In all walks of life, things can swing between good and bad very quickly. The Dark Knight, for instance, opens with five minutes of knockout virtuosity, but the remainder of the film is bloated, boring and tedious. The Wire reached a peerless high-point at the end of its fourth season, but retreated into mediocrity at the start of season five. Similarly, the opening period of Stoke City's visit to Anfield on Tuesday bore about as much resemblance to the rest of the game as Johnny Vegas does to Michelangelo's David.

For the most part, that was because it took a good half-hour or so for Liverpool's centre-backs to get to grips with Stoke's strikers. Once this was done, the game pivoted on its axis and a shaky, uncertain showing from the home side quickly became a slick and exuberant win.

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Given that the visitors’ forward line was comprised of Jon Walters and Peter Crouch, a duo with as many unexpected tricks up their sleeves as a tin of Ronseal, the temptation for Jurgen Klopp, when he looks back over the game, might be to see the opening exchanges as a cause for worry. After all, if that's all it takes to put the wind up Dejan Lovren and Ragnar Klavan, albeit temporarily, what sort of damage could be reaped by Sergio Aguero and chums on New Year's Eve?

Maybe, though, it's just as viable to see Tuesday's game from a different angle altogether. Maybe the very fact that Lovren and Klavan encountered a problem, confronted it, and comprehensively overcame it is as encouraging a chain of events as any plain-sailing clean sheet would have been. After all, there's plenty to be said for players being able to solve their own problems out on the pitch – and it's not something that Liverpool defenders have tended to offer shining examples of in recent times.

Liverpool's Estonian defender Ragnar Klavan (R) pressures Stoke City's Ivorian striker Wilfried Bony Image credit: AFP

Almost exactly three years ago Liverpool also found themselves up against a Stoke side spearheaded by Crouch and Walters. But on that day Martin Skrtel and Kolo Toure couldn’t come up with an answer to the uncompromising agriculturalism of that front two. Liverpool won 5-3, but defensive problem-solving played little part in their victory; it was a microcosm of the season. In fact, coming up woefully short against target-man strikers was a recurring problem of Brendan Rodgers’ reign, one to which neither he nor his defenders could ever find a solution. (Walters, whose record in the Premier League stands somewhere around the one-in-six mark, scored four in seven against Rodgers' sides, while Christian Benteke and Rudy Gestede each averaged a goal a game against Skrtel and co despite playing for the worst Aston Villa team in a generation.)

You sense that getting his players to think themselves through tough situations has been a central drive of Jurgen Klopp's since taking over last October. It's the reason that the more cerebrally challenged players like Skrtel and Alberto Moreno have either been sold or marginalised, their place in the side taken by thinkers like James Milner and Joel Matip. For all the talk of Klopp's sides being founded on legs and lungs, there is a real emphasis on intelligence, too. Heavy metal might sound chaotic, but it's written with thought and poise.

Klopp's transfer record in his tenure thus far tells the story of a manager who recognises as much. The witless duo of Jose Enrique and Mario Balotelli joined Skrtel on the scrapheap this summer; in came Matip and Georginio Wijnaldum, two exemplars of cool-headed canniness, along with the focused energy of Sadio Mane.

In some ways it's odd that Lovren has survived the cull, given how so much of his early bad form was down to positional ill-discipline and thoughtless lunges. That rashness was on show again on Tuesday, when he spent the opening exchanges throwing himself into aerial duels with two shrewd strikers who saw him coming a mile off and took the cheap free-kick every time. Significantly, though, that rashness was addressed and nipped in the bud. That may seem like damnation with faint praise, but in comparison with Skrtel, whose recidivism knew no bounds over nine seasons on Merseyside, it represents a substantial upgrade.

The limitations of Stoke's attack function as a hefty caveat, but defenders untangling themselves from sticky situations has become a rare sight at Anfield of late, and the home crowd will have been rightly heartened by the Klavan-Lovren axis showing a taste for proactive problem-solving. Jordan Henderson shuffling to the right flank in order to help neuter the early threat of Erik Peters, was another example of the same.

In a league awash with money, whose top clubs are effectively blessed with a blank chequebook, any club with comparatively limited resources must focus on marginal gains. Training players – or “educating” them, as a certain manager would say – not just to play their way out of trouble but to think their way out too, can, in theory at least, create some pretty wide margins.

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