Revolutionary Space Analysis in Professional Football

OK, let's think about football. Not just, you know, the players

kicking the ball around, but the actual stage itself, the space,

creating it, using it, shutting it down.

It's this like constant invisible dance happening

underneath everything else. It really is.

It dictates so much of the game. And it's absolutely fundamental

to tactics to success. But how do you actually measure

it scientifically? Well, that's been the challenge

for years. Analysts have tried to get a

handle on it. You know, how do you quantify

who controls what part of the pitch, right?

And the traditional approach, especially once we got all that

player tracking data, involves something called a Voronoi

diagram. Ah yes, the Voronoi diagram

sounds a bit technical, but the basic idea is pretty graspable,

isn't it? Yeah, it is actually.

Basically, you take every player on the field at a specific

moment, OK, and the diagram figures out for any single point

on that pitch which player is the closest geometrically

closest, just pure distance. So it carves up the field like

into little zones. Exactly.

It partitions the whole pitch into these regions, OK.

And every single spot inside one player's region is closer to

that player than to any other player on the field.

Gotcha. So you get this visual map like

OK, right now this patch belongs to player A, that bit to player

B based purely on who's standing closest.

That's the essence of it. It was really the first big step

in trying to visualize and quantify spatial control.

Who seems to own what area just by being positioned there?

And you can see why that would be useful initially.

A snapshot of who's near what. Definitely as a static picture

it was quite insightful when it first came out.

It gave a clear visual of space occupation based only on

proximity. So analysts could look at it and

maybe see potential passing lanes or maybe where things are

getting clogged up. Precisely that you can see if a

defensive line was maybe too spread out or if gaps were

opening up just based on those closestness boundaries.

It was a way to move from just watching and saying good

positioning to something more well measured.

A baseline, Something concrete. The football's are not static,

is it? Far from it.

Not at all. And as people use this

traditional Voronoi model more, well, the cracks started to

show. The limitations became pretty

obvious. Because it's trying to map this

fluid, fast-paced game with all its rules and physical

differences using just this rigid geometry tool.

Exactly. And some recent analysis we've

been looking into really puts a spotlight on those limitations.

Yeah, but excitingly, it also proposes a much, much smarter

way to look at that battle for space.

OK, so it doesn't just throw the idea out, it improves it.

It refines it dramatically. It challenges the core

assumptions that the old Voronoi method relies on, assumptions

that, frankly, just don't match up with a real football match.

And that sounds like our mission for this deep dive.

We're going to unpack this, this innovative new approach, how it

takes spatial analysis in football and really kicks it up

a gear. We'll see how it manages to

weave in really crucial things like, you know, the actual rules

of the game and the fact that, well, players aren't all

identical clones. Right, the individual abilities.

Exactly. It's about getting a picture of

space control that's not just about static positions, but

about who can genuinely effectively use or influence

that space dynamically. But to really appreciate the

leap forward, we should probably just nail down that starting

point first, the traditional Voronoi model.

OK. Yeah, let's cement that.

So as we said, it's all about closest proximity, pure and

simple. Pick any spot on the grass, any

spot. The model finds the player who

is the shortest straight line distance away from that spot,

and boom, that spot belongs to that player's control area in

the diagram. It's like sticking pins in a map

for each player, then drawing lines exactly halfway between

all the nearby pins. Right?

Those lines make the borders. That's a.

Great way to visualize it. It's mathematically clean based

only on those static locations of that one instant.

And that cleanness is good for a basic picture, but maybe masks

the messy reality. That's the trade off for a

simple visual. It gives you a neat breakdown of

territories. You can see player

concentrations. You can see empty zones.

Know these closes too. Yeah.

I can see the initial appeal for positional analysis.

Quick, low OK defenses, compact here, maybe a gap there based on

these geometric zones. Agree.

It gave a number, a picture to something that used to be just

subjective opinion, You know, they control the midfield,

became their midfielders. Voronoi zones cover X percent of

the midfield area. But like any model that

simplifies things, it makes assumptions.

And sometimes those assumptions, well, they distort the truth.

And this new research we're diving into, it really hones in

on 2 massive assumptions the old model makes.

Assumptions that really limit how accurate and useful it is in

a real game. OK, let's unpack this then.

Two major limitations. You said.

Flaws really, that this recent analysis highlights.

What's the first big one? The first one, and maybe the

most glaring when you stop and think about it, is that the

traditional Voronoi model completely, utterly ignores the

rules of the game. Ignores the rules.

Specifically, it ignores the offside rule.

Wait, what? It ignores offside, but that's

huge. Offside shapes almost everything

about attacking play, about how space can be used, especially

near the goal. How can it ignore?

That it just does. It's purely geometric.

It looks at player X's coordinates.

Player Y's coordinates calculates distances.

It has no concept of the ball's position, or the second last

defender, or whether player X is actually standing in an offside

position. So hang on, if a striker makes a

run, gets clearly offside maybe 10 yards past the last defender,

and you run the Voronoi analysis at that exact moment, the model

will still show all that space behind the defense, the space

the striker is closest to as being controlled by him, even

though he's offside. That's exactly what happens.

It calculates control based on proximity period.

So yeah, it happily includes huge chunks of the pitch that,

because the offside rule the player cannot legally or

effectively use for attacking can play at that moment.

Wow, so that space is basically useless, ineffective space, you

might call it. That's a perfect term.

Ineffective space or Dead Space for that attack.

It's space the player might be physically closest to, but they

can't receive a pass there legally.

They can't score from there. If the ball will rhymes then

it's irrelevant for the attack at that instant.

But the traditional model it colors it in and says this is

that player's territory. So you're looking at this map,

this Voronoi diagram, and it's telling you your striker

controls this massive area deep in the opposition half.

But the reality is they can't actually do anything meaningful

in most of that space because they're offside.

That's not just a small error, that's fundamentally misleading

about usable space, isn't it? It's fundamentally misleading

about usable space, yes. The analysis isn't making that

crucial distinction between space that exists geometrically

and space that's actually playable according to the the

rules. It's calculating this

theoretical control based on location, completely blind to

the practical constraints of the game.

It's particularly bad for analyzing attacking threats

because it massively overestimates the areas

attackers can genuinely influence.

It's like planning a journey using a map that shows roads

that are actually closed for construction.

The roads on the map, but you can't drive on it.

Exactly. The space is on the Voronoi

diagram, but the player can't legally play in it.

OK, wow, so limitation #1 ignoring the offside rule, which

means counting ineffective space.

That's a biggie. What's the second major problem

with the old model? The second limitation is all

about the players themselves, their physical abilities.

The traditional Voronoi model works on an assumption of, well,

homogeneity. Homogeneity meaning.

Meaning, it assumes every single player on the pitch is identical

in terms of their physical capabilities.

Specifically, it assumes they all have the exact same maximum

speed and the exact same maximum acceleration.

Hold on. It assumes everyone runs at the

same top speed and everyone accelerates at the same rate.

OK, That's just not reality, is it?

Yeah. I mean, even casually watching a

game, you see massive differences.

You've got players who are lightning fast, others who are

quick off the mark. But maybe lack top end speed and

let's be honest, some who are just slower.

Precisely. Football features an incredible

range of athletic profiles, so assuming everyone is physically

identical is a huge oversimplification.

And why is that a problem for analyzing space?

Because controlling space isn't just about who's standing

closest right now in a static picture, It's dynamic.

It's about who can get to a certain patch of grass first, or

who can influence it most quickly.

OK, I think I see. If you have two players, say

both 10 meters away from a loose ball, but one player has way

better acceleration or higher top speed, if it's further away,

that faster player is going to reach the ball first.

They effectively control that space more decisively, even if

he started at the same distance. The old model misses that

completely. Completely misses it.

It would just draw the halfway line between them and say they

control equal halves of the path to the ball based purely on that

starting distance. It doesn't factor in that one

player might cover those 10 meters much, much faster.

So the player with better speed or acceleration can in reality

control a bigger area dynamically.

They can cover ground faster, close people down quicker, burst

into space before defenders react.

Exactly. Their superior physical

attributes mean their effective area of influence is larger or

reacts quicker than the model suggests.

The traditional model, by assuming everyone moves the

same, gives you this distorted view.

It assigns space based on geography alone, ignoring the

reality that a faster player can dominate that space much more

effectively than a slower player, even if they start eco

distant. It's measuring static proximity,

not dynamic potential or control.

OK, so let me sum up these two big flaws.

The old Voronoi model. Number one, it ignores the

offside rule, so it counts space that's basically useless for

attacking play #2 it pretends all players are physically

identical, ignoring the huge impact of speed and acceleration

on who can actually get to and control space dynamically.

That's the crux of it. It's missing the game's legal

framework for space usability, and it's missing the individual

dynamic capabilities of the players, which means the picture

of space occupation it provides is simplified, often inaccurate,

and doesn't truly reflect how space is contested and used in a

real match. Right.

Which brings us to the really exciting part.

This new model, the one that tackles these problems head on.

This isn't just tweaking the old way, is it?

It sounds like a proper leap forward.

It really is. It's a much more sophisticated

approach. So how does it deal with that

massive offside blind spot? OK.

So the first key innovation is integrating the offside rule

right into the calculation. It's not just about geometry

anymore. It understands the rule.

It understands the context, it knows where the offside line is

based on the second last defender.

It knows where the ball is, it knows where the attacker is

relative to those things. So it's smart enough to say, OK,

this attacker is technically closest to that space behind the

defense, but they're offside, so that space doesn't count as

effectively controlled by them right now.

Exactly that. It runs the spatial calculation

but applies a critical filter based on the offside rule.

It actively distinguishes between effective space areas a

player can legally and realistically influence or

occupy, and ineffective space. The Dead Space we talked about.

Precisely those areas that might be geometrically close but are

unusable for attacking because of offside.

The model essentially filters out or discounts those dead

zones, so the map it produces reflects the playable space, the

space that actually matters tactically at that moment.

Wow. That must clean up the picture

massively, especially when looking at attacking situations.

You're not getting fooled by an offside player or seemingly

dominating territory they can't use.

It gives a far, far more realistic view.

You see the areas that are genuinely controllable and

usable. It's mapping effective presence,

not just physical presence. It reveals the true passing

options, the areas under genuine defensive pressure.

It's like adding real time traffic data to that map app.

Showing you the roads you can actually drive on, not just the

ones that exist. Exactly.

OK, that's huge. Integrating the offside rule

makes it rule aware. Now what about the other big

flop pretending all players are athletic equals?

How does the new model handle the reality of different speeds

and accelerations? This is the other really clever

part. It ditches the homogeneity

assumption entirely. It adjusts the spatial analysis,

refines those Voronoi style areas based on individual player

physical data. Individual data?

How does it get that? Does it just guess?

No guessing. It leverages the wealth of

tracking data we now have from matches.

It looks at a player's history. What's their typical and maximum

Sprint speed? What's their peak acceleration

capability observed over many games?

OK, so it uses historical performance data for each

player, right? And then then when it's figuring

out who controls a point on the pitch, it's not just asking

who's closest, it's asking a more complex question.

Considering where each player is now and knowing their individual

speed and acceleration profiles, who can realistically get to

this point and influence it the fastest?

It factors in the time to reach relative to nearby opponents.

Whoa. OK, so it's not just distance,

it's time. A player who's maybe slightly

further away but has incredible acceleration might be deemed to

control a nearby space more effectively than a closer,

slower player. Precisely.

Or a player with a really high top speed might exert influence

over space much further downfield during a fast break,

because the model knows they can cover that ground much faster

than others. It recognizes that physical

attributes directly translate into dynamic spatial control.

So a player like, well, we'll get specific names later, but a

player known for explosive acceleration, the model would

show them dominating those little pockets of space that

open up suddenly because they can burst into them quicker than

anyone else. Exactly.

Their dynamic control area in the immediate vicinity expands

much more rapidly in the models calculation, and for a player

known for sheer pace over distance, their potential

control zone stretches much further and faster down the

pitch during transitions or when chasing long balls.

So the control areas aren't just static circles anymore, they're

dynamic stretching reacting zones based on how fast each

individual player can move. A faster player zone is

effectively bigger or reacts quicker.

That's a great way to put it. It's a model of dynamic reach

and influence, not just static closeness.

It understands that the battle for space is won by position and

the ability to cover ground, which makes the whole analysis

far more representative of the actual physical and tactical

contest unfolding on the pitch. OK, so bringing it all together,

integrate the offside rule for effective space, factor in

individual speed and acceleration for dynamic reach.

This new model sounds like it's giving us a map that's finally

ruleware, athlete aware, and truly dynamic.

That's exactly the goal and the power of this approach.

It moves beyond simple geometry to something that reflects the

game's rules and the players actual abilities.

It's a much more holistic and frankly, more useful way to

analyze how teams occupy and control the field.

So, OK, this sounds great theoretically, but what does it

actually mean on the ground? For teams, for coaches, for

analysts? How do they use this?

It can't just be about making fancier diagrams.

Oh. Absolutely not.

The practical applications are where this really shines.

First and foremost, as we've been saying, it just gives you a

much more accurate picture of what's actually happening.

You're seeing not just where players are, but where they can

effectively get to and how quickly.

Precisely, and that accuracy directly feeds into gaining

tactical advantages if you understand, based on this model,

which of your players can dynamically dominate larger

effective areas due to their physical profile.

Or where the opponent is weak in that regard.

Exactly. You can identify specific zones

where maybe an opponent's center back lacks acceleration, making

them vulnerable to quick diagonal runs into the space

beside them. Or you might see that your team

consistently loses control of the wide areas during

transitions because your full backs don't have the top end

speed to track back against fast wingers.

So it pinpoints spatial strengths and weaknesses linked

directly to player athleticism, things the old model would just

average out or ignore. Right.

It gives you this granular view of the spatial battlefield and

that and always provides a really solid data-driven

foundation for strategic planning.

How so? Like deciding formations or

tactics. It can influence everything.

If the analysis shows you consistently struggle to control

the midfield space during turnovers because your players

can't accelerate quickly enough to counter press effectively,

that tells you something concrete.

Maybe you need to adjust your defensive shape to minimize the

distances they need to cover. Maybe you need specific training

drills focusing on reaction speed and closing down.

Or maybe longer term it informs your player recruitment.

You actively look for midfielders with a higher

measured acceleration profile. Or flipping it around.

If you're preparing for an opponent and this analysis shows

their left back has relatively poor maximum speed, you might

design specific attacking patterns to isolate your speedy

right winger against them. Playing balls into the space

behind knowing your player has a measurable dynamic advantage in

reaching and controlling that space first.

Exactly Moves tactical planning from gut feeling about pace to

decisions based on quantifiable dynamic control potential.

It gives you evidence. And what about feedback for

players? It enhances visualization

massively. Coaches can use this analysis in

video sessions to show players not just where they were, but

where the effective space actually was, how their speed

could have allowed them to intercept a pass if they'd

reacted a split second sooner, or graphically show how being

offside nullified the space they thought they were attacked.

It makes the feedback much more specific and impactful.

OK, so connecting this back to you listening at home, why

should you care about this model?

Well, because understanding it lets you watch the game with

like a new layer of insight. You stop just seeing players

running around, and you start seeing this invisible dynamic

battle for usable space. A battle shaped by position,

yes, but also by the offside rule, and crucially, by the

individual speed and acceleration of every player out

there. This model gives us a way to

actually see and measure that underlying tactical struggle.

It helps you understand the why behind certain plays or why some

players seem so effective in certain situations.

It adds depth to the viewing experience.

Totally. And this research we've looked

at, it doesn't just talk concepts, it gives us real world

examples. It actually provides data

ranking players on the exact physical metrics that this

sophisticated model uses to determine that dynamic spatial

control. It does, which is fantastic for

grounding the theory. Let's start with the data they

presented on maximum Sprint speed.

OK, maximum Sprint speeds. So this is flat out top end

pace, right? Covering distance quickly.

Think breakaways tracking back long distances.

Exactly that. This is crucial for controlling

space over larger areas, especially in transitions or

when the game gets stretched. The research gives us a top ten

list based on the average maximum Sprint speed players hit

during matches. Not just a one off peak, but

their typical top speed all right.

Let's hear it. Who are the burners according to

this data? Topping the chart, the player

with the highest average maximum Sprint speed is Marvin UD from

UD Las Palmas. He averaged an incredible 26.29

kilometers per hour. 26.29 Kumar That is absolutely flying on a

football pitch. You can just picture him eating

up the ground on the wing or chasing down a through ball.

Serious pace and right behind him it's really tight.

You've got Becker from Real Sociedad at 26.07 kilometers,

then elsewhere Z the Amerio one at 25.93 kilometers.

And Alvaro from Rio, Vayicano breathing down his neck at 25.92

kilometers. Wow, practically neck and neck

there. Less than half a kilometer per

hour separating the top four. Who else is in that elite speed

group? Rounding out the top group we

have Easy Abde from Real Bet is at 25.91km, Ramzani of the UDM

Area Player at 25.88 kilometers, Jay Araujo back at Uni Las

Palmas with 25.87 kilometers, then a Revzong from DL Ave. is a

25.72, Fern Garcia of Real Madrid at 25.66 and Giuliano

also from DL Ave. is completing the top ten at 25.65 kilometers.

A fascinating list, lots of wingers and attacking players as

you might expect. So let's take Marvin nude again

with that chart topping 26.29 kilometer.

OK, so that lead speed means that in situations involving

significant distance, say a ball played 30 or 40 meters into open

space, the model calculates that his potential control area

expands much, much faster and covers a far larger zone

compared to, say, a defender whose top speed might be closer

to 22 kilometers. So if they both start

equidistant from that space. You'd get there significantly

quicker. The model quantifies this.

It shows his dynamic influence zone stretching rapidly

downfield during transitions. It recognizes his ability to

make distant space effective for his team much sooner than most

opponents could. His speed gives him quantifiable

control over that space earlier. So his high top speed

effectively pulls distant space towards him much more

aggressively in the models eyes compared to a slower player.

He dynamically claims it. That's a good way to think about

it. His speed makes him a major

factor over larger distances. But of course, football isn't

only about 40m sprints. No, definitely not.

A lot happens in tight spaces. It's often about that first,

that burst. Exactly.

Which brings us to the second crucial physical trait.

The model incorporates maximum acceleration.

Maximum acceleration. OK, so this isn't top speed.

This is how quickly you can get moving going from zero to 60,

metaphorically speaking, or changing directions sharply.

Precisely. It's about explosive power over

short distances, reacting to a loose ball that's just 5 meters

away, beating a defender with a sudden shift of pace in the

penalty box, winning those initial moments.

And this is arguably just as important, maybe even more so,

in congested areas of the pitch. Absolutely critical.

It determines who wins those immediate battles for space, who

reacts fastest to sudden opportunities or dangers, And

the model quantifies this too. OK, lay it on us.

Who tops the charts for explosive acceleration?

The. Leader in maximum acceleration

based on this research data is Mendes from UDL Miria.

His figure is remarkable, 5.07 meters per second square. 5.07

meters per second squared. OK, let's give you listening

some context. Meters per second squared is the

rate of change velocity. So every second Mendez can

increase the speed by over 5 meters per second.

That's that's incredibly explosive for a human.

Think lightning fast reaction and take off speed.

It's genuinely elite level acceleration and again it's

tight at the top. Following Mendez, you have

Carlos FDAZ from Real Societe at 5.03m stats.

Then your RQI, the target man from RCD New York, is

surprisingly high, perhaps at 5.0 meters around Show Giroux

Zeta from Athletic Club at 4.96 and Diego Lopez from Valencia CF

at 4.92. Metals in Russia.

Mariki at 5.00. Interesting you think of him

more for strength, but clearly he has that initial burst too.

That's a powerful top five. Who else is in the acceleration?

Top 10 Woolacoo pops up again. Alvaro from Rio Vio Cano is 6th

here with 4.86 metals Barrow. Wow, so he's got the top end

speed and the elite acceleration.

That's a dangerous combination for controlling space

dynamically. A nightmare for defenders.

Then you have Strand, Larson from RC, Celta at 4.85 via

Merrill from CATAFA CF at 4.82. Jeremy from VRL CF at 4.79 and

another Rail player Bailey Yu rounding out the top ten at 4.75

meters emeritus. A really interesting mix of

player types in that list too. So back to Mendez at the top

5.07 meters of batters. How does that kind of

acceleration affect his spatial control on the model compared to

how top speed effects Marvin Odes?

OK, so where Yud's top speed dominates distance base,

Mendez's acceleration dominates immediate space.

In contested situations, that 5.07 meter stretch means he can

cover the 1st, say 5 or 10 meters much much faster than a

player with only average acceleration.

So if a ball breaks loose in midfield or a defender makes a

mistake and a small gap appears. The model shows Mendez reaching

that space, establishing control significantly quicker than

opponents nearby his dynamic Voronoi area.

That zone of influence will expand with incredible

suddenness over those short distances right around him.

It's like an instant reaction bubble popping out from him.

He wins the race to those sudden close range spaces before others

can properly react. Exactly.

He can dominate those critical immediate spatial contests

through sheer explosiveness. A player with high acceleration

like that effectively buys themselves time or creates

separation in tight quarters. The model captures this by

showing their dynamic control area, reacting extremely rapidly

near their starting position. It flags players who can create

or deny space through sudden, sharp movements.

So these lists aren't just leaderboards of fastest players,

they're highlighting athletes who specific measurable physical

traits, top speed for distance, acceleration for immediacy,

directly translate into a greater potential for dynamic

spatial control as calculated by this much more sophisticated

athlete aware model. That's the perfect way to

summarize it. It connects the dots between raw

physical capability and it's tangible impact on the tactical

battle for space, viewed through this improved analytical lens.

This really does feel like it brings the whole discussion

together. You take the rules, the offside

rule, defining effective space, and you combine it with the

reality of individual player physics, speed, acceleration,

defining dynamic reach. And this new approach isn't just

tweaking the old Voronoi idea. It feels like it's fundamentally

changing, redefining how we can actually analyze and really

understand that complex dance of field occupation in football.

I think redefining is fair. It moves spatial analysis from a

relatively simple geometric exercise toward a much more

powerful tool, one that integrates the game's actual

rules and the specific physical characteristics of the athletes

playing it. Which gives everyone involved,

analysts, coaches, even us watching a much deeper, much

more realistic insight into that constant tactical battle for

space that underpins everything we see.

It equips people with information about spatial

control that was previously hidden or just guessed at using

simpler methods. It allows tactics training, even

player signings to be informed by more accurate dynamic

picture. It shifts the whole focus from

just where are they standing to, where can they effectively get

to, and how fast. Precisely from static position

to dynamic potential and effective usability.

OK, so let's just quickly trace that journey again for everyone.

We started with the old way, the traditional Voronoi diagram,

mapping space based only on who's closest simple geometry.

Then we really dug into its big problems #1 ignoring the offside

rule, meaning it counted lots of ineffective unusable space #2

pretending all players run the same, ignoring how individual

speed and acceleration dictates dynamic control.

The. Key limitations.

Then we explored this exciting new model, how it tackles those

flaws head on by building in the offside rule so it only

considers effective playable space, and how it uses

individual player data, their actual speed and acceleration to

model dynamic reach, showing who can really get to space fastest,

The core. Innovations.

We talked about the practical payoff, more accurate analysis,

real tactical advantages, better strategic decisions, improved

player feedback, any useful. And finally, we saw the proof in

the pudding with those player rankings seeing who actually

excels in maximum Sprint speed, like Marvin Ode dominating

distance and maximum some acceleration like Mendez

dominating immediate space. And we talked about what the

specific numbers mean for their dynamic spatial control

according to this advanced analysis.

Making the theory to the players.

Yeah, so the big take away here seems to be, well, that the

fight for space in football is incredibly complex.

It's not just about where you stand.

Far from it. It's constantly shaped by

positioning, yes, but also, crucially, by the rules that

govern play, and fundamentally, by the unique athletic engine

inside every player. Their speed, their burst, their

ability to cover ground quickly. And the really exciting thing is

that new scientific approaches like the one we've discussed are

finally giving us the tools to see and measure this fundamental

aspect of the game with unprecedented detail.

OK, so here's something for you to take away and think about

next time you're watching a match.

Try to shift your focus sometimes.

Look away from the ball for a second.

Watch the players moving without it.

Think about the space they're trying to open up with a run, or

the space they're trying to close down with their speed.

Think about how a player's acceleration lets them burst

into a gap, or how another's top speed lets them track back and

prevent a counter. See if you can spot how their

individual athleticism is constantly redrawing those

invisible lines of control on the pitch.

That dynamic map. Exactly.

And here's a final little thought experiment.

Now what you know about effective versus ineffective

space. How does it change things when

you see a player make a run that's clearly offside?

Before, you might have just seen them running into empty space,

but now do you see it as wasted energy and Dead Space?

Or do you see the potential, the effective space they could have

attacked if the timing or the defender's position had been

just slightly different? It adds another layer to

understanding the tactical choices and the what ifs,

doesn't it? Something to Mull over next time

you watch the beautiful game unfold.

Revolutionary Space Analysis in Professional Football

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