Shot Blocking and the State of the Game.

It has long been appreciated that the dynamics of a game subtly alters as time elapses, scorelines alter or remain the same and pre match expectations are met, exceeded or under shot.

This shifting environment has traditionally been investigated using the simple measure of the current score.

This has been unfortunately labelled as games state, when simply "score differential" would have both succinctly described the underlying benchmark being applied, without hinting at a more nuanced approach than just subtracting one score from another.

As I blogged here, the problem is most acute when lumping the not uncommon, stalemated matches together.

Consider a game between a strong favourite and an outsider that finishes goalless.

Whereas the latter more than matches their pregame expectation, the former falls disappointingly short of theirs.

The average expectation at any point in a game can be represented in a number of ways, but perhaps the most intuitive is an estimation of the average number of points a team will pick up based on the relative strengths of themselves and their opponent, at the current scoreline and with the time that remains.

The plot above shows the relative movement of the expected points for a strong favourite playing weaker opposition to a 0-0 conclusion.

The favourite would expect to average around 2.5 points per match up at kick off, decaying exponentially to one actual point at full time.

So at any point in the match we can measure the favourite's current expectation compared to their pregame benchmark and use this to describe their own level of satisfaction with the state of the game.

Game state would be preferable, but that's already taken.

The same is true for the outsider. Their state of the game gradually increases compared to their much reduced pregame expectation.

Although the game is scoreless throughout for each side, things are getting progressively worse for the favourite and better for their opponents.

We can use these shifting state of the game environments to see if they have an effect on in game actions.

Intuitively you would expect the team doing less well compared to their expectations to gradually commit more resources to attack, in turn forcing their opponents onto the defensive.

This may increase shot volume for the former, but it is also likely that these attempts, particularly from open play will fall victim to more defensive actions, such as blocks.

The reverse would seem likely to be true for the weaker team. Although their shot count may fall, with less defensive duties being carried out by their opponents, their sparser shot count may evade more defensive interventions, again such as blocks.

Here's what the modelled fate of a shot from regular play from just outside the penalty area in a fairly central position looks like between two unequal teams as the match progresses.

Data is from a Premier League season via @infogolApp

In building the model, the decay in initial expectation has been used to describe the state of the game for the attacking team when each individual shot was attempted, rather than simply using score differential.

Initially the weaker team is less likely to have their shot blocked, although it is probably more accurate to say that the favoured side is more likely to suffer this fate.

As the game progresses, the better team sees a slight increase in the likelihood that a shot from just outside the box is blocked, perhaps suggesting that their opponents are initially heavily committed to a defensive structure.

The weaker side has a lower initial likelihood that such a shot is blocked, again implying a more normal amount of defensive pressure early in the game. But as the match progresses this likelihood that their shots are blocks falls even more.

This nuanced model appears to be illustrating the classic potential for a prolonged rearguard action from an underdog, followed by a late smash and grab opening goal, mitigated by the relative shot counts from each team.