Quantifying attacking player reliance

Back in 2012, Brendan Rodgers remarked that he has “always thought that if you have three-and-a-half goalscorers in your team, you have got a chance”. This raises the question, are good teams more likely to have their shots and goals spread out amongst the team, or localised in a handful of players? If so, what does this tell us about the nature of the sport.

To test this, we need a metric that can help quantify the distribution of shots within a team. One option would be to use the the Gini coefficient, a common measure of inequality. However, this would not entirely account for the fact that teams with fewer shots, will naturally tend have a more equal distribution of shots. Instead, I have chosen to use the coefficient of variance of teams’ simple expected goal (expected goals being a model for weighting shots based on their likelihood of resulting in a goal). By this measure, a team with a lot of players contributing more equally to their expected goals tally will have a lower coefficient of variance than a team whose shots are coming from only a couple of players.

When we plot this measure against goals scored in the league, we can see a weak correlation:


So that’s it, focusing your attack around fewer players is more effective? Well, not necessarily. Firstly, attacking systems will tend to focus themselves around star players and if we look at where teams are placed along the x axis, it would seem sensible to suggest that teams with high quality strikers will tend t have a higher coefficient of variance. For instance, Blackburn have both Gestede and Rhodes, Watford have Deeney and Ighalo (and Vydra), and Ipswich have Murphy scoring goals for fun. If we can expect top strikers to score goals somewhat independently of the quality of their teammates, then a correlation such as the one seen here would be expected.

So what conclusions can we draw from this, if any? Well, there are obvious limitations in the method used, here. For one thing, a simple shots-based evaluation of a team’s attack will fail capture all the subtleties of attacking contribution and variation. With this and the diffuse nature of the correlation, it would be pernicious to try to draw any large or spectacular conclusions. However, we have at least derived a useful method for determining the spread of xG around a team.


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