Why Inequality is the Key to Unlocking Football

Modern football is full of people seeking for edges. In a game that demands so many decisions in such slim slivers of real time, metrics and principles can enable players to interpret data more quickly. If they try to take it all in without any structure, they may quickly find themselves drowning in information. A team able to make use of more data in less time certainly possesses a valuable advantage.

Think of it this way: if we go shopping for a new car, it’s easy to be overwhelmed by how many fish are in the sea. If we enter a dealership without any tools to compare the various vehicles, we’ll feel like deer in the headlights. Thus, we create a framework beforehand.

Let’s say in our sample scenario that the primary factor in our decision is price. There are loads of other variables that determine the efficacy of any particular prospective automobile, but if we must distill it down to one thing, cost is our #1 differentiator between any two choices. The metric enables us to be excited by back-up cameras and leather upholstery, but firmly plants an anchor in a quantifiable, objective principle that can make the final call. This gives us more confidence as we begin discussions with the salesman.

Thus enters one of footballs fundamental ideas: the notion of numerical superiorities and inferiorities. When opportunities present themselves—think, a parking lot full of brand new sedans—this is an easy and immediate way to evaluate and compare each one’s potential quality.

The nomenclature is intuitive: a superiority is colloquially referred to as having “numbers up” or an “overload”, while an inferiority refers to a situation in which your men are outnumbered.

Just like the price of a shiny new car, this tool lets our players scan the pitch with a numerical structure that can very immediately tell us where any option stands along our scale of idealism.

Imagine a region on the field where you can exploit a defensive unit of n men, by having n+1, n+2, and so forth. This is a green light. Consider yourself a midfielder on the ball with two options, one to the left that sees your winger and fullback against just one opposing defender, or a pass centrally that leaves your 10 closed down by two ravenous 6s. It’s pretty built-in to our decision-making psychology that we’d prefer the first one. There exists a myriad of surplus data to be distracted by, including the players’ body shapes or interspacing, but the metric allows us to rapidly evaluate options without much more additional info.

And sure, the more we’re able to take in, the better, but the sport’s demand for instantaneous decision-making means we might not be able to afford it. With each additional set of data, (contemplating the momentum of the game, the recent yellow card of a particular defender, and so forth), we tack on further degrees of freedom to an already complex problem. The fact of the matter is, few players can even execute these decision-making plays technically-speaking, and with a high enough completion rate, let alone decipher such a wealth of content in the blink of an eye. I like to think of that as realism, not cynicism. Distilling our process down to a constant “how many of us vs. how many of them” can reduce the stress of these choices and increase our execution percentages.

For those that are able to transcend this metric and consider additional factors—great, we have an artist on our hands—but those players won’t be my focus for this article. Moreover, numerical superiorities and inferiorities will likely still serve as a guiding principle for their decisions, too; even if we’re able to compare vehicles by color, the budgetary implications remain the backbone of our purchase. What’s most critical is for everyone within the team to achieve this cognitive baseline, together. We must teach the team to coexist on the same wavelength. If individuals can build upon that, it’s a delightful, extra outcome.

And so, recognizing superiorities and inferiorities becomes one of the primary challenges—and thereby, skills—of modern football. Those that can do it efficiently enter the glimmering parking lot with a ruler in their back pocket, while those that don’t will be dizzied by the variegated colors.

The theory behind superiority searching is as follows: Football is played 10v10 in the middle. In order to earn vital seconds of competitive edge throughout the match, we must constantly search for imbalances that yield momentary advantages in personnel. We decompose the larger game into smaller pods of play that are easier to understand and break down. If we accept even numbers and play 10v10, both sides have a reasonable chance to accomplish their objective—but a 2v1 out wide is much more promising for us. The ebbs and flows of any given match create a variety of these situations spontaneously, but if we can create and exploit them deliberately, we’ll gain the upper hand.

Semantics

There is one particular semantical dilemma we run into when defining these situations in greater detail. When we refer to a superiority or inferiority and a hypothetical decision between the two, are our numbers defined by those preexisting in the space or must we account for the man on the ball joining the play? If we play our fullback 1v1, but immediately overlap him, surely that is to be considered a superiority, right? After all, overlapping is arguably the most commonly used method for “overloading” the opposition.

The answer is yes. If we consider the dynamic mobility of the player on the ball, they’re included in our equation. This adds a useful potency to the player orchestrating the attack—they possess the ability to find overloads, or create them, themselves. If anything, this power underscores the importance of learning to recognize these situations when they arise.

Superiorities

If we have the chance, in attack, to possess the ball with numbers up—we take it.

We ought to expect a certain problem-solving caliber from our players such that with superior numbers, under nearly any circumstances, we always have confidence in beating the opposition. A 1v1 is a skill, highly dependent on individual talent, but a 2v1 is a must-win regardless of personnel. In training, we’ll look to construct various scenarios in which these favorable numbers arise, and look to build confidence and expertise when it comes to capitalizing on them.

One common technique is the deployment of neutral players in training sessions. A third-color player that is always attacking enables the team in possession to always have an advantage. As such, we expect a certain level of proficiency within our team under these conditions. We can tinker with the number of neutrals to experiment with various degrees of superior play.

But a mere possession game featuring neutrals is quite unattractive when it comes to learning how to evaluate and when to exploit superior zones. By adding goals on two sides of the endline, for instance, we incorporate an increasingly gamelike incentive that forces our team to make a choice: which scoring option gives us the better chance? As such, the drill transcends the plane of executing a mere action—maintaining sterile possession—and enters the realm of decision making, the holy bread and butter of finding overloads.

The neutral involved in, say, a 6v6 small-sided game, gives the attacking team a constant overload on one side of the field. The game rapidly becomes a test to see which team can find those numbers-up pockets more than their opponent. Note that such a setup will also begin to unravel nuances like field density, and how having more players in a given region might actually appear to “clog up” seams, but these alternative factors can be mitigated by deliberately playing in large-leaning spaces. We must keep the focus on scanning for numbers alone, but be sure to listen to players as they bring up complicating factors like these. We want them actively thinking about how to solve each problem at hand.

The objective of any drill you devise for this idea ought to provide immediate reward for correct discernment of a superiority. Don’t delay that gratification in its early stages of development. The field should be shallow, with plenty of room to switch the ball horizontally until opportunities make themselves apparent. Evolving from the rudimentary previous examples, the goal should only be accessible once a region is “unlocked”, to encourage true and incisive penetration of these zones, rather than lofted long balls or unguarded pot shots from deep.

Simultaneously, the other virtue of finding proper superiorities is patience. We must pounce when chances appear, but not over compensate, nor force the ball into mediocre areas. As such, drills should have a punitive measure for teams that are too reckless or eager to play into subpar zones—i.e. high-scoring opportunities for the defense upon regaining possession (see the 4 point goals above). They should also be encouraged to probe back and forth until they find numbers up in any given space, undeterred by opposing press (i.e. forbid pinks from entering the defensive zone, above). This may feel unrealistic but we’ll build to the more gamelike forms, slowly. The goal is to develop a calmness and self-restraint that complements the ravenous capture of superior situations.

Another approach is to practice attacking numerically favorable numbers—without the need to pick between choices. Instead of focusing on the distribution facet, we pivot to practice the final stage of definition. By building up confidence in 2v1s or 3v2s on goal, our players will begin to crave these scenarios and look to create them with greater frequency. Naturally, attackers with a vested interest in finding themselves numbers up will generate more opportunities for us to find them in those pockets of space.

The options for building this skill set are truly boundless, and often all very entertaining for the group. Fast-paced finishing drills, as the players will perceive it, are simple and fun. Players or groups can either tally up their converted chances to build competitive spirit within the session, or they may be asked to not think about numbers at all; sometimes it can be best to let them enjoy the flow without keeping score.

Once the ability to discern superiorities is sharpened, and the technique involved in capitalizing on those chances is honed, we’ve set ourselves up quite nicely. That being said, these are concepts that may feel utterly intuitive, but may actually take time for players to begin to absorb. To shift an athletes perception of the game takes time.

Therefore, I’d spruce the learning process up with pointed video and whiteboard sessions with the group. Teach them to look deeper within situations they’ve seen time and time again to find the underlying principles at play. As previously mentioned, overlapping combinations are a highly used, highly self-explanatory example. There are ubiquitous highlight reels in which overlaps lead to crosses and goals—you’ll have no difficulty finding pertinent examples. Perhaps it can help the team visualize to pair that with their own experiences and practice.

Inferiorities

The alternative viewpoint to consider is the circumstance in which your team is not at an numerical advantage, but rather, at a disadvantage. The situation can arise in attack, in defense, or in transitions, but I’ll hold the magnifying glass over goal-scoring sequences. The art of defending when numbers-down requires many more pages to fully flesh out. We’ll save that for another time.

With the ball, if we enter a region in which the opponent overwhelms our soldiers—that is a red light. Often denoted as “playing the ball into pressure”, there exists the occasional moment in which this may be effective, but it’s especially situational and typically route one to turning over possession. If we are to define the parameters of our metric, any time we see an inferiority, halt the troops.

That being said, instead of being dismayed at the sight of choppy waters, the mere notion that we’ve found a zone in which the opposition has more players than we do means there simply must be another region on the pitch in which we are superior. This is fundamental. Both superiorities and inferiorities are delightful to see—it’s just that the former means we’re aa bit more advanced in our exploitation process. When we’re numbers down, it means that opportunity exists—it’s just elsewhere.

Remember, this game is about minutes or even seconds of imbalance. If the opponent moves their pieces to imbalance us in one area, they’ll be stretched, vulnerable, or even vacant in others. If our attacking unit has proper spacing and can recognize these instances, we’ll minimize the time we spend hanging our heads and being bewildered by the swarming defenders, and be quicker to spin on a dime and switch the field.

That’s where the chances will invariably arise. Compact defenses will look to close seams and stay tightly knit, so if we’ve swung the ball to one end of the pitch and it’s all clogged up, our farside players will, very likely, be surveying the wide plots of land that’s opened up for them.

From this idea emerges one of the essential patterns of play in football—the horizontal transitions that occur hundreds of times per match. One side of the field looks iffy, we try the other. We keep playing hot potato to test the opposing backline’s fitness and shifting capabilities, until we are able to stretch them and play through. With enough inner peace, we’ll see numerous inferior situations, but keep our chins up, gradually figuring out a rhythm that unbalances the other team. If we’re good enough at it, we’ll receive several chances, and likely tuck them away. Hurrah!

There are also plenty of strategies that use magnetism (an idea discussed in a previous post that provides a framework for how the movement of some players can dictate that of their opponents) to overload certain areas and create channels nearby. These are comparatively rarer, but mean that totally switching the field isn’t necessarily needed to take advantage of inferiorities. Sometimes, the space is right behind the defenders that’ve crowded a particular area, and so forth.

What is certain is that nearly always, negative passing options to reset or draw the opponent out are on. In the worst case that we’re numbers down and in especially closed quarters, we can simply re-route to our defense, or even our ball-playing goalkeeper to start over. There’s nothing wrong with that. I’d argue that playing negatively is almost invariably better than trotting blindly into pressure.

Many of these skills can be trained with the same exact exercises you may have devised to work on their superior counterparts. The only difference may be a reversal of your coaching points—pausing play to point out an ostensibly negative environment that clearly suggests a positive one lies elsewhere, and to keep looking. One could incentivize the perception of each inferiority as a bonus or multiplier for an eventual scoring chance (i.e. playing out of two inferior zones, and tapping one into the net in the subsequent run of play, accounts for 1 + 2 points). This may be effective initially, but will very quickly devolve into an un-gamelike session where players don’t capitalize on superiorities, as they wait for the defense to regroup and condense, so they can play out of them again and rack up the bonuses. There’s a careful line to walk when it comes to rewarding these mental observations, but it’s easiest achieved by asking guided questions and selecting periodic coachable moments.

Building Intuition

We may also deliberately design drills to train this idea of “knowing when to switch” when increasing levels of pressure are applied. One common one is “Over the River”.

Though the circumstances in this session will never fully create an inferiority in any part of the field, they will force players to work on a task while keeping tabs on changing numbers. The drill effectively decomposes the shifting mechanism of a defense into slow-motion, with only one defender allowed at a time to complete the transition and truly defend. As the attacking team holds onto the ball for longer, more and more players cascade and increase the pressure. When the team in possession is too overwhelmed, they’ll find a way to the now-unoccupied areas of the field.

In my adaptation of the training game above, you can see three teams split up, with 6 players, each. 5 reside in each zone: there are two square spaces on either flank, with one larger “river” spanning across the central zone and halfspaces. The idea is as follows: one team starts possessing in their zone, with one river defender allowed in their box. Each time they hit 5 uninterrupted passes, they earn a point. Each increment of 5 means the river team can send one more player into the square to defend. Witness that progression in the animation, above.

At any time, but most likely when blue feels increasingly out-of-options, two passes may be made to release pressure. One, switches the ball ~over the river~ to the yellow team—allowing them to begin their pursuit of points. The other is a relief-valve pass to their sixth player, representing a negative ball to a blue CB, for instance, in a real game setting. If this occurs, no river defenders are allowed to chase, but their sixth man—essentially a target striker role-player—is freed from the center circle to press. Blue’s pass count for that round of 5 will reset if they play negatively (i.e. Passes: 3 and Points: 2 will become Passes: 0, Points: 2). If the red target sixth man is able to successfully regain possession from the blue CB, the river team earns a point—the only chance the defending team has to add numbers to their scoresheet. The blue team, now under pressure, may play the ball back into the square to resume play, or switch the field themselves to the yellow square.

If red is able to regain possession inside either square, they must find their target man inside the center circle to successfully force a switch with the team that lost possession. This earns no points, but allows the defensive team to attack, now, and get some of their own.

The game incentivizes taking opportunities in the flanks, while monitoring the state of superior play. As the number of defenders increase, the team in possession becomes increasingly close to being outnumbered. Since the space is small for 5 players, they’ll have to decide, collectively, whether they can continue fighting for points, or if it’s better to avoid being switched into the river defender role. Switching the field means they give up the opportunity of achieving personal glory, and give others a chance instead, but they prevent a much more disastrous loss of possession. Over time, the more switches occur, the more tired out the river team will get, if unsuccessful. This plays into real-game dynamics.

Equalities

Our final question left to address is often overlooked: what happens when we’re even? If the match is decided by minutes, or even seconds of imbalance, how do we prevail in the predominant moments of equality?

And it’s a terrifically difficult question. In the time leading up to my writing of this article, I spent days pondering and crowd-sourcing the answers to various questions pertaining to these situations. There were two main ones that stuck with me:

1. Since we can’t use our metric, what factors determine whether we should play into equal numbers or not?
2. If given two opportunities of equal numbers, but of varying degree, which is preferred in attack? Which is preferred in defense?

To answer the first one, we observe the inevitable shortcoming of our devised metric: a method that objectively compares quantifiable data, giving us an inequality indication of which option is better, fails when there is no difference between the two. A 2v1 is green, a 1v2 is red—but what about a 2v2?

When we run into this roadblock, therefore, we’re forced to analyze the circumstances with any of the long list of criteria we were hoping to avoid by using the metric in the first place. We wanted to focus on price so we wouldn’t be distracted by all the different rims and trunk space, but now the cars all cost the same. We’ve got no choice but to compare other, less quantifiable factors.

So what are those considerations?

Personnel: Do we have skillful wingers on the ball, or do we have physical target men? Does the opponent have defenders or a ten as cover? The personas and skillsets that belong to those involved in each pocket of play will dictate our decisions more than ever, now.

Optimization about x and y: In attack, as we’ve explored throughout this article, we find that xG models, alongside intuition, tell us that the optimal zones to score from radiate outwards from the goalmouth. We’d much rather take a shot from the center of the pitch than the flank. As such, we might rate a 2v2 in the middle of our attacking third more favorably than one out wide. Our x-coordinate is best when closest to 1/2 of the field’s width. As for the y-coordinate, we like being advanced down the field if we’re hoping to score. Therefore, the closer we are to goal, the better any equality is.

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Pocket density: How closely packed are the players within our defined bubble? On offense, we’d much prefer a spread out 2v2 than one that’s closely packed. In defense, vice-versa. Low density situations favor the team creating chances, while high density ones clog up seams. When territory is equal, which option grants each interior player with more area?

Territory/Interspacing: Similarly, if we hold numbers equal between our options, which one is more spread out? It’s the same logic as before, open spaces are ideal for runs and creativity, while compact ones make the defense’s life easier.

Positioning and particular conformation: This is the most nuanced criteria. There are an infinite number of configurations that each creative player may approach with a different set of tools to unlock. There are some shapes that some players enjoy, and others they might not—but those things vary from individual to individual. Artists like Mesut Ozil might be able to devise a clever route for solving a certain scenario, while another might struggle. The movement and momentum of players makes these calculations even harder. When presented with the same scenario over and over, players might even try different approaches. It’s an incredibly volatile and gut-based decision-making exercise fueled by instinct. Creating metrics for something like this wouldn’t be a wise mission to embark upon—it’s best we simply train attacking scenarios with organically unfolding permutations.

So which of these are most important? Can we at least create a hierarchy of sub-factors to have at our disposal? Perhaps.

The most natural instinct was listed first, above: who are we working with? This is something that requires little coaching. The players know who they’d prefer to have the ball heading towards the opponent’s goal, vs. those that wouldn’t make us as optimistic. Analyzing the opposition might be a bit more unfamiliar, but it’s easy to recognize that our winger vs. their CM might be less ideal than our winger vs. their fullback. Outside of categorizing these things based on mere positions, throughout the match we’ll witness which players possess which skillsets, and which we’d prefer to engage or avoid in these given pockets of space. Perhaps their fullback is an exquisite attacker but quite faulty at 1v1 defending—maybe that’s actually a good matchup. These gleaned details will augment our understanding and decision-making procedure.

As we dig deeper in search of more geometrically-grounded metrics, we might resort to evaluating x and y, first. It’s easier than the highly-complex process of comparing internal momentum and movements. An option closest to high-xG areas—central and nearest the goal that we’re attacking—is ideal. As an example, playing the ball out wide 1v1 for a cross and eventual header may be a perfectly fine route to goal, but why endure each of those steps, all of which are riddled with inherent variability, if our striker is open 1v1 at the PK spot?

Next we might examine density and territory. These are still somewhat quantifiable, but become increasingly abstract ideas when we place them into real game settings. General inklings may be sufficient to make a decision, especially when the different options are clearly distinct, but this is rarely the case on the field. The likes of Javier Fernandez, FC Barcelona Data Scientist and frequent publication winner in the MIT Sloan Sports Analytics Conference, and Laurie Shaw, a Harvard Statistics Research Scientist, have devised methods for understanding pitch control, with visualization tools that show voronoi diagrams depicting which players “govern” over which parts of the field in any given moment—but even these models are highly lackluster. They only utilize position, and not average player velocity or acceleration—meaning that the shapes are, in my opinion, highly inaccurate. For a player to instinctively be able to process these types of calculations that require lines upon lines of code to somewhat-erroneously show on a post-processing screen.. well, it’s tough, but a select few can do it.

Lastly, we might entertain the instincts that come with various configurations. This activity engages the highest order of cognitive processing, but is often the first or only thing players consider. They try to figure out the exact problem without extracting positional details or interspacing, and can often become stuck. Synergy, chemistry, and communication are all key for these subtle movements to be interpreted and executed upon. It’s like trying to understand the engine without a grasp on the conservation of energy.

Now let’s move onto the second burning question: If given two opportunities of equal numbers, but of varying degree, which is preferred in attack? Which is preferred in defense?

The idea is as follows: we know how to interpret superiorities and inferiorities, and even equalities now, but what about different types of equalities? Of course, a superiority with +2 or +3 is even more of a no-brainer than a +1 advantage. The same goes for when we’re numerically inferior. But what happens when we have two viable options in a 1v1 and a 2v2, with all else equal (i.e. interspacing, field x and y, etc.)? Or a 1v1 and a 3v3? Which of these is best to exploit?

This conundrum isn’t trivial. I arranged the magnets on my tactics whiteboard in the exact configuration shown above, and left the question dangling in my room for a few days. In my efforts to justify the reasoning I’d eventually come up with, I spoke to a friend about the question—this search for a curve that would define where each respective order of equal play, from 1v1 up to 11v11, lies on an axis of idealism or favorability—but his response was precisely opposite what I had preconceived. I was surprised, but intrigued.

I proceeded to reach out to a tactician I respect on Twitter, whose response backed some of my ideas. I then dropped the question in the group chat for the players on my team, and they all seemed united against my thought process. Needless to say, it became clear that this was a hotly contested issue—but I’ve boiled it down to a few essential considerations.

My initial argument was that, if we compare a 1v1 and a 2v2, the situation with fewer players had fewer degrees of freedom, making the problem all-too linear. If we play into an isolated 1v1, the only choice an attacker has is to beat the opponent by dribbling, and the opponent will know that. The parameters are too straightforward and easy to prognosticate. When predictability is high, we favor the defensive unit.

The 2v2, on the other hand, possessed a greater potential for creativity. In a 2v2, the attacking players can combine, make runs behind the defenders, or even still dribble—but the point is that they have more options and more room to cut open the defense. This seemed compelling.

On the other hand, the counterpoints that were brought up, as I scanned my surroundings for alternative views, promoted the antithetical argument. A 1v1 contained fewer defenders to beat. As such, they viewed it as an easier problem to solve. The players in the group chat that responded most immediately were 10s and attacking fullbacks, meaning they were likely confident in their offensive 1v1 ability. It is impossible to ignore the fact that their personal skillset may have swayed their reactions and subsequent reasoning, but the claim was cogent nonetheless.

And while both approaches might appear to clash, they actually support the same idea but from different angles.

One says that the more players we have, the more the opponent will have to coordinate and keep track of, yielding us an advantage. The other states that the more they have, the harder it’ll be for us to break down. With more attackers, more things have to go right (be it the runs or the timing of passes), to succeed. With more defenders, more things have to go right (be it marking or intercepting a split pass), to succeed, too.

The second interpretation declares that the fewer players we have, the fewer artistic possibilities exist as we flatten the problem into one dimension, making it easier for the opponent to compartmentalize and find a solution. The other asserts that the less support they have, the more precarious and vulnerable their defensive situation becomes. With fewer attackers, fewer things have to go wrong (i.e. a skill mis-execution) to fail. With fewer defenders, fewer things have to go wrong (i.e. a mistimed challenge) to fail, too.

It’s almost as if they’re inseparable. But certainly we can’t accept that.

Thus, after leaving the whiteboard hanging for a while longer, and contemplating the question in the moonlit darkness of my evening apartment, I’ve settled on some semblance of a compromise: reductionism prevails in attack, while holism thereby triumphs in defense.

In a sense, 1v1s are like penalties. No matter how good the keeper is—or in our case, the defender—we expect the attacking team to succeed. They’re likely running forward, at pace, against a player backtracking; running in reverse is a grassroots skill in football but an inherently less-fluid and less-natural motion than running as normal. If the focus is to score, they have better visibility of their target and the dynamics that surround it, than the defender, too. The fact of the matter is, no defender is ever delighted to find themselves on an island—as the pressure of protecting the goal is entirely pinned unto them. Some may thrive in these situations—think Aaron Wan Bissaka—but it’s precarious by nature. The fear of embarrassment from being turned inside out by a tricky opponent is also there, and even more so if jeering crowds are present. Think back to the last 1v1 you watched on live television, even against strong defensive opposition. Your gut reaction, or the color commentary’s vocal crescendo was unlikely to be worried for the attacker. These moments are exciting because they often lead to goal, and it’s why counterattacks carry much more edge-of-your-seat energy than a well-pieced together passing sequence. For this very reason, we prefer a 1v1 to a 2v2, a 2v2 to a 3v3, and so forth.

In defense, we simply shift our vantage point. If a 1v1 leaves us on thin ice, we’d prefer an extra defender for support, even if that grants the attacking team another variable to work with. The culpability of potential failure, then, is distributed between two, not just unloaded onto one. If we can choose a 3v3, we’d take it over the 2v2, as well. Ideally, we’ve got all our soldiers behind the ball in an established phalanx, so we’d actually prefer a 9v9 or 10v10 over any of these options. With modern zonal marking systems, defense is more often about collective stability and coordination than it ever is individual brilliance. If man marking were ubiquitous as it is in basketball, for instance, it’d be more important for each player to be solid within their individual duels. But in football, we rely on cover shadows, and offside traps, and shifting so as to avoid “tearing the blanket”—1v1s are unnatural and unwanted.

Further cementing this logic, attack thrives in space while defense is more obstinate in condensed regions. The fewer players in a zone, the more space to exploit. The more defenders, the tighter we’ll pack our region of the field. These are different paths, but they all lead to the same conclusion.

It’s important to note that as we move higher along our string of equality orders, the differences taper off. Which is better for an attacker, a 6v6 or a 7v7? We might assert the former, but the differences are marginal. It is for this very reason that the dynamics at play on the other end of the spectrum are that much more worthy of practice. A 1v1 is an entirely different game than a 7v7. So is a 2v2 or even 3v3. These matchups of high instability are opportunistic for attackers, and potentially disastrous for defenders, which is why they’re so often focused on in training.

Final Thoughts

Thus, we round out our study of numerical inequalities on the football pitch. Superiorities must be taken, while inferiorities mean superiorities lie elsewhere. Equalities are harder to distinguish between, but we now have quasi-metrics with which to handle them. We’ve carved our ruler and drawn on the markings; we’re as ready as we’ll ever be to go to the dealership, and it’s time to buy a new car.

As one last comment, I wish to address the notion that these ideas might overly rigidify a sport that people often wish to see as free-flowing. If we reduce football down to the comparison of numbers in various parts of the field, doesn’t that eliminate some of the spontaneous creativity we’ve grown to love? No. I certainly don’t think it does.

When we examine structures like juego de posicion, a geometric overlay atop the football pitch, it is an act of snatching low-hanging fruit to assume that this will dullen our final product. JdP is a mentality that, when second-nature, creates organic passing options for all players at practically all times. This unveils an even more beautiful brand of football than was available before, and provides a series of metrics to achieve it. The same goes for the recognition of numerical inequalities. Once players become adept at the skill, the bush strokes they produce on the field will be more refined and more calculated. They’ll become more intelligent footballers, which won’t detract from creativity, but rather supplement and cultivate it. The more information they’re able to intake effectively, the better, but if they can take a complex image and distill it to one question: “do we have more or do they?”, our team will begin to function like a well-oiled machine. Football is a constant state of trying to create order from disorder, and this tool can do precisely that.

Till next time.