented by the red dots), the graph is rather flat. Teams that are behind do have a slightly elevated shooting rate,  but comparatively speaking the effect of Game State  at this point in the match is relatively small.  Whether a team is leading, behind or in front makes only a small difference to the shooting rate.

Halfway through the match (the green dots), the slope of the line increases a bit, with a ‘parking’ effect (a reduction in shooting rate when in front) beginning to appear.

Towards the end of the match (the blue dots) the effect of Game State has become substantial. Both the elevated shooting rate when behind and a reduced shooting rate when in front are now clearly apparent.  At this stage in the match, teams that are in front make only 15 shots per 90 minutes, compared to 18 when level and 21.5 when behind.

Next, I looked at whether chasing and parking affected a team’s goal-scoring record over the season. The analysis showed that teams who chased when behind tended to score more goals, which we might expect.

I also expected to find that teams who parked when ahead would conceded fewer goals  - that’s the point of parking right?  But I couldn’t find any evidence for that. Various analyses I tried pointed to  high parkers actually conceding more goals than the low parkers.  A possible explanation is that the teams who tend to park are teams that are poor defensively.  Maybe, we just need a different measure of parking. At any rate,  the evidence seems to show that going into a defensive shell (or at least limiting your own attack) doesn’t reduce goals against.  Hopefully more research will unravel the mystery.