Nicolas Otamendi is the type of footballer who, scuttling in staccato steps like a spider trapped in a jam jar, always looks panicked. And the first half of Manchester City’s 5-0 defeat of Liverpool on Saturday was peak Otamendi, a performance so anxious Mohamed Salah would have faced a more robust challenge from a crisp packet wafting out of his way.

Poor Nicolas is a man forever caught in two minds; unsure of when to press and when to hold, when to stay narrow and when to charge out to the left, the Argentine oscillates frantically between the roles of a left-back and a centre-back. It is a baffling and stressful sight to behold.

But Otamendi is far from the only defender to struggle in a three-man defence this season. Bournemouth’s trio were also dreadful in a 3-0 defeat to Arsenal on Saturday, following a pattern of hapless back-threes that was started by Crystal Palace in the opening day 3-0 loss to Huddersfield Town.

The story of these three games, plus Manchester United 4-0 West Ham United, Liverpool 4-0 Arsenal, Swansea City 0-4 Man Utd, and Chelsea 2-0 Everton was three disorganised centre-backs being torn to shreds.

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A flurry of one-sided matches in the first few weekends of the campaign is nothing out of the ordinary, particularly when tactical fashion blinds managers from making more pragmatic decisions.

Since coming back into vogue, three-at-the-back formations have been tried far too flippantly, appearing more as an afterthought, or a desperate experiment, than as the result of hundreds of hours of in-depth tactical coaching.

But there’s another more pressing reason why defences are falling apart when using a variation of 3-4-3 this year, and it is something that was perfectly exemplified by both Man City (in the first half) and Liverpool (in the second half) last weekend.

Chucking a third central defender into the middle is not simply an addition to an equation, or an extra brick in the wall. It completely changes the base position of each centre-back, counter-intuitively creating more space in central defence for opponents to pass through while dramatically altering the roles of all three charged with closing the gaps. Otamendi should not be blamed for his poor first-half performance: Pep Guardiola was playing the Argentine out of position.

It might seem like an obvious point but rarely do pundits or fans appear to respect the most basic difference between a two and a three, namely how the even distribution of these two numbers across a horizontal axis has no positional overlap: or, in other words, how utilising a third defender changes the position of all three.

Unless featuring in a youth academy that regularly played with three at the back, or diligently re-taught by a great tactician (like Antonio Conte), defenders will inevitably struggle to know what to do, just as a winger might look awkward if asked to play as an inside forward.

Communicating with two players already poses more of a challenge than with one (particularly since the middle defender cannot see both of his team-mates at once), which exacerbates the problems when all three are asked to play a different role.

The wider centre-backs are in a strange no-man’s-land between centre-back and left-back (as Otamendi made so painfully clear on Saturday) and the middle defender is standing in a spot that must feel jarringly unnatural. Square on to the attackers, anything either side can catch him flat-footed in an instant. It is strangely disrespectful of the formation’s unique complexities, then, that Jurgen Klopp suddenly changed to a 3-5-1 for the second half at the Etihad.

Paradoxically, adding a third centre-back creates more gaps, not fewer. The shift in the even distribution of defenders creates two central slots for the attacker to breach where before there was one, and so unless coached perfectly the defence is, foundationally, destabilised by the addition. Less is more.

Pep Guardiola’s segmentation of the football pitch illuminates this point. He famously carves the pitch into 25 quadrilaterals during training sessions to simplify his play-by-play instructions, and according to the Catalan it is the half-spaces – columns just outside the middle, where the likes of Andres Iniesta or David Silva operate – that are most important, because it is these two segments that fall between the opposition’s formation lines.

Except this is no longer true when playing against a back three, as the image below illustrates. Against a back four the main creative options are either sliding passes between centre-back and full-back (a difficult task that is rarely achieved without the ball moving diagonally towards the touchline) or feeding the ball between the two centre-backs, a task which is self-evidently among the most difficult in football. But when the defensive positions have all shunted over, the available passing lines are suddenly more advantageous – and the half-spaces shift accordingly into the dangerous number ten zone.

Most teams, including City on Saturday, compensate for the creation of an extra gateway by playing very narrowly, which is why Premier League wingers (like Salah) so often dominate against a three-man formation by bursting into the enormous space that yawns open between side-centre-back and wing-back.

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Other teams, like Liverpool during the second half of the same game, are wary of the opposition wingers (like Leroy Sane, who hugged the left to great effect) and remain stretched, leaving someone of De Bruyne’s quality to easily cut passes straight through the middle of defence. The arching out-to-in runs Guardiola has been teaching his wingers are never more effective than when facing a back three: De Bruyne found Sane over and over again.

There are, of course, ways of plugging these gaps. Chelsea achieve solidity because their wing-backs stay very deep for long periods of the match to make a well-oiled flat back five, while Tottenham Hotspur are successful because they slowly integrated Eric Dier into this role.

After spending months drifting back from defensive midfield to cover any gaps between Toby Alderweireld and Jan Vertonghen, the three of them could begin to play in an unusually fluid version of the 3-4-2-1 last season. Spurs’ main centre-backs continue to act like a pair, with Dier frequently pushing forward or drifting wherever he is needed most.

Three is sturdier than two: this is the logic that pervades most commentary on the Premier League’s new obsession with 3-4-3s, when in fact – unless hunched deep in a flat back five – the opposite is true. Chelsea’s title triumph in 2016/17 proved it can be a devastating formation, but it requires considerably more work – and more respect – than it is currently being given.

Using three at the back should not be an afterthought or a mid-game experiment, like shifting from 4-2-3-1 to 4-4-2 in search of a late goal. It is a switch that changes the position and role of every single defender; Otamendi, erratic as he may be, never really stood a chance.