# Defensive Metrics – An introduction

Defensive measures are a peculiar thing.

Unlike attacking measures, where it is accepted that more is better (think of shots or possession), the same logic just doesn’t hold true for defensive metrics.  In this piece I’m going to concentrate on interceptions and tackles as the main defensive measures.

In essence a tackle is pressing the man in possession of the ball whereas an interception is caused by a player anticipating where the ball will be played and moving into its line.

In other words:
Tackle = Pressure on Man
Interception = Pressure on Ball

Current Metrics
If you lead the league in numbers of tackles or interceptions does that mean that you are very good at tackling or making interceptions?

It may do, but it may also mean that your team is so bad at holding onto possession that you get substantially more opportunities to attack both the ball and the man than better teams do.

Here, courtesy of whoscored, is the current EPL table for tackles, and it has been ranked in descending order.

Is Crystal Palace really the best team at tackling in the Premier League?

No, I don’t believe they are, and this is the point.  There has been a lot of work in the last year or so on the attacking metrics in football (examples include Expected Goal values, per90 figures and shots from Prime locations) but so far the defensive side of the game has been largely ignored.  There are many reasons for this, including defending being more about a team unit than individual actions and positioning data arguably being more important in trying to understand defence than attack.
But in my opinion there is another more basic problem with trying to ensure that people begin to look at the defensive side of the game from an analytical point of view.

According to wikipedia, a league table is defined as:

“A league table is a chart or list which compares sports teams ….. by ranking them in order of ability or achievement.”

Due to the metric that is currently common place, the use of absolute values, the league tables that rank defensive measures don’t achieve their basic intention, ie ranking the teams in order of ability.  This is a fundamental flaw and one that needs to be eradicated.
In order to achieve the aim of ranking teams on ability, a different system of measuring the defensive actions needs to be introduced.  We need to normalise the defensive actions carried out by each team.

Normalising Defensive Actions
I propose normalising the defensive actions by reference to the number of passes that each team concede.  A tackle or interception can only be attempted when the opposition is in possession of the ball. So by looking at defensive or pressing actions compared to the number of passes that each team conceded we will have a fair basis on which we can rate each team’s ability to tackle or win the ball via an interception.

The table below shows the total number of Interceptions, Tackles, Combined Pressing Actions (sum of Tackles & Interceptions) as well the number of passes conceded by each team during the first 7 games of the 2013/14 EPL season.

[table id=31 /]

The stats for the above table have come from StatsZone and Whoscored, both of which are powered by Opta

PAPI – Passes allowed per Interception
PAPT – Passes allowed per Tackle
PAPPA– Passes allowed per Pressing Action

The final 3 columns in the table show the number of passes that each team has conceded on average for every interception, tackle and combined pressing action (either an interception or a tackle) they have made.
NOTE – In the final 3 columns in the above table the lower the number the better, ie teams allow fewer passes before they perform the Pressing Action.

Take Arsenal as an example. On average they have made an interception every 33 passes they have allowed, a tackle every 24 passes and either a tackle or an interception every 14 passes.

Feel free to play around with the table by sorting the various columns.

Tackles
Revisiting the Tackles table as presented by whoscored we remember that Crystal palace topped the table.  Using the PAPT (Passes allowed per Tackle) measure I would suggest that 6th place would actually be a fairer reflection of their tackling prowess.  The team that allows the fewest number of passes (less than 18) before they are able to get at tackle in is Southampton.  This fact instinctively seems correct as the Southampton manager, Maurico Pochettino, insists on a high press in an attempt to ensure that the Saints win the ball back quickly.

Other teams to note are Man City, Liverpool and Everton who just trail behind Southampton in their efforts to put the opposition under pressure by way of tackling.
At the wrong end of the scale is Fulham who need to see 33 passes being made against them before they are able to apply pressure to the man in possession (tackle).  Perhaps this can help us to understand just why Fulham have been so poor this season.

It is understandable that teams with lower budgets struggle from an attacking point of view, but it is much more difficult to understand why teams such as Fulham and West Brom are so far behind on their tackling rates.  The type of player that can make an impact on how often a team can tackle can be obtained for fractions of the cost of top attacking talent.

Interceptions
Man United top the Interceptions table by snaffling the ball once every 23 passes.  Interestingly, there have been approximately 50% more tackles than interceptions in the EPL so far this season, yet the top two teams on the PAPI (Passes allowed per Interception) metric, Man United and Swansea, actually managed to achieve more interceptions than tackles.
This fact is quite significant and it perhaps suggests that these two teams play on the counter attack by being more interested in breaking up the opposition’s attack by way of an interception which should then lead to a more effective counter of their own.

Seeing Chelsea right at the bottom of the PAPI table seems like a surprise.  It’s not normal to see one of the stronger teams at the bottom of any league table.  Unfortunately for Sunderland, the same can’t be said of them and they hold the same place in the PAPI table as they do in the real league table.

The teams’ style of defence can be quickly seen and compared in this Scatter Plot:

(The chart can be clicked and opened in a separate window for clearer viewing)

Visually a few things jump out at us from that image.

• Chelsea and Sunderland defend using the same styles?
• As a Mourinho team (counter attacking) I wouldn’t have expected to see Chelsea’s with virtually the most infrequent rate of interceptions – they are at the opposite end of the scale to Man United.
• Fulham and West Brom defend in the same way. By this I mean they neither pressurise the ball nor the man.
• Swansea and Southampton are often grouped together as being pressing exponents, but it is clear that, at least over the opening 7 games, Swansea put much less pressure on the man in possession than they do the ball.

Combined Measure
The PAPPA (Passes allowed per Pressing Action) is an aggregated measure that tells us how aggressive a team is in defence on the basis of both tackling and forcing interceptions.

As with the PAPT table, Southampton takes pride of place at the top of the heap and they are being chased up by AVB’s Tottenham with Man United close behind in 3rd place.

Foundation
The figures presented in this piece are the foundation that I believe will lead to further analysis, quantification and understanding of defensive styles and strategies.  The hope is that metrics that actually mean something are brought into use on the defensive side of the game.  Undoubtedly this will then encourage a deeper understanding of how teams defend and the merits of each type of defensive system.

For example, Liverpool and Man City seem to have plenty of aggression which allows them to execute tackles at a high rate (pressure on the man), but they don’t feature as prominently in the PAPI (pressure on the ball) rankings.
Man United are the opposite and then there are teams like Southampton, Tottenham and Everton who are fairly aggressive in both defensive facets.

Are there defined strategies at work here, or with just 7 games played is there still an element of variance in the numbers in these tables?  Time will tell.

Conclusion
I’m conscious that there are many ways to defend, and teams that employ an aggressive high press will tend to appear at the top of these metrics.  That’s not to say that this is the correct way to defend.

The aim of this piece was to begin to quantify and attempt to develop the use of meaningful defensive metrics. As a result we at least can understand show many more passes a team will be allowed to take if they play against a deep lying passive defence (Sunderland) compared to a high energy tacking defence (Southampton) and we can think about making informed decisions about which defensive style is appropriate.

• ilr

Really interesting piece. Just thinking though, isn’t there a bias towards valuing teams that press (either ball or man) so that teams that defend by compacting the team and sitting deep can be undervalued? I think that explains why west brom and hull feature so low on your tables, when in fact both of those teams seem to have had pretty effective defensive performances so far this season (admittedly after a poor first couple of games for wba). I guess this kind of defending, relying on limiting space and positioning is even harder to capture in statistical metrics…

• Colin Trainor

Indeed. I make the point of saying that there is more than one way to defend.

The purpose of this piece was to make sense of the meaningless tackles and interception tables that we see published.

We have the stats to capture the defensive efforts of pressing teams. Next exercise is to suggest which stats or measurements may show how the likes of West Brom and Fulham defend?
I’m currently thinking of things like the number of incomplete passes in final third or number of through balls permitted or entries into penalty area etc.

• ilr

Those ideas sound promising I would think. Also wonder how things like the heat map technology we see sometimes might show defensive positioning, but no idea if/how this could really be quantified. Generally think you might have the right idea judging a team’s defence by measuring numbers of opposition actions rather than their own numbers of tackles etc. Makes sense as it’s about limiting opponents I suppose.

That’s wonderfull you started writing on defence. A few comments from my side,
1. Interceptions and (Succesfull) Tackles are the way to recapture possesion, thus you can see from your statistics which teams try to get possesion with those methods.
2. the alternative way to defend was mentioned in the comment above – stay deep, compact, prevent from shooting. Clear balls, block shots and so on… compactness can be difficult to capture, but blocks, clearances and some general shot preventions is achievable.
3. It might help to see where the tackles were performed/attempted, it can be a hint for compactness or sitting deep.

As seem there is much to do and I’m glad you have started.

• marlon

This reminds me of MiPMoP. Wonder how different it would look using possession rather than passes.

What about shots per final third pass conceded? (For West Brom etc.) A low number would indicate a team that is happy to concede possession in favour of maintaining a compact defensive shape. This is great stuff, but is only really descriptive. To find a good defensive metric, we’d have to find one that correlates well with goals conceded (or perhaps ExpG).

In terms of pressing, I know that opposition time per possession (the average amount of time your opponent spends with the ball, before being dispossessed) has a poor correlation with goals conceded (less than 0.1, I think).

• Colin Trainor

My understanding is that possession is calculated on the number of passes that each team has had. So should be the same.

This was very much an introductory piece and was intended as being descriptive. We need to be able to describe something properly before we can delve in and see the impact it has and work out how to influence it.

As always, much more detail is required. I’ll definitely be revisiting this again.

• marlon

Definitely has descriptive value. Kind of like Ben Mayhew’s charts. I know who scored uses passes for possession, but I think Sqwuaka has the actual numbers.

• Nick

As with average position of players, we must be able to develop an average location for INTs & Tackles. This should give a clue about how high a team presses or how deep they sit. Would also add more description. Then could compare all teams whose average pressure on ball is 21-30 yards out, & 31-40, 41-50, etc.
Good stuff.

• Steve

Great article on Defensive metrics and lots of food for thought here on the best way to analyse defensive effectiveness. I’ve really been enjoying the articles you are posting to statsbomb.

The PAPT vs PAPA diagram is a good one for comparing different approaches towards defending and comparing different teams results and I think normalising by the number of opponents passes gives a good indication of the effectiveness of the team in question at breaking up the opponents play.

It got me thinking around a different metric to help measure Defensive effectiveness and efficiency overall.

Generally the most effective way to defend is to “park the bus” and allow a minimum of opposition shots from dangerous areas, and therefore a small number of shots on target. You will often see this where a team allows a high number of opponents possession, passes and shots but very few from dangerous areas, and thus a low number of high quality shots per game. Games like Chelsea’s Champions League final defeat of Bayern or Inter’s Champions League defeat of Barcelona spring to mind as examples.

In the way that Shot Domination gives an effective view of the balance between defence and offence by measuring how many shots on target a team allows against how many they generate each game, I think it would be interesting to analyse Defensive Effectivness by calculating a metric of how many opponents pass attempts it takes to generate a shot on target.

PAPPA seems to me to be very related to the quality of a defences pressing ability to break up oppositions play (ie: the process of how they defend) but I think if you extended the analysis to compare against an outcomes based metric realted to goals conceeded (like shots on target conceeded per opposition pass attempt) you would have a richer view on the overall effectiveness of a teams defence.

Keep up the great work 🙂

• Colin Trainor

Steve, thanks for leaving that detailed comment and I’m glad that enjoyed it.

This article was my first ever attempt at looking at what defensive metrics could tell us. As I was writing the article I realised that I was really measuring pressing as opposed to pure defending, and I said as much in the article.

I wanted to introduce the concept of normalizing for opposition passes so that the ranking system would start to mean something.

There is so much more to look at from a defensive point of view, and thanks to comments like yours and tweets that readers have sent me I have a few ideas for how to move this forward.

• Sage

I ‘m having a hard time intuiting what PAPPA is because a poor press can be dribbled through as well, and that might be hard to catch using possession. The goal conceded consideration seems very promising.

As a general aside, how were these features selected? I’m a newbie interested in developing useful analytics so I’m curious how to go about that.

• Conjoy

Part of the question surely needs to be what exactly are you trying to measure – volume of pressure, effectiveness of pressure, effectiveness of turnovers, minimisation of opposition good quality chances? Below are a few thoughts on your piece.
For instance, the Swansea (Barca) approach is surely to maximise the first three measures, these teams often struggle if their initial press is broken and then concede high-quality chances. This is compounded by the issue that the Barca approach is also highly energy intensive and thus can lead to these teams tiring late in games.
To look at the different measures:
Volume of pressure: a young team with high energy levels and aggressive approach may attempt a lot of tackles, but be shrugged-off, leading to less effective pressure (see Arsenal circa 2007-2010).
Effectiveness of pressure is measured in the volume of attempts – an aggressive pressing team, but also in the quality of the players – better quality players time their tackles and interceptions better.
The Prem is largely a fast-break league, the effectiveness of challenges (pressure) – how many lead to attacks at the other end?
From a purely defensive stand point, the measure needs to come back to minimising opposition good quality chances.

While I really like your attempt as a starting point, I think its worth noting, that possession does not equate to defensive ability in all cases, see Swansea and Arsenal until last year.
The great Franco Baresi taught Maldini that the perfect game from a defender was one in which he never made a tackle. In fact, Zonal marking did a very good article on the move away from tackling towards interceptions in the last 12-18 months.

• Luke

The characterisation of teams who make a lot of tackles being a high pressing team and teams who intercept more being a counter attacking team is flimsy at best. Prime barca did not have to win lots of tackles. I would imagine they made more interceptions. Was more about getting the opposition to panic and misplace passes.

When it comes to the level of pressing location is clearly of more value than the type of ball recovery.

• Colin Trainor

This article was an introduction into how to make better sense of the pretty much the only defensive measures that sites like whoscored display – interceptions and tackles.

I wanted to show how, by controlling those stats for number of passes conceded, we could at least have those measures mean something.

You will note that (with the exception of the teams wth really low numbers) I didn’t pass any comments as to whether a team defended well or not. This piece was never intended to arrive at those conclusions, as much more work will need to be done to arrive at that place.

Where it goes from here will be important, and there has been a lot of great ideas in the comments that I may incorporate in further looks at this.

But be patient, this was just Step 1 in what will be a long and slow process. I had to start somewhere – we now have a benchmark.

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• Duncan

This was a great icebreaker and I look forward to seeing where things lead. A good defense simply does not concede scoring opportunities, but how to measure it is certainly a devilish question. I guess we have to statistically describe two things; how a team defends, and how effective that defense is. For the former, would a measure of the % of opposition position in final third/close proximity to the box be a way to describe the high vs. low line? I like the idea suggested of the number of passes/attacking movements to quality scoring opportunities as a way of measuring defensive performance, but counter-attacking opposition would likely create positive statistics, even if the results on the pitch were unsuccessful.

• ginolasleftfoot

Loved the topic. Totally agree with the lack of depth when assessing collective and individual defensive actions. I’m intrigued to know what the correlation between overall attempted tackles and interceptions in relation to the successful attempts you’ve used would show?
Are you able to source the equivalent data from the prominent European leagues? It would give an amazing insight to the styles of play.
Finally, I blog for http://espurs.blogspot.co.uk/2013/10/townsend-and-baines-not-hbo-cop-show.html
and would love to use some of your graphics in future pieces. Totally understand if not, but would be awesome if so.
Glad I came across the site.
@ginolasleftfoot

• Colin Trainor

Thanks both to you and Duncan for the comments.

As I said, I’ll revisit this at some time in the future and I would hope to go into more depth in a future examination.
I’m happy for you to use my images so long as you clearly credit me and link to my twitter.

Cheers

• Toshack

Colin,

Good to see importance being made on the defensive side of football!

I know I’m late posting my comment and I appreciate this is early days yet. Still I would like to offer a kind of more “philosophical” view (touching on what Conjoy mentioned):

Defensive play is so much about what is not happening. Not conceding a goal, not conceding the ball, not making mistakes, not making rash challenges, a shot not taken, a cross not made…
And counterintuitive here is the fact that 0>1 when it comes to defence vs. offense. As showed in “The Numbers Game” (based on stats from a decade of PL games ) not conceding a goal will on average give you 2.5 point a game, whereas scoring one goal will on average give you about one point.

It’s also interesting to see Liverpool at the top end of tackles in your piece– as opposed to interceptions – given Xabi Alonso’s statement on tackling (from 2012): “I can’t get into my head that football development would educate tackling as a quality, something to learn, to teach, a characteristic of your play. How can that be a way of seeing the game? I just don’t understand football in those terms. Tackling is a [last] resort and you will need it, but it isn’t a quality to aspire to, a definition”. So for Alonso tackling happens when something goes wrong, not right.

Paolo Maldini rarely made a tackle; he never had to get his legs dirty because he was always in the right place to cut off danger. The best defenders are those who never tackle. The art of good defending is about dogs that don’t bark.

This is in no way written to be critical towards the work you are doing; I’ve been longing for this to come for some time. It’s just to point to how difficult it is to find good defensive metrics, as the defensive work is so much about non-occurrence. I truly believe that we need more defensive metrics as the offensive ones does not tell the full story, far from it, so this is a very good start!

Cheers,
Peter

• Leron

Well Done Colin, very interesting,
If a team makes a pass in the final third in order to break the oppositions lines, which could be classified as an attempted goal scoring chance or dangerous attempt to break the opposition’s defense. This would be classified as an interception by the opposition, while this is is no way the same as a poor pass in midfield which the opposition picks up.
A good team would be instructed to make as many potential defense splitting passes as possible, which potentially would skew the stats, this would also alter the stats of defensive teams. If potential defense splitting passes or final third passes were removed it may change the statistics to show a clearer difference between the teams.

• Abubakar muazu

Impressive. I think teams defensive ability can be more accurate if its calculated by number of key passes a team concided. Defence is the ability to prevent your opposition from creating chances.

• Errorr

This is a really valuable way to interpret stats that are easily accessible to the masses although I am just as disatisfied as everyone else with the lack of quality data.

For a little push back I feel as if many in the analytics community like to focus on preventing chances over defense as a whole. I see defense being implemented in significant possible varieties. Here is how I conceptualize it.

1. Prevent Goals (ultimate purpose of a defense)

Given the above purpose there are 2 ways to achieve the above result
a. prevent a shot through dispossessing other team (covered in this post)
b. force shots to locations with low probabilities of scoring

I’m not sure that one is necessarily superior than the other. When I think of “parking the bus” like what Chelsea did against Barca in Champions League on the way to winning I assume the purpose is more b than a. While high pressing is more a than b. Neither is inherently superior and a dominant defense may well do both.

The hardest part of sports analytics is teasing out random chance from skill.

• Colin Trainor

This piece was really a feeler for me and an introduction into what might be achieved when analysing defensive metrics.
You are correct that I majored on your point (a) in this piece, and that is because I had seen very little / no work in this regard. Myself and a few others had done a lot of work on shot locations, so I wanted to come at it from the otehr side.

Of course, the Holy Grail would be to meld all facets together. That might happen in the future, or might just be too tall a task, but I’m sure I’ll ahve fun trying.

I’ll certainly bear your points in mind for any future work in this area

• Arsenal Hipster

Recommendations
1. Looking at additional available stats like shots conceded per game
2. Analyzing the positions these shots are taken from, to understand which teams concede dangerous/safe shots.
3 . Possibly maybe narrowing your PAPPA down to specific 3rds of the pitch, to better understand where the ball is being won by these teams. I’m not sure the stats needed to do all 9 zones of the field are publicly available though

The PAPPA stat is a good idea, and I wouldnt be surprised at all if such a statistic was being sent to coaches after every game. However you recognize its weakness in that its weighted heavily towards teams that press aggressively. No surprise that Southampton’s defense is at the top of the list.

The question is then how can we account for this and improve this metric. Or even create a new metric that better analyzes teams that tend to sit deep.

Not sure but you’ve got me thinking. Great article btw.

• Colin Trainor

Hi Arsenal Hipster,

Thanks for letting me know that you enjoyed the article and also for your suggestions on improving on the metric.

Like you, this article has helped me to have further thoughts on this side of the game and I’d certainly like to expand on this in the future. I will just say that I tried to stay away from assessing the quality of defensives in this articles, ie I don’t necessarily want to conclude that this is the “best” way to defend.
That’s a whole otehr subject on its own……