The Permeability Index: How efficient are Premier League teams in defending their goal?


Based on figures

Today, I decided to have a look at the defensive side of the game consisting on the goal protection. This consists of a statistical calculation of a final figure –  that I’ll call the Permeability Index – after several steps ; I’ll try to comment as much as I can the point of the various figures and what it means in terms of footballing terms. That’s a test study considering the little amount of stats I’ve at my disposal, and the fact that’s the outcome of a thought about how to be even more precise when it happens to compare teams. One can obviously improve such a study with even more complete stat sheets.

All means are admissible

The start of the study is crystal clear: you start to defend when you lose possession. We can then look at the way teams use to recover the ball ; I used the figures related to the amount of tackles and interceptions per game. The outcome of the opponent’s possession spell is the finishing time, the attempt at goal which happens to be either a goal or not.

The point of the study is to highlight the fact that teams use different approaches, tactics to protect their goal. You can find teams whose approach will be to dominate the possession ; they’ll react quickly when the ball’s lost (considering ball retention needs technical skills, that’s not often coupled with the fact to be a good or solid player to recover the ball ; hence the purpose of the pressing game). At the opposite, some teams prefer to leave the ball to the opponent to the benefit of a better team shape ; they reduce the space between the ball’s average position and their goal. It leaves then more space to counter attack behiond the opponent to reach good positions and try to score.

Tiki-taka and Kick & Rush can actually get along pretty well with each others. Image:

So, basically, a passive approach isn’t worse in any way than a proactive approach. That’s a matter of tactical choice. What I’ll try to show is the relevance of such a gameplan. Is your approach relevant  and/or efficient if you don’t recover the ball quickly and that you concede a lot of chances to the opponent? Everybody will agree it’s not.

Teams don’t enjoy the ball as much as the opponent, because of tactical choices or the players’ technical limits. Every team has then its very own amount of time in which it enjoyed and chased for the ball. As the defending process is about the time when you haven’t the ball, I’ll calculate a ratio between the average time required to attempt a defensive intervention and the average time required to concede a shot. I’ll get the Passivity rate that I’ll take out from the amount of goals conceded, to get the Permeability Index of each team.

I took the figures after the 18th Premier League Gameday. All teams played 18 games but Chelsea and Southampton. That won’t have more than a little impact on the final result as the calculation is based on an amount of minutes. The figures comes from the excellent

Here’s the first table: It’s the raw data that I will use for my second table and final calculation. The rates per game has the only purpose to contextualize the data and figure out how many tackles/interceptions/shots teams use or face in average per game.

Raw data FINAL

Build up to the Permeability Index

Here we come to the second table that I’ll explain the build up.

  • I merged the columns related to the minute per tackle and minute per interception by working out the average amount of time required for a team to execute a defensive intervention.  The shorter the Minute Of Non Possession (MONP) per intervention is, the quicker the team is to react to the loss of the ball.

Arsenal (and most big clubs, thanks to their more technical players) relies on a brand of football based on possession ; then they tend to react quickly in order to recover control of the possession as soon as possible.

West Bromwich as prime example, openly concedes possession in order to wait for the opponent to commit a mistake and then, counter attack him ; it notably underlines their use of zonal marking in midfield. But other teams such as West Ham or Stoke can be known to “park the bus”, hence their 3.78 and 3.19 average minutes before a defensive intervention.

  • With a geometrical view of the distribution of attempts on goal in a given time, a given amount of minutes in average passes between two opponent’s chances. So, in that case, the shorter the time between two chances is, the more you’re exposed. So you better have the ball most of the time or you’re likely to concede a lot of goals.

Andre Villas Boas can be pleased to see that his team concedes the less chances in Premier League when it hasn’t the ball. At the contrary, that’s pretty easy to understand why Reading (or Wigan, QPR), occupy the bottom(s) spot(s) as the Royals concede chances quite often when they’re not in possession.

I’ll now explain my two final calculations, that I hope you won’t regard as a bungling culinary preparation. First of all I’ll make up 4 dummy teams and their due figures in order to make the calculation more meaningful.

I’ll calculate the Passivity rate:


Here’s my 4 dummy teams’ Passivity rate:

Dummy teams final defi

  • Team A: 0.44   Is reactive when the ball is lost, doesn’t concede a lot of chances. The rate is low, that’s a top team likely to head the table.
  • Team B: 0.80  Is reactive when the ball is lost but concede a fair amount of chances. The rate is medium low.
  • Team C: 0.89  Isn’t reactive when the ball is lost but doesn’t concede a lot: The rate is medium high.
  • Team D: 1.60   Isn’t reactive when the ball is lost and concedes a lot. The rate is high. Likely to be your bottom table team.

It’s not relevant to sort teams with the Passivity rate as you can see Southampton (17th on the Premier League table) on the 4st spot alongside City and Arsenal, or West Brom (7th) near the bottom of the table. Teams obviously don’t concede the same amount of goals, the Passivity rate is an indication of how teams behave when the ball’s lost, regardless of the finality.

My idea was to take the Passivity rate out of the goals conceded to get my final figure that I’ll call the Permeability Index.

And here’s the Permeability Index table:

 Permeability index FINAL TABLE 3

You can see the difference between the actual ranking in the Premier League table and the Permeability Index ranking on the right of the table.

Jumbled up observations:

  • Stoke City‘s 9th place in the real table can be explained by their unabiliy to create chances to score considering they’re one of the best teams when it happens to protect their own goal.
  • Manchester United is 8th on the Permeability Index table, mostly because of their defensive liabilities (already 24 conceded, they conceded as much games in the whole 2008/09 season). Sir Alex Ferguson may have predicted such an outcome, reason why he signed Robin van Persie in order to make his team competitive with the unorthodox still common sense approach to outscore the opponent every game ; with the 3-4 win earned in half an hour at Reading as prime example.
  • Surprisingly, Southampton is ranked 11th on the Permeability Index table despite having been said to have a permeable defence. What figures doesn’t show is the kind of situations where Southampton concede chances as the theoretical calculation tends to show they defend quite well their goal for a promoted team. Conceding chances/goals at key moments of the game can be a fair explanation to their actual ranking. Southampton conceded the first goal on 9 occasions, only winning one game (8 defeats). They scored 8 times the first goal, only eventually winning 3 games. We could conclude out of the table that they’re an enthusiast team (reactive when the ball is lost) but probably not experienced enough (more goals conceded compared to the energy spend to recover the ball)
Case study: ‘Last 10 minutes of the game’ simulation at Spurs Lodge, Andre Villas Boas gives the instructions to his defenders.
  • Tottenham is one of the two teams who occupy the same spot on the Permeability Index table and the actual Premier League table. As Andre Villas Boas emphasises on possession and a quick, reactive pressing ; that’s not surprising to notice that they feature a 0.56 passivity rate. They concede the fewest chances when they’re not in possession. But still, they’re 4th. According to the former Chelsea and Porto manager, that’s due to the late goals conceded at the death end of some games (Everton, Manchester City, Norwich City, Norwich, West Brom, Newcastle). So, despite a rather poor and not imaginative approach, relying a lot on the game winning abilities of a couple of individuals ; would Tottenham be an even better team that we could imagine at first sight?
  • More or less 20 units separate Manchester City and Fulham on the Permeability Index; Reading is 15 units behind Fulham considering they average more than 3 minutes before a defensive intervention and that they leave the opponent enjoying chances to score. Without any disrespect to Brian McDermott and his team, Reading looks like much more of a Championship opponent than a Premier League one. Without reinforcements in January, it’s hard to imagine Reading staying up. And I’m not even sure that a couple of signings could actually change that much the current situation.
  • Until which extent can Steve Bould be credited to Arsenal’s second place on the Permeability Index ?
  • At half-season, that’s hard to pretend that Newcastle isn’t at a more ‘deserved’ place on the table. 5th last season, the Toons pay the price of their lack of numerical options to be competitive either in Premier League and Europa League. The suspect form of the individuals that boosted their last season is another reason of that rather anonymous 14th place.
  • Despite the 10 games unbeaten run and despite conceding few chances in average when they haven’t the ball, Chris Hughton’s Canaries are still dragged by their difficult start of the season (4 defeats and 3 draws). It would be interesting to compare their Permeability Index before and after the turning point of Norwich City‘s season ; the tactical readjustments during last October’s international break.
  • If Martin O’Neil can sort his attacking compartment and exploit his striking potential (Fletcher, Gardner, Campbell, Johnson…), Sunderland could experience a similar run of form than last season considering they already have a good defensive base (a lot of players behind the ball though).
  • Fulham conceded 11 goals in his last 6 games, only winning and drawing once. Used to spend the majority of their seasons in between the mid-table and the European spots, Martin Jol has to make sure that performances such as the 0-4 defeat at Anfield are no more than the odd couldn’t care less diplays they’ve accustomed us against top 5 sides the last couple of years.

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