There comes a time in your adolescence as a stats writer when your parents rudely awaken you in the middle of the night, bundle you into a car, and drop you in the middle of a dark forest with nothing but a sharp stick. “It’s time you made your own defensive metric,” they tell you before receding into the darkness. It is a rite of passage every statto must endure alone.

Frightened and cold, you look for shelter. xG, you think. I know xG, good old xG, I can use that for something! But others have been here before, the forest has been hunted barren. What about those bright green diagrams everyone claims to like, could I just use those? Carving numbers into trees with your trusty pointy stick, you get to work.

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As anyone who follows this blog will know, I’m quite interested in space and how teams use it. Today I’m going to look at the territory claimed by defenders and I’m going to propose a metric based on the actions they allow within that territory. It’s just one metric, it’s not the be-all and end-all of measuring defenders or defences, but I think it’s vaguely interesting, and its opinion on a lot of defenders is defensible. It has some flaws that’ll probably be obvious to you, but I’ll mention them as we go.

What does a defender’s territory look like? Here’s how Arsenal looked against Tottenham in the North-London derby:

Here’s Aston Villa’s clean sheet against Manchester City:

And here’s Newcastle from their 1-0 smash and grab against Bournemouth:

These are similar to my shot buildup charts, but for defensive actions. For each defender, we take all their own-half defensive actions (tackles, blocks, interceptions, clearances, aerial challenges and indeed fouls), and draw a line around them. This is their territory, it’s the part of the pitch they seem to want to be responsible for.

Now you could argue we could just split the final third of the pitch into four and assign each slice to a defender, but I think the overlaps are very valuable here – you want to know if a defender drifts inside or out, how far they push forwards etc. Obviously drawing the lines like this leaves gaps – nobody’s taking responsibility right at the edges or corners of the pitch. There’s also the problem of a player that makes a single tackle on the other side of the pitch, stretching their territory, perhaps unfairly. We could add a bit of a buffer zone to these areas, and trim some outliers, but for now I’m happy with them as they are – they are the best way we have of outlining a defender’s territory, based entirely on where the defender tries to defend.

Glancing at the charts above, you’ll notice some players have more territory than others. We want a metric that rewards this, if possible – if a player is bossing the entire danger zone, that’s great, even if you might prefer to see their team-mates step in. So our metric’s first ingredient is the surface area of a defender’s territory.

But the positioning on its own is meaningless, we want to know how much control they exert in that space. For this, we count the number of touches opponents take in the defender’s territory. These aren’t touches as you see them on TV, these are just all the aggregate events we see in the data – passes, dribbles, shots, all the stuff opponents want to do in our half. We have to be careful here to count points inside the territory, and only those that overlap the defender’s time on the pitch.

We combine these by dividing the area by the number of touches, then we weight things by possession and per-ninetify everything. What you should picture is the defender scent-marking their territory (I find it easiest to picture John Terry doing this, for some reason), and then every opposition action diluting that scent more and more. Larger territory will necessarily be exposed to more opposition actions, but good defenders will prevent and repel as much of this as possible. Players that make fewer defensive actions will have tiny territories, but can still score highly by keeping opponents out.

What’s nice about this particular metric is that it doesn’t force you to work out whether tackles or interceptions or aerials or whatever are more important, and it doesn’t require you to look at shots and xG (or expected assists etc). It captures defensive pressure in open play, which is where most defending happens.

So, recapping the algorithm:

Area ÷ Opposition Touches ÷ Possession ÷ Minutes Played × 90

I like to refer to this as ‘Possession-adjusted Territorial Control Held’, or PaTCH. I am not good at acronyms, please suggest more. In the meantime, which defenders have a good PaTCH?

Player	Team	PaTCH
Gabriel Armando de Abreu	Arsenal	596.2
John Terry	Chelsea	302.0
Chris Smalling	Manchester United	268.2
Cedric Ricardo Alves Soares	Southampton	265.4
Nicolás Otamendi	Manchester City	261.9
Matteo Darmian	Manchester United	256.7
Sylvain Distin	Bournemouth	255.1
Eliaquim Mangala	Manchester City	250.1
Sebastian Prödl	Watford	248.4
Virgil van Dijk	Southampton	238.4
Mamadou Sakho	Liverpool	237.2
Joleon Lescott	Aston Villa	233.2
Allan-Roméo Nyom	Watford	226.6
Fabricio Coloccini	Newcastle United	226.4
Aleksandar Kolarov	Manchester City	209.8
Neil Taylor	Swansea City	208.4
Ashley Williams	Swansea City	202.1
Laurent Koscielny	Arsenal	195.3
Simon Francis	Bournemouth	194.4
César Azpilicueta	Chelsea	189.2
Luke Shaw	Manchester United	187.7
Kurt Zouma	Chelsea	185.4
Toby Alderweireld	Tottenham Hotspur	185.0
Ryan Bertrand	Southampton	182.2
Steven Whittaker	Norwich City	176.8
Gareth McAuley	West Bromwich Albion	175.1
Micah Richards	Aston Villa	174.3
Jose Fonte	Southampton	171.8
Russell Martin	Norwich City	171.0
Glen Johnson	Stoke City	170.9
Jeffrey Schlupp	Leicester City	167.3
Daley Blind	Manchester United	163.9
Bacary Sagna	Manchester City	158.7
Phil Jagielka	Everton	158.4
Nathaniel Clyne	Liverpool	158.3
Ciaran Clark	Aston Villa	155.5
Federico Fernandez	Swansea City	150.3
Sebastien Bassong	Norwich City	148.9
Vincent Kompany	Manchester City	146.4
Per Mertesacker	Arsenal	146.0
Martin Kelly	Crystal Palace	145.1
Nacho Monreal	Arsenal	142.1
Craig Cathcart	Watford	139.9
Joel Ward	Crystal Palace	138.1
Martin Skrtel	Liverpool	138.0
Charlie Daniels	Bournemouth	135.7
Ben Davies	Tottenham Hotspur	135.2
Joseph Gomez	Liverpool	134.9
Robbie Brady	Norwich City	134.7
Winston Reid	West Ham United	132.8
Jan Vertonghen	Tottenham Hotspur	132.1
Alan Hutton	Aston Villa	131.9
Jordan Amavi	Aston Villa	128.6
Aaron Cresswell	West Ham United	128.4
Maya Yoshida	Southampton	127.4
Tommy Elphick	Bournemouth	126.6
Héctor Bellerín	Arsenal	119.5
Philipp Wollscheid	Stoke City	119.4
Branislav Ivanovic	Chelsea	117.8
Kyle Walker	Tottenham Hotspur	116.9
Geoff Cameron	Stoke City	116.8
Erik Pieters	Stoke City	116.0
Carl Jenkinson	West Ham United	115.7
Gary Cahill	Chelsea	114.5
Marc Muniesa	Stoke City	114.3
Kyle Naughton	Swansea City	111.3
James Tomkins	West Ham United	110.8
Scott Dann	Crystal Palace	107.7
Steve Cook	Bournemouth	107.0
John Stones	Everton	106.8
Daryl Janmaat	Newcastle United	104.4
Jonny Evans	West Bromwich Albion	103.7
Chris Brunt	West Bromwich Albion	103.1
Ritchie de Laet	Leicester City	103.1
Danny Rose	Tottenham Hotspur	100.0
Wes Morgan	Leicester City	97.4
Robert Huth	Leicester City	95.3
Brendan Galloway	Everton	95.0
Dejan Lovren	Liverpool	92.3
Billy Jones	Sunderland	90.7
Nathan Aké	Watford	90.2
Pape Souaré	Crystal Palace	85.4
Seamus Coleman	Everton	84.6
Massadio Haidara	Newcastle United	83.2
John O’Shea	Sunderland	82.7
Younes Kaboul	Sunderland	80.5
Craig Dawson	West Bromwich Albion	77.5
Chancel Mbemba	Newcastle United	74.0
Damien Delaney	Crystal Palace	70.1
Sebastián Coates	Sunderland	69.1
Patrick van Aanholt	Sunderland	68.4
Brede Hangeland	Crystal Palace	64.6

These are filtered for defenders with 450+ mins (all data from before Saturday’s games), and I’m calculating the average PaTCH over those games. Note: as usual, ballsed up a bit, the graphics show territory marked out in the defender’s own half, the numbers are actually calculated for territory in the final third. But it’s cool, cos comparing the two sets of numbers will make for an interesting article in a bit.

Gabriel is such an outlier because of Arsenal’s 1-0 win over Arsenal, in which Mitrovic got sent off and Newcastle had one shot. Look at the territory:

Now look at the heatmap from the BBC (Newcastle on the left):

Newcastle had one touch in his territory, as far as I can tell, giving an astronomical match PaTCH (yup) in the three-thousands. Anyway, I will think of some better averaging or thresholding to reduce the impact of stuff like this, but still, he sort of earned it.

Elsewhere, you can see the model doesn’t like Sunderland or Crystal Palace much, but is a little bullish on Aston Villa’s defence. Of course this weekend Lescott was benched against Everton, and Villa decided to sit very deep and let Everton play, with horrific results. Everton themselves seem to have ridden their luck a few times – Galloway, Coleman and Stones bomb forward regularly and rely on Barry and McCarthy to pick up the slack in their territory, something I’d like to capture in the numbers at some point. Terry is still good at some stuff, Smalling’s number is consistent with the hype, Otamendi is predictably up there, and Koscielny is doing fine, though he’d probably benefit from that forever delayed defensive midfield signing for Arsenal. Lovren near the bottom, below every Liverpool and Southampton player.

For now, I’m reasonably happy with who shows up at the top and bottom. Over the next few days I’ll play with some historical data to tell some stories, incorporate this metric with a Christmas Shopping piece about defenders, then make some visualisations to see if there’s a good counterpart to the attacking buildup maps.