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Mapping Defensive Metrics

At a minimum, a description of a team’s defensive performance should tell us how many shots are conceded, where they are conceded from, and how they are defended.  We already know quite a bit about first two aspects, but from a statistical point of view our knowledge of the third is still rather sketchy.

In a previous post I described some properties of the defensive metrics collected by Stratagem and in this post I focus on their spatial distribution. All the metrics I describe concern a shooting situation. Defensive Pressure is a measure of how much pressure the defending team exerts on the shot-taker, and ranges from zero indicating no defensive players around, and nobody blocking the shot, to five, indicating intense pressure (a player held while taking a shot, many players tackling the shooter and denying him space to take the shot, or a player crowded out when challenging for a header). Defenders is the number of defenders – including the goalkeeper – between the shooter and the goal. Attackers is the number of attacking team players between the shooter and the goal, plus one for the shot-taker himself. Defensive Advantage is Defenders minus Attackers.

The dataset has been expanded since my last post to contain about 15,400 shots from open play taken in the 2016-17 seasons of La Liga, the Bundesliga, and the EPL. The shots come from 971 matches which represent 91% of the total seasons total.  Penalties and direct free-kicks are excluded and so are shots directly or indirectly following corners and free kicks, but shots directly or indirectly following throw-ins are included.

Defensive Metrics and Assist Type

The first set of charts shows how the defensive metrics vary with shooting distance for three different types of attempt on goal; a shot following a cross-assist, a shot following a pass-assist, and an unassisted shot. (An unassisted shot is usually either a shot from range, where the “assist” contributes only marginally to the chance, or more importantly in the present context where a player creates a chance for himself by maneuvering into a shooting position.)  The bands are standard errors, and tend to spread out at the left-hand side of the plots because there are fewer shots at longer distance from goal.  I use the Opta x-coordinate to represent shooting distance, as it is familiar to most analysts.

First, the chart at the top left shows that for all types of attempt, Defensive Pressure is highest in the space between the 18 yard and 6 yard lines. There is a suggestion a cross-assisted shot at the 18 yard line is slightly less pressured than a pass-assisted or unassisted shot from the same position.

The chart at the top right shows that the number of defenders falls as the shooting position approaches the goal line. However, unassisted shots have to clear consistently more defenders than pass-assisted shots.  Cross-assisted shots show a slightly different pattern, with the number of defenders at first increasing and then decreasing as the shot location approaches the 18-yard line.

Finally, the chart at the bottom left shows that the number of attackers falls with shooting distance, and that there are consistently fewer attackers in front of the goal for an assisted pass than for a cross or unassisted pass.

What perhaps is most interesting here is that for pass-assisted shots there are both fewer attackers and fewer defenders between the shooter and the goal than for other types of shot.  To see the net effect, the next chart shows the Defensive Advantage  for the three types of attempt.


We can clearly see that pass-assisted shots are less well defended than the other types of attempt at most shooting distances.  This can explain a feature of xG models. In some xG models, pass-assisted shots are more likely to produce goals than unassisted shots; the lower defensive advantage could explain why.

Defensive Metrics and Goals Conceded

The next chart compares teams with good and bad defensive records. The ‘good’ teams are the three teams in each league conceding the fewest goals per match and the ‘bad’ teams are the three teams in each league conceding the most goals per match.

Teams with bad defensive records concede shots somewhat closer to the goal-line (average 14.5 m) than teams with good records (average 15.7 m) and also concede considerably more shots per match (10 as opposed to 6.9).

Perhaps surprisingly there is very little difference between the two groups in the way that shots are defended.  Teams conceding fewer goals exert slightly more pressure just on the 6-yard line, and have slightly more defenders in front of goal in front of the 18-yard line, but the differences look too small to be meaningful.


Defensive Metrics and Conversion Rate Allowed

The Conversion Rate Allowed (CVRa) is calculated by dividing the number of goals conceded by the number of shots conceded. A high CVRa indicates that shots conceded are likely to results in goals, and a low CVRa indicates they are less likely. I contrast the three teams in each league with the highest CVRa with the three having the lowest.  High and low CVRa teams concede almost exactly the same number of shots per match, 8.0 and 7.9 respectively.  However, there is a noticeable difference in the average x-coordinates of conceded shots. High CVRa teams concede on an average  about 1.3 metres closer to the goal line than low CVRa teams do. This is probably one reason why they concede relatively more goals per shot.  But that is not the only reason. Defensive metrics for the two groups are shown below.

Low CVRa teams exert substantially more pressure around the 6-yard line; this might signal a greater willingness to tackle, and confidence in not conceding a penalty; or it may signify a goal-keeper willing to challenge the incoming striker.  Low CVRa teams also maintain a superior defensive advantage at virtually all distances from the goal.

Heat Maps

The chart below maps the overall distributions of defensive pressure, the number of defensive players and defensive advantage.


The chart below compares defensive pressure between leagues.

The chart indicates that defensive pressure in La Liga is noticeably lower than in the Premier League or the Bundesliga.  Teams in the Bundesliga seem to apply slightly more pressure in front of the 18-yard line than Premier League teams.

The chart below compares the spatial distributions of defender numbers.

Teams in La Liga have more defenders in front of goal than teams in the other competitions, especially in the region between the goal line and the 6 yard line.

The chart below compares the spatial distributions of defensive advantage.

Once again, La Liga teams stand out from Premier League and Bundesliga teams, maintaining a higher defensive advantage close to the goal line.

Overall, La Liga teams seem to exert less defensive pressure on shots than teams in the other leagues, but position more defenders in front of goal, and maintain a higher defensive advantage.


The defensive metrics described in this post are all conditional on shots being taken; they cannot tell us about shots that might have been taken but weren’t, which isa key factor in defending well and preventing goals. So far, my approach has been largely descriptive; but there is clearly much more to be explored in this neck of the analytic woods. Given the interest in expected goals models it is natural to ask how much more explanatory power these kinds of metrics can add to current models. I hope to be writing something about that in future.

This article was written with the aid of StrataData, which is property of Stratagem Technologies. StrataData powers the StrataBet Sports Trading Platform, in addition to StrataBet Premium Recommendations