Approximating game paths and the defensive shell hypothesis

Recently, I looked at game states in the Championship; however, by taking some of the ideas presented by Dan Altman, namely the idea that score can be interpreted as path-dependent rather than a state variable, we can shed more light on the effect that goals have on shot ratios. In short, being path-dependent simply means that how a game state is reached is significant. In my previous post, I treated all the time spent at +1 as equivalent. However, a team can reach the +1 game state either by scoring a goal at +0, or by conceding from +2. A path oriented approach treats both of these instances as separate rather than lumping them together. By taking into account which team scored the previous goal (i.e. is Game State decreasing or increasing, we can further investigate how goals change games.

Total Shot Share


Expected Goals Ratio


This would appear to suggest, along with the effect of time on score effects (see Garry Gelade’s excellent piece and this gif), that defensive shelling occurs when the leading team is under more pressure; it suggests that having just scored, teams are more likely to be outshot especially towards the end of matches. The position of the blue line (teams having just scored) relative to the pink in these two plots agrees with the defensive shell rationalisation, as touched upon in the previous post on game states. Having just scored, teams take fewer shots (blue lower than pink on total shots); however, those shots that they do take tend to be of better quality (blue higher than/similar to pink on xG).


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